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Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 481, "matching_sections": 79, "matching_sources": 10, "aliases": 2 }, "aliases": [ "admittance", "admittances" ], "sources": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 136, "section_count": 17, "concepts": [ "Admittance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 109, "section_count": 15, "concepts": [ "Admittance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 73, "section_count": 13, "concepts": [ "Admittance" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 68, "section_count": 9, "concepts": [ "Admittance" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 55, "section_count": 9, "concepts": [ "Admittance" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 16, "section_count": 5, "concepts": [ "Admittance" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 9, "section_count": 4, "concepts": [ "Admittance" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 7, "section_count": 3, "concepts": [ "Admittance" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 2, "concepts": [ "Admittance" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 2, "concepts": [ "Admittance" ] } ], "priority_sections": [ { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 16: Induction Motor", "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 28, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... econdary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = - se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = - . We thus have, ge = magnetic energy current, ge* = loss of power oy hyster...", "... f (R = reluctance of magnetic circuit per pole, as dis- cussed in Chapter X., it is A^^ft*. * Complete discussion hereof, see Chapter XXV. INDUCTION MOTOR. 241 Thus, from the hysteretic loss, and the reluctance, the constants, g and b, and thus the admittance, Fare derived. Let rQ = resistance per primary circuit ; XQ = reactance per primary circuit ;..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-20", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 20: Single-Phase Induction Motors", "location": "lines 21538-22301", "status": "candidate", "occurrence_count": 23, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-20/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-20/", "snippets": [ "... sity - the total volt-amperes excitation of the single-phase induction motor must be the same as of the same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exci...", "... e same motor on polyphase circuit, it follows that by operating a quarter-phase motor from single-phase circuit on one primary coil, its primary exciting admittance is doubled. Operating a three-phase motor single-phase on one circuit its primary exciting admittance is trebled. The self-inductive primary impedance is the same single-phase as polyphase..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-109", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 22, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... admit- tance per circuit Y = g - jb and self-inductive impedances ZQ = rQ + jxQ and Zi = TI + jxi per circuit with the same motor operating as single-phase motor from one pair of termi- nals, the single-phase exciting admittance is Y' = 3 Y (so as to give, the same volt-amperes excitation 3 eF), the primary 330 ELEMENTS OF ELECTRICAL ENGINEERING self-...", "... by the armature magnetization equal to the main magnetic flux produced by the impressed e.m.f. If an accurate calculation of the motor at intermediate speed and at standstill is required, the changes of effective exciting admittance and of secondary impedance, due to the decrease of the quadrature flux, have to be considered. At synchronism the total..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-17", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 17: The Alternating-Current Transformer", "location": "lines 16521-17716", "status": "candidate", "occurrence_count": 21, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-17/", "snippets": [ "... y much smaller. Symbolic Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i - jbo, of the transformer. The resistance and reactance...", "... c Method 149. In symbolic representation by complex quantities the transformer problem appears as follows: The exciting current, /oo, of the transformer depends upon the primary e.m.f., which dependence can be represented by an admittance, the \"primary admittance,\" Fo = g^i - jbo, of the transformer. The resistance and reactance of the primary and the..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 12: Effective Resistance And Reactance", "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 20, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... z - where z is determined by the magnetic characteristic of the iron and the shape of the magnetic and electric circuits - the impedance is represented, in phase and intensity, by the symbolic expression, Z - r -{- jx =^ z '&\\n a -\\- jz cos a; and the admittance by, 1 ^ g - JO = - Bin a - J- cos a = y sm a - jy cos a. The quantities z, r, x, and y, g,...", "... REACTANCE 129 m.m.f., / - effective current, since I\\/2 = maximum current, the magnetic flux, (R (R Substituting this in the equation of the counter e.m.f. of self- induction, E = V2 irfn^ 10\"', we have „ 2 wnJI 10-« ^= ^ 5 hence, the absolute admittance of the circuit is y = ^^ -^^^E = 2^f^T where 10« , , a = ^ - 5, a constant. 2 Trrr Therefore, the..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 10: Effective Resistance And Reactance", "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 18, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... s, - where s is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, - the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z = r - jx = z sin a - jz cos a ; and the admittance by, Y = g + j b = - sin a -j- j - cos a = y sin a -f- jy cos a. z z The quantities, z, r...", "... (R = magnetic reluctance of a circuit, £FA = maximum M.M.F., I - effective current, since /V2 = maximum cur- rent, the magnetic flux, (R (R Substituting this in the equation of the counter E.M.F. of self-induction we have (R hence, the absolute admittance of the circuit is (RIO8 = a& E ~ 2 TT n*N ~ N ' 108 where a = , a constant. 2 TT n Therefore, the..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 14: The Alternating-Current Transformer", "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 17, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... PHENOMENA. Symbolic Method. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of th...", "... hod. 134. In symbolic representation by complex quantities the transformer problem appears as follows : The exciting current, 700, of the transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of the primary and the secon..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 17, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "CHAPTER VIII ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 48. If in a continuous-current circuit, a number of resistances, Ti, r2, ?'3, . . ., are connected in series, their joint resistance, R, is the sum of the individual resistances, K = ri + r2 + ra + . . . If, however, a number o ...", "... refore. The joint resistance of a number of series-connected resistances is equal to the sum of the individual resistances; the joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-17", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Theory Section 17: Impedance and Admittance", "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 16, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "17. IMPEDANCE AND ADMITTANCE 82. In direct-current circuits the most important law is Ohm's law, e -i or e r ir, or r = -.> where e is the e.m.f. impressed upon resistance r to produce current i therein. Since in alternating ...", "... t i therein. Since in alternating-current circuits a current i through a resistance r may produce additional e.m.fs. therein, when apply- a ing Ohm's law, i - - to alternating-current circuits, e is the IMPEDANCE AND ADMITTANCE ' 99 total e.m.f. resulting from the impressed e.m.f. and all e.m.fs. produced by the current i in the circuit. Such counter..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 10: F", "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 16, "concepts": [ "Admittance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... - where z is determined by the mag- netic characteristic of the iron, and the shape of the magnetic and electric circuits, - the impedance is repre- sented, in phase and intensity, by the symbolic expression, Z =^ r ^ jx = ;? sin a - jz cos a ; and the admittance by, K = ^ + y ^ = - sin a + y - cos a = >» sin a + jy cos a. z z The quantities, xr, r, ;...", "... .M.F., / = effective current, since / V2 = maximum cur- rent, the magnetic flux, ^ IF^ «/V2 (R CR • Substituting this in the equation of the counter E.M.F. of self-induction, ^=V2 7r^«*10-», , J, 27r«^^Z10-» we have E = ; (R hence, the absolute admittance of the circuit is ^= VJM^ = -^ = (R10« a^ E 2irn^N N' , 10» where a = - - - , a constant. Therefo..." ] } ], "concordance_links": [ { "concept_id": "admittance", "label": "Admittance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/admittance/" } ] }, { "page_slug": "complex-quantities", "page_title": "Complex Quantities", "concept_ids": [ "complex-quantities" ], "concept_labels": [ "Complex Quantities" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. 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Similarly - Multiplying by - j jneans lagging the wave by one-quarter period. Since j^ = - 1, it is j = v^^=n:; and j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the syste...", "... imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the system of ordinary numbers, this definition of j = V - 1 does not contradict its original introduction as a distinguishing index. For the Algebra of Complex Quantities see Appendix I. For a more complete discussion thereof see \" Engineering Mathema..." ] }, { "section_id": "engineering-mathematics-chapter-01", "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_label": "Chapter 1: The General Number", "location": "lines 915-3491", "status": "candidate", "occurrence_count": 11, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... rature with each other can be expressed by the plus si^n, and the result of combination thereby expressed by OB^-BP = 3+2j. THE GENERAL NUMBER. 17 Such a combination of an ordinary number and a quadra- ture number is called a general number or a complex quantity. The quadrature number jh thus enormously extends the field of usefulness of algebra, by a...", "... ors in space. In the quaternion calculus methods have been devised to deal with space problems. The quaternion calculus, however, has not yet found an engineering appHcation comparable with that of the general number, or, as it is frequently called, the complex quantity. The reason is that the quaternion is not an algebraic quantity, and the laws of a..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 5: Symbouc Mbthod", "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 10, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... ing the wave through one-quarter period. Fig. 24, Similarly, - Multiplying by - / means advancing the wave through -one-quarter period. since y^ = ~ 1, y = V- 1 ; that is, - j is the imaginary unity and the sine wave is represented by a complex imaginary quantity ^ a -\\- jb. As the imaginary unit j has no numerical meaning in the system of ordinary nu...", "... ry quantity ^ a -\\- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition ofy = V- 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagra..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 30: Quartbr-Fhase System", "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 9, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... ual distribution of load, but are liable to become un- balanced at unequal distribution of load ; the three-wire quarter-phase system is unbalanced in voltage and phase, even at equal distribution of load. APPENDICES APPENDIX I. ALGEBRA OF COMPLEX IMAGINARY QUANTITIES. INTRODUCTION. 267. The system of numbers, of which the science of algebra treats, f...", "... ction under any circumstances, the system of abso- lute numbers has to be expanded by the introduction of the negative number: - a = (- 1) X a, where (- 1) is the negative unit. Thereby the system of numbers is subdivided in the 270,271] COMPLEX IMAGINARY QUANTITIES. 403 positive and negative numbers, and the operation of sub- traction possible for al..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 32: Quarter-Phase System", "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 9, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... al distribution of load, but are liable to become un- balanced at unequal distribution of load ; the three-wire quarter-phase system is unbalanced in voltage and phase, even at equal distribution of load. APPENDICES. APPENDIX I. ALGEBRA OF COMPLEX IMAGINARY QUANTITIES. INTRODUCTION. 296. The system of numbers, of which the science of algebra treats, f...", "... of subtraction under any circumstances, the system of abso- lute numbers has to be expanded by the introduction of the negative number: _ « = (_ 1) X «, .where (- 1) is the negative unit. Thereby the system of numbers is subdivided in the COMPLEX IMAGINARY QUANTITIES. 491 positive and negative numbers, and the operation of sub- traction possible for a..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 5: Symbolic Method", "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 9, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "... ing the wave through one-quarter period. Fig. 24. Similarly, - Multiplying by - j means advancing the wave through one-quarter period. since y'2 = - 1, j = V- 1 ; that is, - j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary num...", "... ary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition of/ = V- 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagra..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 5, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... combined give the total E.M.F., - Iz = lWr' + x\\ Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances , when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in th...", "... ts are pro- duced by the same E.M.F., such as in cases where Ohm's law is expressed in the form, -?• It is preferable, then, to introduce the reciprocal of impedance, which may be called the admittance of the circuit, or Z As the reciprocal of the complex quantity, Z =^ r - jxy the admittance is a complex quantity also, or 64 AL TERN A TING-CURRENT PH..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 5, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "... .M.F., Ix ; both combined give the total E.M.F., - Since E.M.Fs. are combined by adding their complex ex- pressions, we have : The joint impedance of a number of series-connected impe- dances is the sum of the individual impedances, when expressed in complex quantities. In graphical representation impedances have not to be added, but are combined in t...", "... s are produced by the same E.M.F., such as in cases where Ohm's law is expressed in the form, -I- It is preferable, then, to introduce the reciprocal of impedance, which may be called the admittance of the circuit, or >-*• As the reciprocal of the complex quantity, Z = r -jx, the admittance is a complex quantity also, or Y = g+jb; 54 ALTERNATING-CURRE..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 2: Long-Distance Transmission Line", "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 5, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "... (8) By equation (1), E ld' Y~dl' and substituting herein equation (8) gives E -A,™ + A*-\" , (9) 286 TRANSIENT PHENOMENA or, substituting (7), E =\\/A1e+vl+A,e-vi . (10) The integration constants A1 and A2 in (8), (9), (10), in general, are complex quantities. The coefficient of the exponent, F, as square root of the product of two complex quantities, a...", "... A*-\" , (9) 286 TRANSIENT PHENOMENA or, substituting (7), E =\\/A1e+vl+A,e-vi . (10) The integration constants A1 and A2 in (8), (9), (10), in general, are complex quantities. The coefficient of the exponent, F, as square root of the product of two complex quantities, also is a complex quantity, therefore may be written V = a - jp, (11) and substituting..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 4, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... ints, these points representing the abso- lute values of potential (with regard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in...", "... egard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are..." ] } ], "concordance_links": [ { "concept_id": "complex-quantities", "label": "Complex Quantities", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/complex-quantities/" } ] }, { "page_slug": "conductance", "page_title": "Conductance", "concept_ids": [ "conductance" ], "concept_labels": [ "Conductance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. 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Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 321, "matching_sections": 60, "matching_sources": 11, "aliases": 2 }, "aliases": [ "conductance", "conductances" ], "sources": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 86, "section_count": 10, "concepts": [ "Conductance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 79, "section_count": 10, "concepts": [ "Conductance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 72, "section_count": 7, "concepts": [ "Conductance" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 31, "section_count": 13, "concepts": [ "Conductance" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 21, "section_count": 3, "concepts": [ "Conductance" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 8, "section_count": 3, "concepts": [ "Conductance" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 8, "section_count": 3, "concepts": [ "Conductance" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 8, "section_count": 4, "concepts": [ "Conductance" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 5, "section_count": 5, "concepts": [ "Conductance" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 2, "section_count": 1, "concepts": [ "Conductance" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 1, "section_count": 1, "concepts": [ "Conductance" ] } ], "priority_sections": [ { "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 26, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "CHAPTER VIII ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 48. If in a continuous-current circuit, a number of resistances, Ti, r2, ?'3, . . ., are connected in series, their joint resistance, R, is the sum of the individual resistances, K = ri + r2 + ra + . . . If, however, a number of resistances ...", "... ir joint resistance, R, cannot be expressed in a simple form, but is represented by the expression 1 R = Ti n rz Hence, in the latter case it is preferable to introduce, instead of the term resistance, its reciprocal, or inverse value, the term conductance, g = ~- If, then, a number of conductances, 9iy Qij ds, • ' ' are connected in parallel, their j..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 23, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEFTANCE. 38. If in a continuous-current circuit, a number of resistances, rj, rj, rg, . . . are connected in series, their joint resistance, Ry is the sum of the individual resistances ^ = ^1 + ^2 + 'a + • • • If, however, a number of resistance ...", "... , their joint resistance, R^ cannot be expressed in a simple form, but is represented by the expression : - rx n r^ Hence, in the latter case it is preferable to introduce, in- stead of the term resistance^ its reciprocal, or inverse value, the term conductance^ g =\\ J r. If, then, a number of con- ductances, gxy g%i g^y . . . are connected in paralle..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 23, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 38. If in a continuous-current circuit, a number of resistances, ?\\, r%, r3, . . . are connected in series, their joint resistance, R, is the sum of the individual resistances If, however, a number of resistances are connected in multiple ...", "... ce, R, cannot be expressed in a simple form, but is represented by the expression : - = J_ _l_ JL + J_ + /*! /*2 ^3 Hence, in the latter case it is preferable to introduce, in- stead of the term resistance, its reciprocal, or inverse value, the term conductance, g = 1 / r. If, then, a number of con- ductances, g^, g^, gz, . . . are connected in parall..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 10: Effective Resistance And Reactance", "location": "lines 6957-8383", "status": "candidate", "occurrence_count": 19, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-10/", "snippets": [ "... of E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The energy coefficient of current, a._ Energy component of current Total E.M.F. is called the effective conductance of the circuit. EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ Wattle...", "... he true ohmic resistance in such way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \" effective susceptance,\" to make the calculation appli- cable to general altern..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 17, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... ge due to a line of given resistance and reactance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference; that is, by varying the admittance, Y = g - jh, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power - that is, upon the l...", "... shunt- ing the circuit with a reactance, and will be increased by a shunted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assumed to consist of two branches, a conductance, g, - the non-inductive part of the circuit - shunted by a susceptance, h, which can b..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 17, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... due to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference; that is, by varying the admittance, Y = g + Jb, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power, - that is, upon the...", "... a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 receiver circuit can be assumed to consist of two branches, a conductance, g^ - the non-inductive part of the circuit, - shunted by a susceptance, by which can be..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 17, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... e to a line of given re- sistance and inductance depends upon the phase difference in the receiver circuit, and can be varied and controlled by varying this phase difference ; that is, by varying the admittance, Y = g -f jb, of the receiver circuit. The conductance, gy of the receiver circuit depends upon the consumption of power, - that is, upon the...", "... uit with a reactance, and will be increased by a shunted inductance, and decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, - the non-inductive part of the circuit, - shunted by a susceptance, b, which can be..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 10: F", "location": "lines 8269-10499", "status": "candidate", "occurrence_count": 16, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-10/", "snippets": [ "... f E.M.F. Total current It is called the effective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The energy coefficient of current, _ Energy component of current ^ Total E.M.F. is called the effective conductance of the circuit. § 733 EFFECTIVE RESISTANCE AND REACTANCE. 105 In the same way, the value, _ W...", "... he true ohmic resistance in such way as to represent a larger expenditure of energy. In dealing with alternating-current circuits, it is necessary, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,'* and \" effective susceptance,\" to make the calculation appli- cable to general alter..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-12", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 12: Effective Resistance And Reactance", "location": "lines 10718-13483", "status": "candidate", "occurrence_count": 14, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-12/", "snippets": [ "... of e.m.f. Total current It is called the elective resistance of the circuit, since it represents the effect, or power, expended by the circuit. The power coeffi- cient of current, Power component of current ^ \" Total e.m.f. ' is called the effective conductance of the circuit. Ill 112 ALTERNATING-CURRENT PHENOMENA In the same way, the value, Wattless...", "... he true ohmic resistance in such way as to represent a larger expenditure of power. In dealing with alternating-current circuits, it is necessarj-, therefore, to substitute everywhere the values \"effective re- sistance,\" \"effective reactance,\" \"effective conductance,\" and \"effective susceptance,\" to make the calculation applicable to general alternati..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 13, "concepts": [ "Conductance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... the induced E.M.F., E, in the equation it follows that, The loss of power by eddy currents is propor- tional to the square of the E.M.F., and proportional to the electric conductivity of the iron ; or, H^=aJS^y. Hence, that component of the effective conductance which is due to eddy currents, is that is. The equivalent conductance due to eddy currents...", "... wer by eddy currents is propor- tional to the square of the E.M.F., and proportional to the electric conductivity of the iron ; or, H^=aJS^y. Hence, that component of the effective conductance which is due to eddy currents, is that is. The equivalent conductance due to eddy currents in the iron is a constant of the magnetic circuit ; it is indepen- de..." ] } ], "concordance_links": [ { "concept_id": "conductance", "label": "Conductance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/conductance/" } ] }, { "page_slug": "dielectric-loss", "page_title": "Dielectric Loss", "concept_ids": [ "dielectricity", "dielectric-field", "dielectric-constant" ], "concept_labels": [ "Dielectricity", "Dielectric Field", "Dielectric constant" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. 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Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, ...", "CHAPTER XIV DIELECTRIC LOSSES Dielectric Hysteresis 116. Just as magnetic hysteresis and eddy currents give a power component in the inductive reactance, as \"effective resistance,\" so the energy losses in the dielectric lead to a power component in the condensive reactance, which may be repre- ..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-02", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 2: The Electric Field", "location": "lines 1003-1658", "status": "candidate", "occurrence_count": 114, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-02/", "snippets": [ "... hile power flows through the conductors A, power is con- sumed in these conductors by JV[ conversion into heat, repre- sented by ^2r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. - Electric Field of Conductor. The conductor is surrounded by a...", "... wn in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielect...", "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, whic...", "... gether between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielect..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-02", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 2: The Electric Field", "location": "lines 883-1530", "status": "candidate", "occurrence_count": 114, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-02/", "snippets": [ "... While power flows through the conductors A, power is con- sumed in these conductors by conversion into heat, repre- sented by i?r. This, however, Fig. 7. is not all, but in the space surrounding the conductor cer- tain phenomena occur: magnetic and electrostatic forces appear. Fig. 8. - Electric Field of Conductor. The conductor is surrounded by a mag...", "... wn in Fig. 8. By the return conductor, the circles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielect...", "... ircles 10 THE ELECTRIC FIELD. 11 are crowded together between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, whic...", "... gether between the conductors, and the magnetic field consists of eccentric circles surrounding the conductors, as shown by the drawn lines in Fig. 9. An electrostatic, or, as more properly called, dielectric field, issues from the conductors, that is, a dielectric flux passes between the conductors, which is measured by the number of lines of dielect..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-19", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Theory Section 19: Fields of Force", "location": "lines 7737-7990", "status": "candidate", "occurrence_count": 81, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-19/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-19/", "snippets": [ "... e earth, and water to run down hill - and this space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is...", "... is space thus is a field of gravitational force, the earth the gram- motive force. In the space surrounding conductors having a high potential difference, we observe a field of dielectric force, that is, electro- static or dielectric forces are exerted, and the potential difference between the conductors is the electromotive force of the dielectric fi..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 10: Continual And Cumulative Oscillations", "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 60, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... enon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillatin...", "... hen, with an overlap of successive oscillations, no dead period occurs, during which the energy, which oscillates during the next wave train, is supplied to the line, this energy must be supplied during the oscillation, that is, there must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hy...", "... echanism, by which the hysteresis cycle supplies the energy of continual oscillations, has been investigated in the case of the hunting of synchronous machines,* but is still practically un- known in the case of continual oscillations between magnetic and dielectric energy in electric circuits. Recurrent oscillations, as in Fig. 59, must be or very so..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-23", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 1: The Constants Of The Electric Circuit", "location": "lines 1317-1992", "status": "candidate", "occurrence_count": 59, "concepts": [ "Dielectricity", "Dielectric Field", "Dielectric constant" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-23/", "snippets": [ "... rostatic actions. The magnetic action is a maximum in the direction concen- tric, or approximately so, to the conductor. That is, a needle- shaped magnetizable body, as an iron needle, tends to set itself in a direction concentric to the conductor. The electrostatic action has a maximum in a direction radial, or approximately so, to the conductor. Tha...", "... etizable body, as an iron needle, tends to set itself in a direction concentric to the conductor. The electrostatic action has a maximum in a direction radial, or approximately so, to the conductor. That is, a light needle- shaped conducting body, if the electrostatic component of the field is powerful enough, tends to set itself in a direction radial...", "... as that factor of the electric power P which is proportional to the electrostatic field. Current i and voltage e, therefore, are mathematical fictions, factors of the power P, introduced to represent respectively the magnetic and the electrostatic or \" dielectric \" phenomena. The current i is measured by the magnetic action of a circuit, as in the amm...", "... cuit, as in the electrostatic voltmeter, or by producing a current i by the voltage e and measuring this current i by its magnetic action, in the usual voltmeter. The coefficients L and (7, which are the proportionality factors of the magnetic and of the dielectric component of the electric field, are called the inductance and the capacity of the circ...", "... city, C, is proportional to the section and inversely proportional to the length of the electrostatic field of the con- ductor: ^ *A G = T, (20) where K is a constant of the material filling the space surround- ing the conductor, which is called the \"dielectric constant,\" or the \" specific capacity/' or \" permittivity.\" Usually the section and the len...", "... electric constant,\" or the \" specific capacity/' or \" permittivity.\" Usually the section and the length of the different parts of the electrostatic circuit are different, and the capacity therefore has to be calculated piecemeal, or by integration. The dielectric constant K of different materials varies over a relative narrow range only. It is approxi..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 11: Foucault Or Eddy Currents", "location": "lines 8384-9380", "status": "candidate", "occurrence_count": 58, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-11/", "snippets": [ "... mutual inductance ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considere...", "... ce ; ^ = effective reactance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the reactance of self-inductance. Or, Mutual inductance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy...", "... ance consumes energy and decreases the self- inductance. Dielectric and Electrostatic Phenomena. 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, con- densance has an energy component also, namely, dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 54, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... b = - ^-^^^ - ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be consider...", "... ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutual itidtutance consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the ener...", "... ce consumes energy and decreases the self- inductatice. Dielectric and Electrostatic Phenomena, 98. While magnetic hysteresis and eddy currents can be considered as the energy component of inductance, cori- densance has an energy component also, called dielectric hysteresis. In an alternating magnetic field, energy is con- sumed in hysteresis due to m..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 52, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "... inkages of the mag- netic flux to the current, £ = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force...", "... = ?- (i) i/ where = magnetic flux or number of lines of magnetic force, and n the number of times which each line of magnetic force interlinks with the current i. The capacity is the ratio of the dielectric flux to the voltage, where \\f/ is the dielectric flux, or number of lines of dielectric force, and e the voltage which produces it. With a sin..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 6: Double-Energy Transients", "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 52, "concepts": [ "Dielectricity", "Dielectric Field" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "... energy is stored by the current i, as magnetic field. To = -, (2) r where L = inductance = coefficient of energy storage by the cur- rent, r = resistance = coefficient of power dissipation by the current. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES...", "... urrent. If the energy is stored by the voltage e, as dielectric field, the duration of the transient would be TV - -, (3) g 59 60 ELECTRIC DISCHARGES, WAVES AND IMPULSES. where C = capacity = coefficient of energy storage by the volt- age, in the dielectric field, and g = conductance = coefficient of power consumption by the voltage, as leakage conduc..." ] } ], "concordance_links": [ { "concept_id": "dielectricity", "label": "Dielectricity", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/dielectricity/" }, { "concept_id": "dielectric-field", "label": "Dielectric Field", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/dielectric-field/" }, { "concept_id": "dielectric-constant", "label": "Dielectric constant", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/dielectric-constant/" } ] }, { "page_slug": "distributed-constants", "page_title": "Distributed Constants", "concept_ids": [ "distributed-constants", "wave-propagation" ], "concept_labels": [ "Distributed Constants", "Wave Propagation" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. 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TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length - where the frequency becomes zero - that the effect of the damping constant on the frequency and the wave length is negligi...", "... the fre- quency constant q and the wave length constant k can be neglected, that is, frequency and wave length assumed as inde- pendent of the energy loss in the circuit. Usually, therefore, the equations (74) and (75) can be applied in dealing with the traveling wave. In these equations the distance traveled by the wave per second is used as unit len..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 8: Traveling Waves", "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 27, "concepts": [ "Distributed Constants", "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given by the expression i = ioe-\"^ cos ((/> T CO - 7), ^ . . e = eoe~\"' sin ((^ =F co - 7), where -7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the c...", "... ^o [1 + cos 2 ( =F CO -7)], (5) and the average flow of power is po = avg p, (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling w..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 8: Traveling Waves", "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 27, "concepts": [ "Distributed Constants", "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "LECTURE VIII. TRAVELING WAVES. 33. In a stationary oscillation of a circuit having uniformly distributed capacity and inductance, that is, the transient of a circuit storing energy in the dielectric and magnetic field, current and voltage are given ^by the expression i = iQe~ut cos (0 T co - 7), ) e = e0e~ut sin ( T co - 7), ) where 0 is the time angle...", "... tance angle co, and at any time t, that is, time angle <£, then is p = ei, = e0ioe~2ut cos ( T co - 7) sin (0 =F co - 7), = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the ci...", "... = = eQiQe-2ut cos2 co - 7), and the average flow of power is p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. Fo..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 23, "concepts": [ "Distributed Constants" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many ...", "... hole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi nitely near together, as diagrammatically shown in Fig. 83. iiiimiiiiumiiiT TTTTTTTTTT.TTTTTTTTTT i Fig. 83. Distributed Capacity. In this case the intensity as well as phase of the current, and consequently of the c..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 3: Standing Waves", "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 15, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm2)2; (97) hence, if k2 > LCm2, R2 = tf- LCm2; and if /c2 < LCm..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-12", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 12: Dibtbisnted Capacity, Inductance, Besistance, And", "location": "lines 11564-12672", "status": "candidate", "occurrence_count": 11, "concepts": [ "Distributed Constants" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-12/", "snippets": [ "... capacity is distributed over the whole length of the conductor, so that the circuit can be considered as shunted by an infinite number of infinitely small condensers infi. nitely near together, as diagrammatically shown in Fig. 83. 8 3 S Fig, 83. Distributed Capacity. In this case the intensity as well as phase of the current,, and consequently of the...", "... .M.Fs., but also the currents, at the beginning, end, and different points of the conductor, are different in intensity and in phase. Where the capacity effect of the line is small, it may with sufficient approximation be represented by one con- §103] DISTRIBUTED CAPACITY. 151 denser of the same capacity as the line, shunted across the line. Frequentl..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Inductive Discharges", "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 10, "concepts": [ "Distributed Constants", "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge...", "... rgy, of complex circuit 507 of energy in oscillation of complex circuit 507, 521 Transformation ratio at transition point of wave 529 of voltage and current at transition point 529 Transformer, alternating, operating oscillating-current generator 87 distributed capacity 342 quarter-wave oscillation 312 starting 44 and magnetic saturation 180 Transient...", "... 2 + nno 07 c 1 75 + .008 487 1 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit a...", "... ator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transi..." ] }, { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 8, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... nner, thus giving rise (to very different wave shapes of the impulses. So some impulses may rise very rapidly, with •A. I. E. E. Transact. March, 1907: \"Lightning Phenomena in Electric Circuits.\" LIGHTNING AND LIGHTNING PROTECTION 273 extremely steep wave front, and slowly die down. Others may rise slowly, then suddenly fall and reverse, or a series o...", "... interference between the reflected waves, the incoming waves and the waves passing over the reactances, and so give rise to systems of standing waves or oscillations, similarly as an ocean wave rolling on to a sloping beach breaks up into surf. Where a traveling wave is reflected, the combination of the reflected wave and the incoming wave produces a..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-15", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 15: Distributed Capacity, Inductance, Resistance, And Leakage", "location": "lines 15410-16076", "status": "candidate", "occurrence_count": 8, "concepts": [ "Distributed Constants" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-15/", "snippets": [ "CHAPTER XV DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE 127. In the foregoing, the phenomena causing loss of energy in an alternating-current circuit have been discussed; and it has been shown that the mutual relation between current and e.m.f. can be expressed by two of ...", "... ceding chapter - to circuits containing iron and other materials producing energy losses outside of the electric conductor. 128. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or 168 DISTRIBUTED CAPACITY 169 other source of negative reactance is shunted across the circuit at a definite..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-44", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 4: Distributed Capacity Of High-Potential Transformers", "location": "lines 23179-23585", "status": "candidate", "occurrence_count": 8, "concepts": [ "Distributed Constants" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-44/", "snippets": [ "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages - 100;000 volts and more, or even considerably ...", "CHAPTER IV. DISTRIBUTED CAPACITY OF HIGH-POTENTIAL TRANSFORMERS. 40. In the high-potential coils of transformers designed for very high voltages phenomena resulting from distributed capacity occur. In transformers for very high voltages - 100;000 volts and more, or even considerably less in small transformers - the high- potential coil contains a large nu..." ] } ], "concordance_links": [ { "concept_id": "distributed-constants", "label": "Distributed Constants", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/distributed-constants/" }, { "concept_id": "wave-propagation", "label": "Wave Propagation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/wave-propagation/" } ] }, { "page_slug": "electric-waves", "page_title": "Electric Waves", "concept_ids": [ "electric-waves", "wave-propagation", "electrical-radiation" ], "concept_labels": [ "Electric waves", "Wave Propagation", "Electrical Radiation" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as a connector between optical radiation, wireless or high-frequency waves, and transmission-line behavior. Keep wavelength, frequency, velocity, and source context visible.", "totals": { "occurrences": 176, "matching_sections": 20, "matching_sources": 6, "aliases": 10 }, "aliases": [ "Electric waves", "electric-waves", "standing wave", "traveling wave", "travelling wave", "wave front", "wave propagation", "electric radiation", "electrical radiation", "radiant energy" ], "sources": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 83, "section_count": 12, "concepts": [ "Wave Propagation", "Electrical Radiation" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 32, "section_count": 2, "concepts": [ "Wave Propagation" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 31, "section_count": 2, "concepts": [ "Wave Propagation" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 19, "section_count": 6, "concepts": [ "Electric waves", "Wave Propagation", "Electrical Radiation" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 8, "section_count": 1, "concepts": [ "Wave Propagation" ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 3, "section_count": 2, "concepts": [ "Electric waves", "Wave Propagation" ] } ], "priority_sections": [ { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-53", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 4: Traveling Waves", "location": "lines 30244-31450", "status": "candidate", "occurrence_count": 33, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-53/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 20. As seen in Chapter III, especially in electric power cir- cuits, overhead or underground, the longest existing standing wave has a wave length which is so small compared with the critical wave length - where the frequency becomes zero - that the effect of the damping constant on the frequency and the wave length is negligi...", "... the fre- quency constant q and the wave length constant k can be neglected, that is, frequency and wave length assumed as inde- pendent of the energy loss in the circuit. Usually, therefore, the equations (74) and (75) can be applied in dealing with the traveling wave. In these equations the distance traveled by the wave per second is used as unit len..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 8: Traveling Waves", "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 26, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... y dis- tance angle co, and at any time t, that is, time angle 0, then is p = ei, = eo^e~2\"* cos (0 =F co - 7) sin (0 =F co - 7), = ^6-^«'sin2(0Ta>-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the c...", "... ^o [1 + cos 2 ( =F CO -7)], (5) and the average flow of power is po = avg p, (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power along the circuit is called a traveling w..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 8: Traveling Waves", "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 26, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... tance angle co, and at any time t, that is, time angle <£, then is p = ei, = e0ioe~2ut cos ( T co - 7) sin (0 =F co - 7), = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the ci...", "... = = eQiQe-2ut cos2 co - 7), and the average flow of power is p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a traveling wave. It occurs very frequently. Fo..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-52", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 3: Standing Waves", "location": "lines 29316-30243", "status": "candidate", "occurrence_count": 15, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-52/", "snippets": [ "CHAPTER III. STANDING WAVES. 14. If the propagation constant of the wave vanishes, h = 0, the wave becomes a stationary or standing wave, and the equa- tions of the standing wave are thus derived from the general equations (50) to (61), by substituting therein h = 0, which gives R2 = V(k2 - LCm2)2; (97) hence, if k2 > LCm2, R2 = tf- LCm2; and if /c2 < LCm..." ] }, { "section_id": "radiation-light-and-illumination-lecture-01", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "location": "lines 608-1548", "status": "candidate", "occurrence_count": 13, "concepts": [ "Electric waves", "Wave Propagation", "Electrical Radiation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... uch low frequencies, but such very low frequencies NATURE AND DIFFERENT FORMS OF RADIATION. 15 have been observed in the radiations of bodies of very low tem- perature, as liquid air, or in the moon's rays. 7. Very much longer waves, however, are the electric waves. They are used in wireless telegraphy, etc. I here connect (Fig. 12) FIG. 12. the conde...", "... e terminals, and the arrival of the electric wave at A2 causes a small spark to jump across the gap Gv which closes the circuit of the tungsten lamp L, thereby lighting it as long as the wave train continues. 16 RADIATION, LIGHT, AND ILLUMINATION. The electric waves used in wireless telegraphy range in wave lengths from 100 feet or less to 10,000 feet...", "... ery great, due to the low frequency, - 3 X 1010 a 60-cycle alternating current gives a wave length of ^ = 500 X 10\" cm. or 3100 miles - the distance to which the field of the circuit extends is an insignificant fraction only of the wave length, and the wave propagation of the field thus is usually not considered. Electric waves of higher frequencies t...", "... s is the time required by the light 18,800 to travel 10 miles, this gives the velocity of light as 10 •* > lo,oOU or 188,000 miles per sec. The velocity of light in air, or rather in empty space, thus is 188,000 miles or 3 X 1010 cm. per sec. For electrical radiation, the velocity has been measured by Herz, and found to be the same as the velocity of..." ] }, { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 8, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... nner, thus giving rise (to very different wave shapes of the impulses. So some impulses may rise very rapidly, with •A. I. E. E. Transact. March, 1907: \"Lightning Phenomena in Electric Circuits.\" LIGHTNING AND LIGHTNING PROTECTION 273 extremely steep wave front, and slowly die down. Others may rise slowly, then suddenly fall and reverse, or a series o...", "... interference between the reflected waves, the incoming waves and the waves passing over the reactances, and so give rise to systems of standing waves or oscillations, similarly as an ocean wave rolling on to a sloping beach breaks up into surf. Where a traveling wave is reflected, the combination of the reflected wave and the incoming wave produces a..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Inductive Discharges", "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 8, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... 2 + nno 07 c 1 75 + .008 487 1 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit a...", "... ator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transi..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-09", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 9: Oscillations Of The Compound Circuit", "location": "lines 5521-6088", "status": "candidate", "occurrence_count": 6, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-09/", "snippets": [ "LECTURE IX. OSCILLATIONS OF THE COMPOUND CIRCUIT. 38. The most interesting and most important application of the traveling wave is that of the stationary oscillation of a com- pound circuit, as industrial circuits are never uniform, but consist of sections of different characteristics, as the generating system, transformer, line, load, etc. Oscillograms o...", "... section must have a second exponential time decrement, S = UQ - U, (2) which represents power transfer from the section to other sections, or, if s is negative, power received from other sections. The oscil- lation of every individual section thus is a traveling wave, with a power-transfer constant s. As UQ is the average dissipation constant, that is..." ] }, { "section_id": "radiation-light-and-illumination-lecture-02", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 2: Relation Of Bodies To Radiation", "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 6, "concepts": [ "Electric waves", "Wave Propagation", "Electrical Radiation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation a...", "... ndex between any two media is derived as the ratio of their refractive indices against a third medium, as, for instance, against air. 24 RADIATION, LIGHT, AND ILLUMINATION. 11. Incidentally, it is interesting to consider the corresponding relations in electric waves. In an electric circuit, the speed of propagation of an electric wave is, when neglect...", "... in the present instance. Let then Sl = speed of propagation in medium A, S2 = speed of propagation in medium W. Then, while the center of the beam moves the distance EC, the back edge, in the denser medium, a moves only the distance DI = -^EC, and the wave front of the »i back half of the beam thus changes to CI while that of the front half of the bea...", "... of the front half of the beam, which is still in the medium A, remains GC. Then, while the front edge of the beam moves from G to H, the center and the whole back half of the beam moves in the denser o medium TF, only the distance CK = - 2 GH, and the wave front «i of the beam, in the medium TF, now is EL. That is, due to the difference in velocity in...", "... , in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determ..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-17", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 4: Traveling Waves. 457", "location": "lines 1112-1147", "status": "candidate", "occurrence_count": 6, "concepts": [ "Wave Propagation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-17/", "snippets": [ "CHAPTER IV. TRAVELING WAVES. 457 20. Different forms of the equations of the traveling wave. 457 CONTENTS. xxiii PAGE 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling c ...", "CHAPTER IV. TRAVELING WAVES. 457 20. Different forms of the equations of the traveling wave. 457 CONTENTS. xxiii PAGE 21. Component waves and single traveling wave. Attenua- tion. 459 22. Effect of inductance, as loading, and leakage, on attenu- ation. Numerical example of telephone circuit. 462 23. Traveling sine wave and traveling cosine wave. Ampli- tu..." ] } ], "concordance_links": [ { "concept_id": "electric-waves", "label": "Electric waves", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/electric-waves/" }, { "concept_id": "wave-propagation", "label": "Wave Propagation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/wave-propagation/" }, { "concept_id": "electrical-radiation", "label": "Electrical Radiation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/electrical-radiation/" } ] }, { "page_slug": "ether", "page_title": "Ether", "concept_ids": [ "ether" ], "concept_labels": [ "Ether" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as a historical-language and field-theory boundary page. The current corpus places most ether hits in Steinmetz's relativity lectures, where ether is treated alongside the rise of Faraday-Maxwell field language; the earlier radiation source uses it in the wave-theory-of-light setting. That distribution matters.", "totals": { "occurrences": 66, "matching_sections": 6, "matching_sources": 3, "aliases": 3 }, "aliases": [ "Ether", "aether", "ether" ], "sources": [ { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 59, "section_count": 3, "concepts": [ "Ether" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 6, "section_count": 2, "concepts": [ "Ether" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 1, "section_count": 1, "concepts": [ "Ether" ] } ], "priority_sections": [ { "section_id": "four-lectures-relativity-space-lecture-02", "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_label": "Lecture 2: Conclusions From The Relativity Theory", "location": "lines 736-2388", "status": "candidate", "occurrence_count": 52, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-02/", "snippets": [ "... obser- vation. The law of conservation of matter thus had to be abandoned and mass became a manifestation of energy. The law of gravitation has been recast, and the force of gravitation has become an effect of inertial motion, like centrifugal force. The ether has been abandoned, and the field of force of Faraday and Maxwell has become the fundamental...", "... ion miles. Therefore the principal value of the relativity theory thus far consists in the better conception of nature and its laws which it affords. Some of the most interesting illustra- tions of this will be discussed in the following pages. B. THE ETHER AND THE FIELD OF FORCE Newton's corpuscular theory of light explained radiation as a bombardmen..." ] }, { "section_id": "four-lectures-relativity-space-lecture-04", "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_label": "Lecture 4: The Characteristics Of Space A. The Geometry Of The Gravitational Field", "location": "lines 3595-6820", "status": "candidate", "occurrence_count": 6, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-04/", "snippets": [ "... ge, 47 field, 18 ElUptic geometry, 64, 72, 74 trigonometry, 77 Energy equivalent of mass, 44 field, 22, 46 kinetic, 47 and mass, 41 of wave, 22 123 124 INDEX Entity energy, 24 Equations of transformation to moving system, 25, 27 Ether, 12, 14 as solid, 14 drift, 14 fallacy of conception, 16 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean...", "... NDEX Entity energy, 24 Equations of transformation to moving system, 25, 27 Ether, 12, 14 as solid, 14 drift, 14 fallacy of conception, 16 illogical, 18 unnecessary, 17 waves, 18 Euclid, 71 Euclidean geometry, 64, 72, 74 F Fallacy of ether conception, 16 Faraday, 12, 17 Field, centrifugal, 47 dielectric, 18 electromagnetic, 21 electrostatic, 18 gravit..." ] }, { "section_id": "radiation-light-and-illumination-lecture-01", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "location": "lines 608-1548", "status": "candidate", "occurrence_count": 5, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... icity and extremely low density, and it must penetrate all substances since no vacuum can be produced for this medium, because light passes through any vacuum. Hence it cannot be any known gas, but must be essen- tially different, and has been called the \"ether.\" Whether the ether is a form of matter or not depends upon the definition of matter. If ma...", "... w density, and it must penetrate all substances since no vacuum can be produced for this medium, because light passes through any vacuum. Hence it cannot be any known gas, but must be essen- tially different, and has been called the \"ether.\" Whether the ether is a form of matter or not depends upon the definition of matter. If matter is defined as the..." ] }, { "section_id": "four-lectures-relativity-space-lecture-03", "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "year": 1923, "section_label": "Lecture 3: Gravitation And The Gravitational Fleld", "location": "lines 2389-3594", "status": "candidate", "occurrence_count": 1, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/four-lectures-relativity-space/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/four-lectures-relativity-space/lecture-03/", "snippets": [ "LECTURE III GRAVITATION AND THE GRAVITATIONAL FLELD A. THE IDENTITY OF GRAVITATIONAL, CENTRIFUGAL AND INERTIAL MASS As seen in the preceding lecture, the conception of the ether as the carrier of radiation had to be abandoned as incompatible with the theory of relativity; the conception of action at a distance is repugnant to our reasoning, and its place..." ] }, { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 1, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... ions. There are different forms of energy, all convertible into each other, as magnetic energy, electric energy, heat energy, mechanical momentum, radiating energy, etc. The latter, radi- ating energy, is a vibratory motion of a hypothetical medium, the ether, which vibration is transmitted or propagated at a velocity of about 188,000 miles per second..." ] }, { "section_id": "radiation-light-and-illumination-lecture-02", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 2: Relation Of Bodies To Radiation", "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 1, "concepts": [ "Ether" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "... less and, as will be seen, is different for different frequencies. 22 RADIATION, LIGHT, AND ILLUMINATION. Assume then, in Fig. 15, a beam of light B striking under an angle the boundary between two media, as air A and water W, the vibration of the ether particles in the beam of light is at right angles to the direction of propagation BC, and successiv..." ] } ], "concordance_links": [ { "concept_id": "ether", "label": "Ether", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/ether/" } ] }, { "page_slug": "harmonics-wave-shape", "page_title": "Harmonics And Wave Shape", "concept_ids": [ "frequency", "alternating-current", "wave-length" ], "concept_labels": [ "Frequency", "Alternating Current", "Wave Length" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 4634, "matching_sections": 317, "matching_sources": 15, "aliases": 15 }, "aliases": [ "Frequency", "cycles per second", "frequencies", "frequency", "periodicity", "a.c.", "alternating current", "alternating currents", "alternating-current", "Wave length", "wave length", "wave lengths", "wave-length", "wave-lengths", "wavelength" ], "sources": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 758, "section_count": 41, "concepts": [ "Frequency", "Alternating Current" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 751, "section_count": 88, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 561, "section_count": 55, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 549, "section_count": 63, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 386, "section_count": 90, "concepts": [ "Frequency", "Alternating Current" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 356, "section_count": 25, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 343, "section_count": 20, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 331, "section_count": 50, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 184, "section_count": 31, "concepts": [ "Frequency", "Alternating Current" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 138, "section_count": 16, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 119, "section_count": 14, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 61, "section_count": 12, "concepts": [ "Frequency", "Alternating Current" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 60, "section_count": 5, "concepts": [ "Frequency", "Alternating Current" ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 31, "section_count": 8, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 6, "section_count": 5, "concepts": [ "Alternating Current" ] } ], "priority_sections": [ { "section_id": "theory-calculation-electric-apparatus-chapter-11", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 244, "concepts": [ "Frequency", "Alternating Current" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plie ...", "... sist* of a magnetic circuit interlinked with two sets of electric circuits, the primary and the secondary, which are mounted rotatably with regards to each other. It transforms between primary electrical and secondary electrical power, and also between FREQUENCY CONVERTER 177 electrical and mechanical power. As the frequency of the re- volving seconda...", "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, an ...", "CHAPTER XII FREQUENCY CONVERTER OR GENERAL ALTERNATING- CURRENT TRANSFORMER 103. In general, an alternating-current transformer conafete of a magnetic circuit, interlinked with two electric circuits or sets of electric circuits, the primary circuit, in which power, sup- plied by the impressed voltage, is consumed, and the secondary circuit, in which a cor..." ] }, { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 118, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions...", "... ECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low frequencies, that is only a few millions of millions of cycles...", "... of voltage, and vice versa; and so limits itself. While therefore arcs can be operated on a constant cur- rent system, to run arc lamps on constant potential, some cur- rent limiting device is necessary in series with the arc, as a resistance; or, in an alternating current circuit, a reactance. The voltage consumed by the resistance is proportional to...", "... a constant current circuit, with series connection of from 50 to 100 lamps on one circuit. With the exception of a few of the larger cities, all the street lighting by arc lamps in this country is done by constant current systems, either direct current or alternating current. For direct current constant current supply, separate arc light machines have...", "... ce, from heat energy by raising a body to a 230 GENERAL LECTURES high temperature. Then the heat energy is converted into radi- ation and issues from the heated body, as for instance an incan- descent lamp filament, as a mass of radiations of different wave lengths, that is, different frequencies. All kinds of frequencies appear : from very low freque...", "... ury arc at low temperature gives. Possibly, since the oxygen atom is so much lighter than the silver atom, its fre- quency of vibration is much higher, which means that resonance effects and destruction of the molecules take place only with a much shorter wave length of radiation, or much higher frequency. Vice versa, it seems that these frequencies w..." ] }, { "section_id": "radiation-light-and-illumination-lecture-01", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "location": "lines 608-1548", "status": "candidate", "occurrence_count": 101, "concepts": [ "Frequency", "Alternating Current", "Wave Length" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "... from each other by a fractional wave length is called iridescence. Iridescent colors, for instance, are those of mother-of-pearl, of opal, of many butterflies, etc. Light, therefore, is a wave motion. NATURE AND DIFFERENT FORMS OF RADIATION. 1 The frequency of radiation follows from the velocity of light, and the wave length. The average wave length o...", "... of radiation follows from the velocity of light, and the wave length. The average wave length of visible radiation, or light, is about lw = 60 microcentimeters,* that is, 60 X 10~8 cm. (or about ^, and thus approxi- mately with the current [, is proportional to tin* frequency of the 362 ELECTRICAL APPARATUS impressed voltage, /, to the field strength, 4>, and to the number of field turns, n„. «o = 2jirfn0* 10~8. (26) 3. The impedance voltage of the motor: e' = IZ (27) and: Z = r + jx, where r = total effective resistance of fi..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-14", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 14: The Alternating-Current Transformer", "location": "lines 11605-12682", "status": "candidate", "occurrence_count": 32, "concepts": [ "Impedance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-14/", "snippets": [ "... transformer depends upon the primary E.M.F., which dependance can be rep- resented by an admittance, the \" primary admittance,\" °f tne transformer. Fig. 105. The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic densi...", "... The resistance and reactance of the primary and the secondary circuit are represented in the impedance by Z0=r0- jx0, and Zl=rl- j xl . Within the limited range of variation of the magnetic density in a constant potential transformer, admittance and impedance can usually, and with sufficient .exactness, be considered as constant. Let n0 = number of pr..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 24: Synchronous Motor", "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 32, "concepts": [ "Impedance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "... hod, we may in the following, as an example of the graphical method, treat the action of the synchronous motor graphically. Let an alternator of the e.m.f., Ei, be connected as synchron- ous motor with a supply circuit of e.m.f., Eo, by a circuit of the impedance, Z. If £\"0 is the e.m.f. impressed upon the motor terminals, Z is the impedance of the mo...", "... ion of the synchronous motor graphically. Let an alternator of the e.m.f., Ei, be connected as synchron- ous motor with a supply circuit of e.m.f., Eo, by a circuit of the impedance, Z. If £\"0 is the e.m.f. impressed upon the motor terminals, Z is the impedance of the motor of generated e.m.f., Ei. If Eq is the e.m.f. at the generator terminals, Z is..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-109", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Apparatus Section 3: Induction Machines: Single -phase Induction Motor", "location": "lines 20428-21157", "status": "candidate", "occurrence_count": 27, "concepts": [ "Impedance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-109/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-109/", "snippets": [ "... main magnetic flux plus the current producing in the secondary the exciting current of the cross magnetic flux. In reality it is slightly less, especially in small motors, due to the drop of voltage in the self-inductive impedance and the drop of quadrature mag- netic flux below the impressed primary magnetic flux caused thereby. In the secondary at s...", "... )262a!. Since in the single-phase motor only one primary circuit but a multiplicity of secondary circuits exist, all secondary circuits are to be considered as corresponding to the same primary cir- cuit, and thus the joint impedance of all secondary circuits must be used as the secondary impedance, at least at or near syn- chronism. Thus, if the arma..." ] } ], "concordance_links": [ { "concept_id": "impedance", "label": "Impedance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/impedance/" } ] }, { "page_slug": "inductance-capacity", "page_title": "Inductance And Capacity", "concept_ids": [ "inductance", "electrostatic-capacity", "energy-storage-fields" ], "concept_labels": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as an energy-storage pair. The archive should keep magnetic-flux and dielectric-flux language visible before reducing everything to modern lumped L and C notation.", "totals": { "occurrences": 5084, "matching_sections": 267, "matching_sources": 15, "aliases": 13 }, "aliases": [ "inductance", "inductive", "mutual inductance", "self-inductance", "capacitance", "capacity", "condenser", "condensers", "electrostatic capacity", "energy of the field", "energy stored", "stored energy", "stored in the field" ], "sources": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 1164, "section_count": 83, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 586, "section_count": 46, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 575, "section_count": 52, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 520, "section_count": 32, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 510, "section_count": 27, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 399, "section_count": 41, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 368, "section_count": 69, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 343, "section_count": 29, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 329, "section_count": 28, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 137, "section_count": 24, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 93, "section_count": 10, "concepts": [ "Inductance", "Electrostatic Capacity" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 30, "section_count": 8, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 14, "section_count": 2, "concepts": [ "Inductance", "Electrostatic Capacity" ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 9, "section_count": 5, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ] }, { "source_id": "america-and-new-epoch", "source_title": "America and the New Epoch", "occurrence_count": 7, "section_count": 4, "concepts": [ "Electrostatic Capacity" ] } ], "priority_sections": [ { "section_id": "theory-calculation-electric-circuits-chapter-14", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 193, "concepts": [ "Inductance", "Electrostatic Capacity" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... escent lamps, the constant direct current is usually derived by rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by means of constant or variable inductive reactances, and may be produced by the combination of inductive and condensive reactance...", "... rectification of constant alternating-current supply circuits. Such constant alternating currents are usually produced from constant- voltage supply circuits by means of constant or variable inductive reactances, and may be produced by the combination of inductive and condensive reactances; and the investigation of different methods of producing const...", "... es a good application of the terms \"impedance,\" admittance,\" etc., and offers a large number of problems or examples for the symbolic method of dealing with alternating-current phenomena. Even outside of arc lighting, such combinations of inductance and capacity which t«nd toward constant-voltage constant-cur- rent transformation are of considerable i...", "... = r{l + jk) where k = tangent of the angle of lag = -; H Fig 116. CONSTANT'CURRENT TRANSFORMATION 257 let the receiver circuit be shunted by a constant condensive react- ance, Xe'f let then: ^ = potential difference of receiver circuit or the condenser terminals, / = current in the receiver circuit, or the \"secondary current,'' /i = current in the con..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 6: Oscillating Currents,", "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 120, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "CHAPTER VI. OSCILLATING CURRENTS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather limited: synchronous machines or ordinary alternators can give economically and ...", "... ly is this energy dissipated, that is, the faster the oscillation dies out. With a resistance of the circuit sufficiently low to give a fairly well sustained oscillation, the frequency is, with sufficient approximation, 45. The constants, capacity, C, inductance, L, and resistance, r, have no relation to the size or bulk of the apparatus. For instance...", "CHAPTER VI. OSCILLATING CURRENTS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather limited: synchronous machines or ordinary alternators can ...", "... because of the small pitch per pole of the machine, etc., so that 1000 cycles probably is the limit of generation of constant potential alternating currents of appreciable power and at fair efficiency. For smaller powers, a few kilowatts, by using shunted capacity to assist the excitation, and not attempting to produce constant potential, single-phase...", "... an effective resistance, which increases the rapidity of the decay of the oscillation, and thus limits the power, and, when approaching the critical value, also lowers the frequency. This is obvious, since the oscillating current is the dissipation of the energy stored electrostatically in the condenser, and the higher the resistance of the circuit, t...", "... d pencil scratch on a piece of porcelain. Therefore the size or bulk of condensers and reactors depends not only on C and L but also on the voltage and current which can be applied continuously, that is, it is approximately pro- Ce2 W portional to the energy stored, - and - , or since in electrical OSCILLATING CURRENTS 69 engineering energy is a quant..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 10: Continual And Cumulative Oscillations", "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 105, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... grams, Figs. 62 to 65, were taken on an artificial transmission line.* Oscillations of the type 64 and 65 are industrially used, as ''sing- ing arc, \" in wireless telegraphy, and are produced by shunting a suitable arc by a circuit containing capacity and inductance in series with each other. Fig. 62. - Semi -continuous Recurrent Oscillation of Arcing...", "... in Figs. 59 and 60, while in high-potential trans- former windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these phenomena is however still extremely incomplete. LECTUEE XI, INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 46. As inductance an...", "... ANDJMPULSES grams, Figs. 62 to 65, were taken on an artificial transmission line.* Oscillations of the type 64 and 65 are industrially used, as ''sing- ing arc, \" in wireless telegraphy, and are produced by shunting a suitable arc by a circuit containing capacity and inductance in series with each other. Fig. 62. - Semi -continuous Recurrent Oscillati...", "... of the oscilla- tion is insufficient to cause a discharge over the lightning arrester. The only effective protection seems to be a continuous dissipa- tion of the oscillating energy by a resistance closing the oscillat- ing circuit. In general, a moderate capacity would be connected in series with such damping resistance, and would be chosen so as to...", "LECTURE X. CONTINUAL AND CUMULATIVE OSCILLATIONS. 43. A transient is the phenomenon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Inductive Discharges", "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 103, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "CHAPTER IX. INDUCTIVE DISCHARGES. 64. The discharge of an inductance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high induct ...", "CHAPTER IX. INDUCTIVE DISCHARGES. 64. The discharge of an inductance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacit ...", "... uctance into a transmission line may be considered as an illustration of the phenomena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and ind...", "... omena in a complex circuit comprising sections of very different constants; that is, a combination of a circuit section of high inductance and small resistance and negligible capacity and conductance, as a generating station, with a circuit of distributed capacity and inductance, as a transmission line. The extreme case of such a discharge would occur...", "... ontinuous current 27 polyphase or rotating field 192, 197 oscillation of cables and lines Ill, 117 Static, see Electrostatic. phenomena 13, 105 Stationary waves 439, 442 Steel, effective penetration of alternating current 378 INDEX 571 PAGE Stored energy of complex circuit 515 Stranded conductor, effective resistance of current distribution 370 Stray..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-13", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 13: Distributed Capacity, Inductance, Resistance, And Leakage", "location": "lines 9741-11604", "status": "candidate", "occurrence_count": 97, "concepts": [ "Inductance", "Electrostatic Capacity" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-13/", "snippets": [ "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ...", "... ensers infi nitely near together, as diagrammatically shown in Fig. 83. iiiimiiiiumiiiT TTTTTTTTTT.TTTTTTTTTT i Fig. 83. Distributed Capacity. In this case the intensity as well as phase of the current, and consequently of the counter E.M.F. of inductance and resistance, vary from point to point ; and it is no longer possible to treat the circuit in t...", "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many ...", "CHAPTER XIII. DISTRIBUTED CAPACITY, INDUCTANCE, RESISTANCE, AND LEAKAGE. 107. As far as capacity has been considered in the foregoing chapters, the assumption has been made that the condenser or other source of negative reactance is shunted across the circuit at a definite point. In many cases, how- ever, the capacity is distributed over the whole le ..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-10", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 10: Inductance And Capacity Of Round Parallel Conductors", "location": "lines 6089-7274", "status": "candidate", "occurrence_count": 96, "concepts": [ "Inductance", "Electrostatic Capacity" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-10/", "snippets": [ "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their ...", "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductan ...", "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tio ...", "LECTURE X. INDUCTANCE AND CAPACITY OF ROUND PARALLEL CONDUCTORS. A. Inductance and capacity. 43. As inductance and capacity are the two circuit constants which represent the energy storage, and which therefore are of fundamental importance in the study of transients, their calcula- tion is discussed in the following. The inductance is the rat ..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-27", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 5: Resistance, Inductance, And Capacity In Series Condenser Charge And Discharge", "location": "lines 4072-5311", "status": "candidate", "occurrence_count": 90, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-27/", "snippets": [ "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- ...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser equals the impressed e.m.f., et =•...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial differe ...", "CHAPTER V. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES. CONDENSER CHARGE AND DISCHARGE. 29. If a continuous e.m.f . e is impressed upon a circuit contain- ing resistance, inductance, and capacity in series, the stationary condition of the circuit is zero current, i = o, and the poten- tial difference at the condenser e ...", "... t the condenser at the moment t = 0. Inversely, since in a circuit containing inductance and capac- ity two electric quantities must be given at the moment of start of the phenomenon, the current and the condenser poten- tial - representing the values of energy stored at the moment t = 0 as electromagnetic and as electrostatic energy, respec- tively -..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-10", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 10: Instability Of Circuits : The Arc", "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 89, "concepts": [ "Inductance", "Electrostatic Capacity", "Energy Storage in Fields" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... ithout voltage drop, and the voltage thus has to be taken up by the shunt resistance, ri, giving the same con- dition of stability as with an arc in a constant-current circuit, shunted by a resistance, paragraph 89. If, in addition to the capacity, C, an inductance, L, and some re- sistance, r, are shunted across the circuit. A, of a rising volt-amper...", "... istance, r, current and voltage vary simultaneously or in phase, current and voltage in the condenser branch circuit also must be in phase with each other, that is, the Fig. 87. frequency of the oscillation in Fig. 87 is that at which capacity, C, and inductance, L, balance, or is the resonance frequency. If circuit. A, in Fig. 87 is an arc circuit, a...", "... nd the arc «■ 1.D ^ iin \\ C^ -' litn \\ V ^^ fn \\ in \\ \\ ■ ^ ■m ~- ^ .0 ■^ >^ ~ rn ^ ^ m ^ 5- ^ y' ^ ^ ^ ^ ^ i: Fig. 79. . ia shunted by a condenser, the condenser nmkes the arc unstable and puts it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are ce...", "... ■ 1.D ^ iin \\ C^ -' litn \\ V ^^ fn \\ in \\ \\ ■ ^ ■m ~- ^ .0 ■^ >^ ~ rn ^ ^ m ^ 5- ^ y' ^ ^ ^ ^ ^ i: Fig. 79. . ia shunted by a condenser, the condenser nmkes the arc unstable and puts it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circui...", "... ELECTRIC CIRCUITS cumulative surges, hunting, etc. They may be considered as transients in which the attenuation constant is zero or negative. In the transient resulting from a change of circuit conditions, the energy which represents the difference of stored energy of the circuit before and after the change of circuit condition, is dissi- pated by th..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-29", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 7: Resistance, Inductance, And Capacity In Series In Alternating-Current Circuit", "location": "lines 6798-7825", "status": "candidate", "occurrence_count": 89, "concepts": [ "Inductance", "Electrostatic Capacity" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-29/", "snippets": [ "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive re ...", "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J...", "CHAPTER VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = ...", "... R VII. RESISTANCE, INDUCTANCE, AND CAPACITY IN SERIES IN ALTERNATING-CURRENT CIRCUIT. 65. Let, at time t = 0 or 0 = 0, the e.m.f., e = E cos (0 - 00), (1) be impressed upon a circuit containing in series the resistance, r, the inductance, L, and the capacity, C. The inductive reactance is x = 2 TT/L 1 and the condensive reactance is xc = > 2 7T/C J wh..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-18", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 20: Single-Phase Commutator Motors", "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 84, "concepts": [ "Inductance", "Electrostatic Capacity" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... current motor, voltage is consumed by the counter e.m.f. of rotation, which represents the power output of the motor, and by the resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- t...", "... quires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- factor, the combination of a strong armature and a we...", "... thus affords an easy means of producing the equivalent of a leading current. Therefore, the alternating-current commutator is one of the important methods of compensating for lagging: currents. Other methods are the use of electrostatic or electro- lytic condensers and of overexcited synchronous machines. Based on this principle, a number of designs o..." ] } ], "concordance_links": [ { "concept_id": "inductance", "label": "Inductance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/inductance/" }, { "concept_id": "electrostatic-capacity", "label": "Electrostatic Capacity", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/electrostatic-capacity/" }, { "concept_id": "energy-storage-fields", "label": "Energy Storage in Fields", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/energy-storage-fields/" } ] }, { "page_slug": "lightning-surges", "page_title": "Lightning And Surges", "concept_ids": [ "lightning-surges", "protective-reactance" ], "concept_labels": [ "Lightning and Surges", "Protective reactance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 648, "matching_sections": 70, "matching_sources": 12, "aliases": 9 }, "aliases": [ "arrester", "arresters", "impulse", "impulses", "lightning", "surge", "surges", "Protective reactance", "protective-reactance" ], "sources": [ { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 271, "section_count": 6, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 111, "section_count": 22, "concepts": [ "Lightning and Surges" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 104, "section_count": 10, "concepts": [ "Lightning and Surges" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 98, "section_count": 10, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 21, "section_count": 5, "concepts": [ "Lightning and Surges" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 14, "section_count": 5, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 9, "section_count": 4, "concepts": [ "Lightning and Surges" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 7, "section_count": 1, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 5, "section_count": 3, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 4, "section_count": 2, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 3, "section_count": 1, "concepts": [ "Lightning and Surges" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1, "concepts": [ "Lightning and Surges" ] } ], "priority_sections": [ { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 169, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... hing has yet been done in this direction systematically and intelligently, but all has been done by trial which at the best usually means producing more light than necessary, and throw- ing away the excess of diffused light by absorption. APPENDIX II LIGHTNING AND LIGHTNING PROTECTION Paper read before the Annual Convention of the National Electric Li...", "... een done in this direction systematically and intelligently, but all has been done by trial which at the best usually means producing more light than necessary, and throw- ing away the excess of diffused light by absorption. APPENDIX II LIGHTNING AND LIGHTNING PROTECTION Paper read before the Annual Convention of the National Electric Light Associatio..." ] }, { "section_id": "general-lectures-electrical-engineering-lecture-11", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 11: Lightning Protection", "location": "lines 4931-5294", "status": "candidate", "occurrence_count": 84, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-11/", "snippets": [ "ELEVENTH LECTURE LIGHTNING PROTECTION W\"~l HEN the first telegraph circuits were strung across the country, lightning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, how ...", "ELEVENTH LECTURE LIGHTNING PROTECTION W\"~l HEN the first telegraph circuits were strung across the country, lightning protection became necessary, and ■^ was given to these circuits at the station by connecting spark gaps between the circuit conductors and the ground. When, however, electric light and power circuits made their appearance, this protection..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-08", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 8: Traveling Waves", "location": "lines 5279-6124", "status": "candidate", "occurrence_count": 32, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-08/", "snippets": [ "... = ^6-^«'sin2(0Ta>-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, po, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and the...", "... (4) = eo^■oe-2\"' cos^ (0 T co - 7), 6o^o [1 + cos 2 ( =F CO -7)], (5) and the average flow of power is po = avg p, (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, jpo, and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : pi =^%-2\"*cos2((/)Tco-7). (7) Such a flow of power alo..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-08", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 8: Traveling Waves", "location": "lines 4745-5520", "status": "candidate", "occurrence_count": 32, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-08/", "snippets": [ "... = ^|V2«=Fco-7), (2) and the average power flow is Po = avg p, (3) = 0. Hence, in a stationary oscillation, or standing wave of a uni- form circuit, the average flow of power, p0, is zero, and no power flows along the circuit, but there is a surge of power, of double frequency. That is, power flows first one way, during one-quarter cycle, and...", "... In this case the flow of power is (4) P = = eQiQe-2ut cos2 co - 7), and the average flow of power is p0 = avg p, (5) (6) Such a wave thus consists of a combination of a steady flow of power along the circuit, p0) and a pulsation or surge, pi, of the same nature as that of the standing wave (2) : Such a flow of power along the circuit is called a trave..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-45", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 5: Distributed Series Capacity", "location": "lines 23586-23947", "status": "candidate", "occurrence_count": 24, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-45/", "snippets": [ "... elements of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit constitutes a circuit with distributed series capacity. An illustration of such a circuit' is afforded by the so-called \" multi-gap lightning arrester,\" as shown diagrammatically in Fig. 90, which consists of a large number of metal...", "... of the circuit are short enough so as to be represented, approximately, as conductor differentials, the circuit constitutes a circuit with distributed series capacity. An illustration of such a circuit' is afforded by the so-called \" multi-gap lightning arrester,\" as shown diagrammatically in Fig. 90, which consists of a large number of metal cylinder..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 10: Continual And Cumulative Oscillations", "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 16, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "... ulative oscillation thus involves an energy and frequency transformation, from the low-frequency or con- tinuous-current energy of the power supply of the system to the high-frequency energy of the oscillation. 119 120 ELECTRICAL DISCHARGES, WAVES AND IMPULSES This energy transformation may be brought about by the transient of energy readjustment, res...", "... oscillation, that is, there must be such a phase displacement or lag within the oscil- lation, which gives a negative energy cycle, or reversed hysteresis loop. Thus, essential for such a continual oscillation is the 124 ELECTRICAL DISCHARGES, WAVES AND IMPULSES existence of a hysteresis loop, formed by the lag of the effect be- hind the cause. Such a..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-42", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 2: Long-Distance Transmission Line", "location": "lines 19339-21720", "status": "candidate", "occurrence_count": 15, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-42/", "snippets": [ "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same vel ...", "CHAPTER II. LONG-DISTANCE TRANSMISSION LINE. 3. If an electric impulse is sent into a conductor, as a trans- mission line, this impulse travels along the line at the velocity of light (approximately), or 188,000 miles per second. If the line is open at the other end, the impulse there is reflected and returns at the same velocity. If now at the moment whe..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 7: Line Oscillations", "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 12, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic - and dielectric - , and a transient component, by which the total stored energy decreases. Considering only the periodic component, the maximum value of magnetic energy m...", "... e of dielectric '^'^e^gy- Li„^ Ce, 0 \"^^0 (1) where Iq = maximum value of transient current, 60 = maximum value of transient voltage. This gives the relation between Bq and Iq, ^^ = Jl ,^ = 1, (2) where Zq is called the natural impedance or surge impedance, 2/0 the natural or surge admittance of the circuit. As the maximum of current must coincide wit..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-07", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 7: Line Oscillations", "location": "lines 3956-4744", "status": "candidate", "occurrence_count": 12, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy 7\" /j'2 f^ r/>2 surges between magnetic -^- and dielectric - , and a transient £i A component, by which the total stored energy decreases. Considering only the periodic component, the maximum mag...", "... must equal the maximum dielectric energy, Lio2 _ Ceo2 \"2\" ~2~' where i0 = maximum transient current, e0 = maximum transient voltage. This gives the relation between eQ and io, e0 V/L_ 1 i-0 = \\C-ZQ-yQ' where ZQ is called the natural impedance or surge impedance, y0 the natural or surge admittance of the circuit. As the maximum of current must coincide..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 11, "concepts": [ "Lightning and Surges" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "... the change occurs at the moment when the two currents ii and 12 have the greatest difference, as shown in Fig. 15C, that is, at a point one-quarter period or 90 degrees distant from the intersec- tion of ii and 12. 32 ELECTRIC DISCHARGES, WAVES AND IMPULSES. If the current ii is zero, we get the starting of the alternating current in an inductive circ...", "... sient currents also is zero. Since the three transient curves ii^, 12^, 4° are pro- portional to each other fas exponential curves of the same dura- tion T = -\\ and the sum of their initial values is zero, it follows 84 ELECTRIC DISCHARGES, WAVES AND IMPULSES. that the sum of their instantaneous values must be zero at any moment, and therefore the sum..." ] } ], "concordance_links": [ { "concept_id": "lightning-surges", "label": "Lightning and Surges", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/lightning-surges/" }, { "concept_id": "protective-reactance", "label": "Protective reactance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/protective-reactance/" } ] }, { "page_slug": "oscillation-damping", "page_title": "Oscillation And Damping", "concept_ids": [ "oscillation", "damping", "resonance" ], "concept_labels": [ "Oscillation", "Damping", "Resonance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 1618, "matching_sections": 127, "matching_sources": 13, "aliases": 10 }, "aliases": [ "oscillating", "oscillation", "oscillations", "oscillatory", "damped", "damping", "decrement", "logarithmic decrement", "resonance", "resonant" ], "sources": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 578, "section_count": 55, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 233, "section_count": 14, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 227, "section_count": 15, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 152, "section_count": 12, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 112, "section_count": 14, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 89, "section_count": 11, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 81, "section_count": 10, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 38, "section_count": 7, "concepts": [ "Oscillation", "Damping", "Resonance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 32, "section_count": 19, "concepts": [ "Oscillation", "Resonance" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 27, "section_count": 4, "concepts": [ "Oscillation", "Damping" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 22, "section_count": 5, "concepts": [ "Oscillation", "Resonance" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 16, "section_count": 6, "concepts": [ "Oscillation", "Resonance" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 11, "section_count": 6, "concepts": [ "Oscillation", "Damping", "Resonance" ] } ], "priority_sections": [ { "section_id": "theory-calculation-electric-circuits-chapter-18", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 18: Oscillating Currents", "location": "lines 31657-33200", "status": "candidate", "occurrence_count": 87, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-18/", "snippets": [ "CHAPTER XVIII OSCILLATING CURRENTS Introductioii 181. An electric current varying periodically between constant maximum and minimum values - that is, in equal time intervals repeating the same values - is called an alternating current if the arithmetic mean value equals zero; a ...", "... nts in which the amplitude of each following wave bears to that of the pre- ceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is, in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations - ^for instance of the pendulum - ^i...", "... even in comparison with the time of one alternating half-wave. Characteristic con- stants of the oscillating current are the period, T, or frequency, / = 7p, the first amplitude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscillating current will thus be represented by the product of a periodi...", "... at of the oscillating wave, E = ec\"*** cos { - 0), is tan jS = - {tan (0 - ^) + «}• Hence, it is increased over that of the alternating sine wave by the constant, a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angu- l...", "... oscillating discharge is Z = 0, that is, 1 o / ^ ^ 1^ T \\r^C 2aL 2L If r = 0, that is, in a circuit without resistance, we have a = 0, / = /=^j that is, the currents are alternating with no decre- 2 \"n\"^ LC ment, and the frequency is that of resonance. If ^ty-^-t < 0, that is, r > 2-1/7^, a and / become imaginary; that is, the discharge ceases to be o...", "... lator, constant current, 251 Reluctivity, 43 curve, 46 Remanent magnetism, 43 Resistance, 1 effective, of leaky conductor, 333 of line in series circuits, 306 negative effective, of arc, 191 Resistivity, magnitude of different conductors, 42 Resonance of transformer with har- monics of magnetic bridged gap, 151 Resonant wave screens, 157 Resonating ci..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-10", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 10: Instability Of Circuits : The Arc", "location": "lines 17632-21381", "status": "candidate", "occurrence_count": 84, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-10/", "snippets": [ "... eoretical work has been done, more or less systematically, on transients, and a great mass of information is thus available in the literature. These transients are more ex- tensively treated in \"Theory and Calculation of Transient Elec- tric Phenomena and Oscillations,\" and in \" Electric Discharges, Waves and Impulses, '' and therefore will be omitted...", "... - ^ y' ^ ^ ^ ^ ^ i: Fig. 79. . ia shunted by a condenser, the condenser nmkes the arc unstable and puts it out; the available supply voltage, however, starts it again, and so periodically the arc starts and extinguishes, aa an \"oscillating arc.\" 84. There are certain circuit elements which tend to produce instability, such as arcs, pyroelectric conduc...", "... umulative oscillation of some arc in the 200 ELECTRIC CIRCUITS system, and building up to high stationary waves, have frequently been observed. The \"arcing ground\" as recurrent single impulses, the \"arcing ground oscillation'' as more or less rapidly damped recurrent oscillations in transmission lines - of frequencies from a few hun- dred to a few tho...", "... ry simultaneously or in phase, current and voltage in the condenser branch circuit also must be in phase with each other, that is, the Fig. 87. frequency of the oscillation in Fig. 87 is that at which capacity, C, and inductance, L, balance, or is the resonance frequency. If circuit. A, in Fig. 87 is an arc circuit, and the resistance, r, in the shunt...", "... Ci = Co - e, thus is in phase with the alternating current, ii, that is, capacity, C, and inductance, L, neutralize. Thus, the only pulsation of current and voltage, which could occur in a circuit, A, shimted by capacity and inductance, is that of the resonance frequency of capacity and inductance. Suppose the circuit. A, is a dead resistance. The vol..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 6: Oscillating Currents,", "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 76, "concepts": [ "Oscillation", "Damping" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "CHAPTER VI. OSCILLATING CURRENTS, 44. The charge and discharge of a condenser through an inductive circuit produces periodic currents of a frequency depending upon the circuit constants. The range of frequencies which can be produced by electro- dynamic machinery is rather li ...", "... ything for high frequency, a limit is reached in the frequency available by electrodynamic generation. It becomes of importance, therefore, to investigate whether by the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current approaches the effect of an alternating current only if the damping is small, th...", "... trodynamic generation. It becomes of importance, therefore, to investigate whether by the use of the condenser discharge the range of frequencies can be extended. Since the oscillating current approaches the effect of an alternating current only if the damping is small, that is, the resistance low, the condenser discharge can be used as high frequency...", "... ndred thousands of cycles. At frequencies between 500 and 2000 cycles, the use of iron in the reactive coil has to be restricted to an inner core, and at frequencies above this iron cannot be used, since hysteresis and eddy currents would cause excessive damping of the oscil- lation. The reactive coil then becomes larger in size. 47. Assuming 96 per c..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-10", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 10: Continual And Cumulative Oscillations", "location": "lines 6804-8485", "status": "candidate", "occurrence_count": 75, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-10/", "snippets": [ "LECTURE X. CONTINUAL AND CUMULATIVE OSCILLATIONS. 43. A transient is the phenomenon by which the stored energy readjusts itself to a change of circuit conditions. In an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, ...", "... an oscilla- tory transient, the difference of stored energy of the previous and the after condition of the circuit, at a circuit change, oscillates between magnetic and dielectric energy. As there always must be some energy dissipation in the circuit, the oscillating energy of the transient must steadily decline, that is, the transient must die out, a...", "... discharge over the lightning arrester. The only effective protection seems to be a continuous dissipa- tion of the oscillating energy by a resistance closing the oscillat- ing circuit. In general, a moderate capacity would be connected in series with such damping resistance, and would be chosen so as to allow the high frequency to pass practically uno...", "... imentally produced in Hues and high-potential transformer windings. The continual oscillations in transmission lines usually seem to be recurrent oscillations, as in Figs. 59 and 60, while in high-potential trans- former windings, due to their much lesser damping, continuous oscillations seem to be more common, as in Fig. 46. Our knowl- edge of these...", "... l arcing ground oscillation in Figs. 44 and 45, page 98. In Fig. 44, the beginning of the disturbance, apparently a harmonic of the generator wave builds up by the energy supply through a beginning arc, and then builds down again, by being slightly out of resonance with a multiple of the natural frequency of the circuit. In Fig. 45, the arc has comple...", "... gy of the oscillation which gives its destructiveness thus is not limited to the small amount of the stored magnetic and dielectric energy of the system, but is supplied continuously from the engine or turbine power. 3. The continual oscillation is not a resonance phenomenon which depends on the frequency of the exciting disturbance just coinciding wi..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-54", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 5: Free Oscillations", "location": "lines 31451-32708", "status": "candidate", "occurrence_count": 74, "concepts": [ "Oscillation", "Damping" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-54/", "snippets": [ "CHAPTER V. FREE OSCILLATIONS. 28. The general equations of the electric circuit, (50) and (51), contain eight terms: four waves: two main waves and their reflected waves, and each wave consists of a sine term and a cosine term. The equations contain five constants, namely: the fre ...", "... rminal condi- tions of the problem. Upon the values of these integration constants C and C' largely depends the difference between the phenomena occurring in electric circuits, as those due to direct currents or pulsating currents, alternating currents, oscillating currents, inductive dis- charges, etc., and the study of the terminal conditions thus i...", "... t (237) = 2 Z0 v LC in a half-wave oscillation, J and MV £~w< = e ~ .-^T. (246) ^0 is the wave length, and thus - the frequency, of the funda- mental wave, with the velocity of propagation as distance unit. It is interesting to note that the time decrement of the free oscillation, e~ut, is the same for all frequencies and wave lengths, FREE OSCILLATIO..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 32: Quarter-Phase System", "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 71, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... epresented by the points of half axis OB upwards ; the negative imaginary numbers are represented by the points of half axis OB' downwards ; the complex imaginary numbers are represented by the points outside of the coordinate axes. APPENDIX II. OSCILLATING CURRENTS. INTRODUCTION. 308. An electric current varying periodically between constant maximum...", "... rents in which the amplitude of each following wave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, - for instance of the pendu- lum,- i...", "... even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency N = 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of V ^ ! I...", "... at of the oscillating wave E = *?e~a* cos (<£ - to) is tan /3 = - {tan (<£ - w) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular...", "... on of an oscillating discharge is Z = 0, that is, ~ ~ / .1 r 2aL 2Z~ ~1' If r = 0, that is, in a circuit without resistance, we have a = 0, Af = 1 / 2 TT VZT ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 H r2 C - 1 < 0, that is, r > 2 V2T/T, a and N become imaginary ; that is, the discharge c..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 30: Quartbr-Fhase System", "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 68, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... represented by the points of half axis OB upwards ; the negative imaginary numbers are represented by the points of half axis OB downwards ; the complex imaginary numbers are represented by the points outside of the coordinate axes. APPENDIX II. OSCILLATING CURRENTS. INTBODUCnON. 279. An electric current varying periodically between constant maximum a...", "... rents in which the amplitude of each following wave bears to that of the preceding wave a constant ratio. Such currents consist of a series of waves of constant length, decreasing in amplitude, that is in strength, in constant proportion. They are called oscillating currents in analogy with mechanical oscillations, - for instance of the pendu- lum, -...", "... even in comparison with the time of one alternating half- wave. Characteristic constants of the oscillating current are the period T or frequency .■V= 1/7\", the first ampli- tude and the ratio of any two successive amplitudes, the latter being called the decrement of the wave. The oscil- lating current will thus be represented by the product of s^ s:...", "... of the oscillating wave E ^ re\"** cos (<^ - w) is tan ^3 = - {tan (<^ - u>) + a} . Hence, it is increased over that of the alternating sine wave by the constant a. The ratio of the amplitudes of two consequent periods is E, A is called the numerical decrement of the oscillating wave, a the exponential decrement of the oscillating wave, a the angular d...", "... condition of an oscillating discharge is ^ = 0, that is, ' 2aL 2zVr«C a = c If r = 0, that is, in a circuit without resistance, we have a ^ Oj jV=1/2v VZ C ; that is, the currents are alter- nating with no decrement, and the frequency is that of resonance. If 4 Z/ r« C - 1 < 0, that is, r > 2 VZT^, a and N become imaginary ; that is, the discharge cea..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-43", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 3: The Natural Period Of The Transmission Line", "location": "lines 21721-23178", "status": "candidate", "occurrence_count": 67, "concepts": [ "Oscillation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-43/", "snippets": [ "... (lightning), or oscillates because of a sudden change of load, as a break of circuit, or in general a change of circuit conditions, as closing the circuit, etc. The discharge of a condenser through a circuit containing self- inductance and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the ca...", "... ce and resistance is oscillating (provided the resistance does not exceed a certain critical value depending upon the capacity and the self-inductance) ; that is, the discharge current alternates with constantly decreasing intensity. The frequency of this oscillating discharge depends upon the capacity C and the self -inductance L of the circuit, and..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Inductive Discharges", "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 67, "concepts": [ "Oscillation", "Damping", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... (401) is the voltage E2 by substi- cos If + At the grounded end of the line X = stituting (403) into (401), is 7 ~ - U(jt, V (404) the current 72, by sub- (405) An inductance discharging into the transmission line thus gives an oscillatory distribution of voltage and current along the line. 68. As example may be considered the three-phase high- potent...", "... 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamenta...", "... lectric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, 394 Commutation and rectification 222 as transient phenomenon 40 Commutator, rectifying 229 Complex circuit, of waves 498 power and energy 513 resultant time decrement 504 traveling wave 468 Compound wave at transition point 532 Condenser, also see Capacity. charge,...", "... g wave 468 Compound wave at transition point 532 Condenser, also see Capacity. charge, inductive 18 noninductive 18 circuit of negligible inductance 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 efficiency, decrement and output 72 frequency 62 general equations 60 size and rating 69 starting on alternating voltage...", "... ves 449, 452 grounded 303 half-wave oscillation 333 inductive discharges 542 infinitely long 305 natural period 280, 320 open 299 opening under load 112, 118 phase difference 296 quarter-wave 306, 313, 315 oscillation 322 radiation 283 resonance frequency 279 with higher harmonics 280 short-circuit oscillation 113, 118 starting 111,117 transient terms..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-07", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 7: Line Oscillations", "location": "lines 4370-5278", "status": "candidate", "occurrence_count": 52, "concepts": [ "Oscillation", "Resonance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-07/", "snippets": [ "LECTURE VII. LINE OSCILLATIONS. 28. In a circuit containing inductance and capacity, the tran- sient consists of a periodic component, by which the stored energy surges between magnetic - and dielectric - , and a transient component, by which the total stored energy decreases. Con ...", "... voltage, and inversely, if the one is represented by the cosine function, the other is the sine function; hence the periodic com- ponents of the transient are ii = Iq cos (0 - 7) ei = eo sm (0 - 7) ) where 0 = 2 Tft, (4) and is the frequency of oscillation. The dissipative or \" transient \" component is M = €-\"', (6) 72 LINE OSCILLATIONS. T6 where u 2...", "... ent, etc., it follows that at very high frequencies the line responds to any frequency, has no definite frequency of oscillation, but oscillations can exist of any frequency, provided this frequency is sufficiently high. Thus in long trans- mission lines, resonance phenomena can occur only with moderate frequencies, but not with frequencies of hundred..." ] } ], "concordance_links": [ { "concept_id": "oscillation", "label": "Oscillation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/oscillation/" }, { "concept_id": "damping", "label": "Damping", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/damping/" }, { "concept_id": "resonance", "label": "Resonance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/resonance/" } ] }, { "page_slug": "power-factor", "page_title": "Power Factor", "concept_ids": [ "power-factor" ], "concept_labels": [ "Power Factor" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 671, "matching_sections": 101, "matching_sources": 11, "aliases": 4 }, "aliases": [ "power factor", "power-factor", "wattless component", "wattless current" ], "sources": [ { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 206, "section_count": 14, "concepts": [ "Power Factor" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 133, "section_count": 18, "concepts": [ "Power Factor" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 89, "section_count": 14, "concepts": [ "Power Factor" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 83, "section_count": 24, "concepts": [ "Power Factor" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 54, "section_count": 5, "concepts": [ "Power Factor" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 39, "section_count": 12, "concepts": [ "Power Factor" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 35, "section_count": 5, "concepts": [ "Power Factor" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 18, "section_count": 2, "concepts": [ "Power Factor" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 11, "section_count": 4, "concepts": [ "Power Factor" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 2, "section_count": 2, "concepts": [ "Power Factor" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 1, "section_count": 1, "concepts": [ "Power Factor" ] } ], "priority_sections": [ { "section_id": "theory-calculation-electric-apparatus-chapter-18", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 20: Single-Phase Commutator Motors", "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 64, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... resistance, which represents the power loss. In addition thereto, in the alternating-cur rent motor voltage is consumed by the inductance, which is wattless or reactive and therefore causes a lag of current behind the vol- tage, that is, a lowering of the power-factor. While in the direct- current motor good design requires the combination of a strong...", "... While in the direct- current motor good design requires the combination of a strong field and a relatively weak armature, so as to reduce the armature reaction on the field to a minimum, in the design of the alter- iiatiiig-current motor considerations of power-factor predominate; that is, to secure low self-inductance and therewith a high power- fact..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-03", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 50, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... ating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-factor in an induction motor, the magnetizing current, that i«, the current which produces...", "... erload capacity has to be met, etc. In such motors of necessity the exciting current or current at no-load - which is practically all magnetizing current - is a very large part of full-load current, and while fair efficiencies may nevertheless be secured, power-factor and apparent efficiency necessarily are very low. As illustration is shown in Fig. 2..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-14", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 14: Constant-Potential Constant-Current Trans Formation", "location": "lines 24023-27995", "status": "candidate", "occurrence_count": 42, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-14/", "snippets": [ "... n series with this circuit. The impedance of this circuit then is Z = r + jxof and, absolute, and thus the current, / = ^* = -^ (1) ^ r + jxo and the absolute value is eo Co the phase angle of the supply circuit is given by (2) and the power factor. tan ^0 = - (3) T cos ^0 = -• (4) z ^ ^ If in this case, r is small compared with Xq, it is ,-^£o _-l (5...", "... l theorem. V • • • \\xj hence, : (6) 6o I = - Xo 2xo2^8xo* -r . . . that is, for small values of r, the current, z, is approximately constant, and is 6o I = - Xo CONSTANT-CURRENT TRANSFORMATION 247 For small values of r, the power-factor cosfl - - is very low, however. Allowing a variation of current of 10 per cent, from short- circuit or no-load, r =..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 16: Induction Motor", "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 28, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... e the motor is in operation. 256 ALTERNATING-CURRENT PHENOMENA. Since, necessarily, ri<*, ''<•< and since the starting current is, approximately, 7 =f , we have, Ta < would be the theoretical torque developed at 100 per cent efficiency and power factor, by E.M.F., E0, and current, /, at synchronous speed. Thus, T0 ~IY (29) and hence, substituted in (22), / = and E = -° U~a/ (cos /?Z + y sin /?/) + Cs +aZ (cos /M - j sin /?Z) (30) 11. As an example, consider the problem of delivering, in a three-phase system, 200 amperes per phase, at 90 per cent power factor lag at 60,000 volts per phase (or between line and neutral) and 60 cycles, at the end of a transmi...", "... 53 - 0.9 j) 10~3 Zi p = ^= (0.208 + 0.047 /) 10 + 3. 293 (31) Counting the distance I from the receiving end, and choosing the receiving voltage as zero vector, we have E = E0 = e0 = 60,000 volts, and the current of 200 amperes at 90 per cent power factor, 87 j, and substituting these values in equations (25) gives / = (226 + 14.4 j) e+al (cos pl-j si..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-108", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Apparatus Section 2: Induction Machines: Polyphase Induction Motor", "location": "lines 19166-20427", "status": "candidate", "occurrence_count": 15, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-108/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-108/", "snippets": [ "... im- pressed e.m.f. EQ) enters in the equation of current, magnetism, etc., as a simple factor, in the equations of torque, power input and output, and volt-ampere input as square, and cancels in the equation of efficiency, power-factor, etc., it follows that the current, magnetic flux, etc., of an induction motor are propor- tional to the impressed e....", "... induction motor are propor- tional to the impressed e.m.f., the torque, power output, power input, and volt-ampere input are proportional to the square of the impressed e.m.f., and the torque- and power efficiencies and the power-factor are independent of the impressed voltage. In reality, however, a slight decrease of efficiency and power- factor occ..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 11: Phase Control", "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 15, "concepts": [ "Power Factor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ltage, e, is greatest if the current, /, is in phase with the voltage, e - less if the current is not in phase. Inductive reactance in series with the receiving circuit, e, at constant impressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise...", "... creasing drop of voltage with increasing load, caused by the resistance, r, that is, to maintain constant voltage, or even a voltage, e, which rises with the load on the receiving circuit, at constant voltage, Co, at the generator side of the line. Or the wattless component of the current can be varied so as to maintain unity power-factor at the gener..." ] } ], "concordance_links": [ { "concept_id": "power-factor", "label": "Power Factor", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/power-factor/" } ] }, { "page_slug": "power-limiting-reactors", "page_title": "Power-Limiting Reactors", "concept_ids": [ "power-limiting-reactor", "protective-reactance" ], "concept_labels": [ "Power-Limiting Reactor", "Protective reactance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as a practical power-system stability and protection page. The theory matters because Steinmetz is dealing with station behavior, synchronism, short-circuit current, and recovery.", "totals": { "occurrences": 70, "matching_sections": 15, "matching_sources": 7, "aliases": 8 }, "aliases": [ "Power limiting reactor", "current limiting reactor", "power limiting reactor", "power-limiting reactor", "power-limiting-reactor", "reactor", "Protective reactance", "protective-reactance" ], "sources": [ { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 21, "section_count": 4, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 19, "section_count": 3, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 16, "section_count": 4, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 10, "section_count": 1, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 2, "section_count": 1, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 1, "section_count": 1, "concepts": [ "Power-Limiting Reactor" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 1, "section_count": 1, "concepts": [ "Power-Limiting Reactor" ] } ], "priority_sections": [ { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-28", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 6: Oscillating Currents,", "location": "lines 5312-6797", "status": "candidate", "occurrence_count": 12, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-28/", "snippets": [ "... t means that reactors, condensers, and resistors are rated in kilowatts or kilo volt-amperes, just as other electrical appa- ratus, and this rating characterizes their size within the limits of design, while a statement like \"a condenser of 10 mf. \" or \"a reactor of 100 mh.\" no more characterizes the size than a Statement like \"an alternator of 100 am...", "... ce equals the condensive reactance. The same current is in both at the same terminal voltage. That means that the volt-amperes consumed by the inductance equal the volt-amperes consumed by the capacity. The kilovolt-amperes of a condenser as well as of a reactor are proportional to the frequency. With increasing frequency, at constant voltage impresse..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-106", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Apparatus Section 9: Alternating-current Transformer: Reactors", "location": "lines 18813-18948", "status": "candidate", "occurrence_count": 10, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-106/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-106/", "snippets": [ "IX. Reactors (Reactive Coils, Reactances) 129. The reactor consists of one electric circuit interlinked with a magnetic circuit, and its purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading vo ...", "... purpose is, not to transform power, but to produce wattless or reactive power, that is, lagging current, or what amounts to the same, leading voltage. While therefore theoretically we cannot speak of an ''efficiency\" of a reactor, since there is no power output, nevertheless in the in- dustry the expression \" efficiency of a reactive coil\" is gener- a..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-16", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 16: Load Balance Of Polyphase Systems", "location": "lines 29302-30428", "status": "candidate", "occurrence_count": 10, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-16/", "snippets": [ "... sformation. Thus mechanical momentum acts as energy-storing device in the use as phase bal- ancer, of the induction or the synchronous machine. Electrically, energy is stored by inductance and by capacity. The question then arises, whether by the use of a reactor, or a condenser, con- nected to a suitable phase of the system, an unequally loaded polyp...", "... single-phase alternator reduces the pulsation of the field flux, but also increases the momentary short-circuit stresses. Thus, it is of interest to study the question of balancing unbal- anced polyphase circuits by stationary energy-storing devices, as reactor or condenser. 164. Let a voltage, e = E cos (1) be impressed upon a non-inductive load,..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 9, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ism with each other. If then the load distribution between the alternators differs from the distribution of their driving power, electric power is transferred over the impedance z, current flows and a phase displacement 2co occurs between the two sides of the reactor z. In this case, the phase angle w is constant, and not periodically fluctuating as i...", "... d to keep in synchronism with each other. Coming now to the consideration of the relation between Fisk Street B and Quarry Street Station, during the trouble of September 18th, 1919: (6.) Four 12,000KW alternators in Fisk Street B, out of synch- ronism over a power limiting reactor with three 14,000 KW alter- nators in Quarry Street, the latter in syn..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Report Record 4: Record of Four Troubles", "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 6, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... rs in Fisk B and in Northwest Station did not pull into step with each other, but remained out of synchronism; the voltage at the busbars of these two stations remained practically zero, and an excessive current fed into Fisk B from Quarry Street, heating the power limiting reactor B. f ) After 7 minutes, the tie line between Fisk Street B and Quarry...", "... voltage at the busbars of these two stations remained practically zero, and an excessive current fed into Fisk B from Quarry Street, heating the power limiting reactor B. f ) After 7 minutes, the tie line between Fisk Street B and Quarry Street, that is, the power limiting reactor B, was opened, and Quarry Street and Fisk A, came back to normal. About..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-15", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 15: Constant-Voltage Series Operation", "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 6, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... rcuit. n = number of consuming devices (lamps) in series. p = fraction of burned-out lamps. g a= conductance of lamp. (15) 302 ELECTRIC CIRCUITS and let 6 1 = shunted susceptance with the lamp in circuit, that is, exciting susceptance of reactor or auto- transformer, and y = \\/g^ + bi^ = admittance of complete consuming device. 62 = shunted susceptanc...", "... e of reactor or auto- transformer, and y = \\/g^ + bi^ = admittance of complete consuming device. 62 = shunted susceptance with the lamp burned out and let c = - = exciting current as fraction of load ^ current: c < 1. a = ^- = saturation factor of reactor or - auto transformer: o > 1. (16) (17) it is, then: voltage of lamp and reactor: voltage of reac..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-section-02-discussion-of-recommendations", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Report Section 3: Discussion of Recommendations", "location": "PDF pages 12-16, lines 721-1138", "status": "pdf-text-extracted-candidate", "occurrence_count": 5, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-02-discussion-of-recommendations/", "snippets": [ "... he Commonwealth Edison Company of Chicago, is by no means too high. Necessarily, however, these power limiting reactors also limit the synchronizing power be- tween the station sections. Thus if in a station section as Fisk Street A, which is connected by one power limiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown o...", "... imiting reactor to the rest of the system, full load of 60,000 KW is suddenly thrown off as by a short circuit at the busbars dropping out the synchronous machines in the substations while full steam supply is still on, the synchronizing power coming over the power limiting reactor is insufficient to hold the station in step, and the station breaks sy..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-08", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 8: Shaping Of Waves By Magnetic Saturation", "location": "lines 12962-16963", "status": "candidate", "occurrence_count": 3, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-08/", "snippets": [ "... tion, for / - 20, may possibly be due to an inaccuracy in the hysteresis cycle of Fig. 55, a too great steepness near the zero value, rather than being actual.) It is interesting to realize, that when measuring the reactance of a closed magnetic circuit reactor by voltmeter and ammeter readings, it is not permissible to vary the voltage by series resi...", "... t one-thousandth gap length, and with an air-gap of 1 per cent, length, only a moderate peakedness remains at the highest saturation, while at lower saturation the voltage wave is practically a sine. 73. Even a small air-gap in the magnetic circuit of a reactor greatly reduces the wave-shape distortion, that is, makes the voltage wave more sinusoidal,..." ] }, { "section_id": "engineering-mathematics-chapter-03", "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_label": "Chapter 3: Trigonometric Series", "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 2, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... t. io6. Example lo. An alternating-current generator, of generated e.m.f. e = 2500 volts, internal resistance ro = 0.25 ohms, and synchronous reactance a:o = 10 ohms, is loaded by a circuit comprising a resistor of constant resistance r = 20 ohms, and a reactor of reactance x in series with the resistor r. What value of reactance x gives maximum outpu...", "... 000i-6 = 0.78125Xl0i6-8; hence, e = 1373 volts for maximum efficiency at full load. and e = 938 volts for maximum efficiency at half load. 117. Example 18. (a) Constant voltage 6 = 1000 is im- pressed upon a condenser of capacity C = 10 mf., through a reactor of inductance L = 100 mh., and a resistor of resist- ance r = 40 ohms. What is t.hp maximum v..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-31", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Divided Circuit", "location": "lines 9228-10474", "status": "candidate", "occurrence_count": 2, "concepts": [ "Power-Limiting Reactor" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-31/", "snippets": [ "... directly com- parable with the phenomena on a 60-cycle circuit. A better conception of the size or magnitude of inductance and capacity is secured. Since inductance and capacity are mostly observed and of importance in alternating-current cir- cuits, a reactor having an inductive reactance of x ohms and i amperes conveys to the engineer a more definit...", "... inductive reactance of x ohms and i amperes conveys to the engineer a more definite meaning as regards size: it has a volt-ampere capacity of tfx, that is, the approximate size of a transformer of half this capacity, or of a ^2x - -watt transformer. A reactor having an inductance of L henrys and i amperes, however, conveys very little meaning to DIVID..." ] } ], "concordance_links": [ { "concept_id": "power-limiting-reactor", "label": "Power-Limiting Reactor", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/power-limiting-reactor/" }, { "concept_id": "protective-reactance", "label": "Protective reactance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/protective-reactance/" } ] }, { "page_slug": "radiation", "page_title": "Radiation", "concept_ids": [ "radiation", "light", "electrical-radiation" ], "concept_labels": [ "Radiation", "Light", "Electrical Radiation" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as the bridge from physics to illumination engineering: Steinmetz treats radiation as energy in transit before later lectures convert that physical idea into measurement, lamps, flux, distribution, and visual response.", "totals": { "occurrences": 3132, "matching_sections": 93, "matching_sources": 13, "aliases": 10 }, "aliases": [ "Radiation", "radiant energy", "radiation", "radiations", "Light", "light", "luminous", "visible light", "electric radiation", "electrical radiation" ], "sources": [ { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 2387, "section_count": 28, "concepts": [ "Radiation", "Light", "Electrical Radiation" ] }, { "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "occurrence_count": 407, "section_count": 14, "concepts": [ "Radiation", "Light" ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 159, "section_count": 6, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 63, "section_count": 19, "concepts": [ "Radiation", "Light", "Electrical Radiation" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 24, "section_count": 6, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 18, "section_count": 9, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 18, "section_count": 12, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 16, "section_count": 8, "concepts": [ "Radiation", "Light" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 12, "section_count": 6, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 8, "section_count": 5, "concepts": [ "Light" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 7, "section_count": 3, "concepts": [ "Radiation", "Light" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 7, "section_count": 3, "concepts": [ "Radiation", "Light" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 6, "section_count": 4, "concepts": [ "Light" ] } ], "priority_sections": [ { "section_id": "general-lectures-electrical-engineering-lecture-17", "source_id": "general-lectures-electrical-engineering", "source_title": "General Lectures on Electrical Engineering", "year": 1908, "section_label": "Lecture 17: Arc Lighting", "location": "lines 9920-12795", "status": "candidate", "occurrence_count": 359, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/general-lectures-electrical-engineering/lecture-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/general-lectures-electrical-engineering/lecture-17/", "snippets": [ "... to do any more strictly with a problem of physics, but that we are on .the borderland between applied physics, that is engineering, and physiology. Light is not a physical quantity, but it is the physiological effeot exerted upon the human eye by certain radiations. There are different forms of energy, all convertible into each other, as magnetic ener...", "... locity of about 188,000 miles per second; and it is a transverse vibration, differing from the vibratory energy of sound in this respect, that the sound waves are longitudinal, that is, the vibration is in the direction of the beam, while the vibration of radiation is transverse. Radiating energy can be derived from other forms of energy, for instance...", "... e circuit. With the exception of a few of the larger cities, all the street lighting by arc lamps in this country is done by constant current systems, either direct current or alternating current. For direct current constant current supply, separate arc light machines have been built, and are still largely used. In these machines, inherent regulation...", "... into the arc circuit supplied from the constant potential source, and by separating or coming together, vary in reactance with the load, and thereby maintain constant current. While the alternating current arc lamp is less efficient, that is, gives less light for the same power, than the direct cur- rent arc lamp, the disadvantages of the use of numer..." ] }, { "section_id": "radiation-light-and-illumination-lecture-05", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 5: Temperature Radiation", "location": "lines 3946-5076", "status": "candidate", "occurrence_count": 292, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-05/", "snippets": [ "LECTURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is rai ...", "LECTURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is raised by heating a body by the transformation of chemic ...", "... TURE V. TEMPERATURE RADIATION. 34. The most common method of producing radiation is by impressing heat energy upon a body and thereby raising its tem- perature. Up to a short time ago this was the only method avail- able for the production of artificial light. The temperature is raised by heating a body by the transformation of chemical energy, that i...", "... the radiator and thus increasing radiation power, its temperature first rises proportional to the power input and then slower and ultimately approaches proportionality with the fourth root of the power output: 4/p- T =V - • ll V kA 72 RADIATION, LIGHT, AND ILLUMINATION. In Fig. 27 is shown the radiation curve, with the temperatures T as ordinates and..." ] }, { "section_id": "radiation-light-and-illumination-lecture-03", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 3: Physiological Effects Of Radiation", "location": "lines 2366-3638", "status": "candidate", "occurrence_count": 276, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-03/", "snippets": [ "LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with ...", "LECTURE III. PHYSIOLOGICAL EFFECTS OF RADIATION. Visibility. 20. The most important physiological effect is the visibility of the narrow range of radiation, of less than one octave, between wave length 76 X 10~6 and 39 X 1Q-6. The range of intensity of illumination, over which the eye can see with practically equal comfort, is enormous: the average intens...", "... fferences in intensity without measuring them. The photo- graphic camera realizes it. An exposure taken in T^ second with TV opening of the diaphragm in full sunlight usually gives a better photograph than an exposure of 10 minutes at full opening, in the light of the full moon. The ratio of time of exposure in the two cases, however, is about 1 to 1,...", "... loudless sky, less than white reflecting clouds. As the surface of the moon's disk, of one-half degree diameter, is about TffsWtf the surface of the sky, it thus follows that the daylight reflected from the sky is about 100,000 times more intense than the light of the full moon. The organ by which we perceive the radiation, the human eye (Fig. 20), co..." ] }, { "section_id": "radiation-light-and-illumination-lecture-12", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 12: Illumination And Illuminating Engineering", "location": "lines 16485-17445", "status": "candidate", "occurrence_count": 268, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-12/", "snippets": [ "... ities with which we have to deal in illumi- nating engineering thus are : The intensity of the light source or the illuminant, and its brilliancy, that is, the flux density at the surface of the illuminant; The flux of light, that is, the total visible radiation issuing from the illuminant; 256 ILLUMINATION AND ILLUMINATING ENGINEERING. 257 The light...", "... ible radia- tion of the mercury lamp or a Moore tube as well as that of a point source - by adding all the flux densities intercepted by any surface enclosing the source of light. In a point source of light, the intensity, in candles, is the total 258 RADIATION, LIGHT, AND ILLUMINATION. flux of light, in lumens, divided by 4 x. In any illuminant which...", "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; ...", "LECTURE XII. ILLUMINATION AND ILLUMINATING ENGINEERING. 110. Artificial light is used for the purpose of seeing and distinguishing objects clearly and comfortably when the day- light fails. The problem of artificial lighting thus comprises con- sideration of the source of light or the illuminant; the flux of light issuing from it; the distribution of the..." ] }, { "section_id": "radiation-light-and-illumination-lecture-10", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 10: Light Flux And Distribution", "location": "lines 9389-12573", "status": "candidate", "occurrence_count": 250, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-10/", "snippets": [ "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the distribution of the light flux throughout spa ...", "... coordinates does not give a fair representation of the total light flux, or the mean spherical intensity of the light source, but on the contrary frequently is very misleading. When com- paring different polar curves of intensity distribution, it is 188 RADIATION, LIGHT, AND ILLUMINATION. impossible to avoid the impression of the area of the curve as...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided ...", "LECTURE X. LIGHT FLUX AND DISTRIBUTION. 86. The light flux of an illuminant is its total radiation power, in physiological measure. It therefore is the useful output of the illuminant, and the efficiency of an illuminant thus is the ratio of the total light flux divided by the power input. In general, the ..." ] }, { "section_id": "radiation-light-and-illumination-lecture-02", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 2: Relation Of Bodies To Radiation", "location": "lines 1549-2365", "status": "candidate", "occurrence_count": 197, "concepts": [ "Radiation", "Light", "Electrical Radiation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-02/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-02/", "snippets": [ "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light wa ...", "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation ...", "LECTURE II. RELATION OF BODIES TO RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation a...", "... RADIATION. 9. For convenience, the total range of known radiations can be divided into two classes, the electric waves and the light waves, which are separated from each other by the blank space in the middle of the spectrum of radiation (Fig. 14). Under light waves we here include also the invisible ultra-red radiation and the ultra-violet radiation...", "... , in the theory of transient electric phenomena and oscillations.* The radiation may be of a single frequency, that is, a single wave; or a mixture of different frequencies, that is, a mixture of different and frequently of an infinite number of waves. Electric radiation usually is of a single frequency, that is, of the frequency or wave length determ..." ] }, { "section_id": "radiation-light-and-illumination-lecture-01", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 1: Nature And Different Forms Of Radiation", "location": "lines 608-1548", "status": "candidate", "occurrence_count": 195, "concepts": [ "Radiation", "Light", "Electrical Radiation" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-01/", "snippets": [ "LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by b ...", "LECTURE I. NATURE AND DIFFERENT FORMS OF RADIATION. 1. Radiation is a form of energy, and, as such, can be produced from other forms of energy and converted into other forms of energy. The most convenient form of energy for the production of rad- iation is heat energy, and radiation when destroyed by being intercepte ...", "... energy of the latter is very much greater; a sufficiently sensitive heat-measuring instrument, as a bolometer, shows the heat produced by the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first st...", "... produced by the interception of the rays of the mercury lamp or the rays of the moon. The most conspicuous form of radiation is light, and, therefore, it was in connection with this form that the laws of radiation were first studied. 1 2 RADIATION, LIGHT, AND ILLUMINATION. 2. The first calculations of the velocity of light were made by astronomers in...", "... s is the time required by the light 18,800 to travel 10 miles, this gives the velocity of light as 10 •* > lo,oOU or 188,000 miles per sec. The velocity of light in air, or rather in empty space, thus is 188,000 miles or 3 X 1010 cm. per sec. For electrical radiation, the velocity has been measured by Herz, and found to be the same as the velocity of..." ] }, { "section_id": "radiation-light-and-illumination-lecture-09", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 9: Measurement Of Light And Radiation", "location": "lines 8511-9388", "status": "candidate", "occurrence_count": 195, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-09/", "snippets": [ "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one ...", "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it impinge on one contact of a thermo-co ...", "LECTURE IX. MEASUREMENT OF LIGHT AND RADIATION. 74. Since radiation is energy, it can be measured as such by converting the energy of radiation into some other form of energy, as, for instance, into heat, and measuring the latter. Thus a beam of radiation may be measured by having it ...", "... ut 0.4 per cent, a change of one millionth corresponds to a temperature rise °f ?tfW deg. cent. Thus, by the bolometer, extremely small amounts of radiation can be measured, as, for instance, the power of the moon's radiation, etc. 166 MEASUREMENT OF LIGHT AND RADIATION. 167 The total radiation energy of a body for a given time can be measured by abso..." ] }, { "section_id": "radiation-light-and-illumination-lecture-11", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 11: Light Intensity And Illumination", "location": "lines 12574-16484", "status": "candidate", "occurrence_count": 154, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-11/", "snippets": [ "... l illumination is l 7 cos and the vertical illumination is . 7 cos2 sin (4) (5) (6) (7) (8) where 7 is the intensity of the light source in the direc- tion . Inversely, to produce a uniform total illumination, i0, on the 228 RADIATION, LIGHT, AND ILLUMINATION. horizontal plane P, the intensity of the light source must vary with the angle ac...", "... 087 132.00 152.0 133.00 90 0 00 00 00 103. Therefore, in the problem, as it is usually met, of pro- ducing uniform intensity i0 over a limited area, subtending angle 2 aj beneath the light source, the intensity of the light source 230 RADIATION, LIGHT, AND ILLUMINATION. FIG. 96. FIG. 97, LIGHT INTENSITY AND ILLUMINATION. 231 should follow (11) for 0 <...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the ...", "LECTURE XI. LIGHT INTENSITY AND ILLUMINATION. A. INTENSITY CURVES FOR UNIFORM ILLUMINATION. 102. The distribution of the light flux in space, and thus the illumination, depends on the location of the light sources, and on their distribution curves. The character of the required illumi- nation depends on the purpose for which it is used: a general illumina..." ] }, { "section_id": "radiation-light-and-illumination-lecture-06", "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "year": 1909, "section_label": "Lecture 6: Luminescence", "location": "lines 5077-6608", "status": "candidate", "occurrence_count": 149, "concepts": [ "Radiation", "Light" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/radiation-light-and-illumination/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/radiation-light-and-illumination/lecture-06/", "snippets": [ "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, r ...", "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion of the r...", "LECTURE VI. LUMINESCENCE. 43. All methods of producing radiation, and more particularly light, other than the temperature radiation or incandescence, are generally comprised by the name luminescence. Some special cases of luminescence have already been discussed in the phe- nomena of fluorescence and phosphorescence, represented by the conversion ...", "... phorescence is the production of radiation from the energy stored in the phosphorescent body. This energy may be derived from internal changes in the body, as slow combustion, or may have been received by the body at some previous time - as by exposure to light a calcium sulphide screen absorbs the energy of incident radiation, stores it in some form,..." ] } ], "concordance_links": [ { "concept_id": "radiation", "label": "Radiation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/radiation/" }, { "concept_id": "light", "label": "Light", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/light/" }, { "concept_id": "electrical-radiation", "label": "Electrical Radiation", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/electrical-radiation/" } ] }, { "page_slug": "reactance", "page_title": "Reactance", "concept_ids": [ "reactance" ], "concept_labels": [ "Reactance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. 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With an inductive reactance inserted in series to an alt^^r- 245 246 ELECTRIC CIRCUITS nating-current non-...", "... rted in series to an alt^^r- 245 246 ELECTRIC CIRCUITS nating-current non-inductive circuit, at constant-supply voltage, the current in this circuit is approximately constant, as long as the resistance of the circuit is small compared with the series inductive reactance. Let ^0 = Co = constant impressed alternating voltage; r = resistance of non-induc..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-12", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 12: Reactance Of Induction Apparatus", "location": "lines 22634-23465", "status": "candidate", "occurrence_count": 62, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-12/", "snippets": [ "CHAPTER XII REACTANCE OF INDUCTION APPARATUS 109. An electric current passing through a conductor is ac- companied by a magnetic field surrounding this conductor, and this magnetic field is as integral a part of the phenomenon, as is the energy dissipation by the resistance o ...", "... d \"non-inductive\" circuit. With continuous current in stationary conditions, the inductance, L, has no effect on the energy flow; with alternating current of frequency, /, the inductance, L, consumes a voltage 2 x/Li, and is, therefore, represented by the reactance, x = 2x/L, which is measured in ohms, and differs from the ohmic resistance, r, merely..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-09", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 9: Circuits Containing Resistance, Inductive Reactance, And Condensive Reactance", "location": "lines 4674-6992", "status": "candidate", "occurrence_count": 59, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-09/", "snippets": [ "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a cl ...", "CHAPTER IX CIRCUITS CONTAINING RESISTANCE, INDUCTIVE REACTANCE, AND CONDENSIVE REACTANCE 53. Having, in the foregoing, re-established Ohm's law and Kirchhoff 's laws as being also the fundamental laws of alternating- current circuits, when expressed in their complex form, E = ZI, or, 7 = YE, and \"EE = 0 in a closed circuit, S/ = 0 at ..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 58, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... ngle 2w. That is, the one alternator has the voltage phase ( to), the other the voltage phase (0+w). We may assume the alternators as of equal voltage, since a voltage difference superposes on the synchronizing energy current due to the phase difference, a reactive magnetizing current due to the voltage difference without materially changing the en...", "... [ = 2E sin co sin (2) and the interchange currentwbeteen the alternators is: 2E . i = sin co sin ( a) (3) where: z = r2+x 2 is the impedance of the circuit between the two alternators, and the phase angle a is given by: x tan a = - r and: r= resistance x = reactance of the circuit between the alternators (including their internal resistances and re..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-22", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 22: Armature Reactions Of Alternators", "location": "lines 23971-25134", "status": "candidate", "occurrence_count": 52, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-22/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-22/", "snippets": [ "... ective self-induction, that is, instead of the counter m.m.f. of the armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar i...", "... is, instead of the counter m.m.f. of the armature reaction, the e.m.f. considered, which would be generated by the magnetic flux, which the arma- ture reaction would produce. That is, both effects are com- bined in an effective reactance, the \"synchronous reactance.\" While armature reaction and self-inductance are similar in ARMATURE REACTIONS OF ALTE..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-13", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 13: Reactance Of Synchronous Machines", "location": "lines 23466-24022", "status": "candidate", "occurrence_count": 43, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-13/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-13/", "snippets": [ "CHAPTER XIII REACTANCE OF SYNCHRONOUS MACHINES 119. The synchronous machine - ^alternating-current generator, synchronous motor or synchronous condenser - consists of an armature containing one or more electric circuits traversed by alternating currents and synchronously revo ...", "... ts and synchronously revolving relative to a unidirectional magnetic field, excited by direct current. The armature circuit, like every electric circuit, has a resistance, r, in which power is being dissipated by the current, /, and an in- ductance, L, or reactance, a; = 2 irfL^ which represents the mag- netic flux produced by the current in the armat..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-15", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 15: Constant-Voltage Series Operation", "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 42, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... he second lamp in circuit. However, in general such arrange- ment is too complicated for use. As practically all such circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance...", "... circuits would be alternating-current circuits, and thus alternating currents only need to be considered, the question arises, whether a reactance shunting each lamp would not give the desired effect. Suppose each lamp, of resist- ance, r, is shunted by a reactance, x, which is sufficiently large not to withdraw too much current from the lamp: assumin..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-03", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 4: Induction Motor With Secondary Excitation", "location": "lines 5555-8554", "status": "candidate", "occurrence_count": 39, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-03/", "snippets": [ "... characteristic of the induction machine is, that the magnetic field is excited by an alternating current derived from the alter- nating supply voltage, just as in the alternating-current trans- former. As the alternating magnetizing current is a wattless reactive current, the result is, that the alternating-current input into the induction motor is al...", "... he latter may be. That is, the induction motor remains asynchronous, increases in slip with increase of load. 5. Excitation by a condenser in the secondary circuit of the induction motor. As the magnetizing current required by the induction motor is a reactive, that is, wattless lagging current, it does not require a generator for its production, but..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 11: Phase Control", "location": "lines 9767-10717", "status": "candidate", "occurrence_count": 38, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-11/", "snippets": [ "... ng circuit, causes the voltage, e, at the receiver circuit to decrease with increasing current, /, through the resistance. The decrease of the voltage, e, is greatest if the current, /, is in phase with the voltage, e - less if the current is not in phase. Inductive reactance in series with the receiving circuit, e, at constant impressed e.m.f., eo, c...", "... pressed e.m.f., eo, causes the voltage, e, to drop less with a unity power-factor current, 7, but far more with a lagging current, and causes the voltage, e, to rise with a leading current. While series resistance always causes a drop of voltage, series inductive reactance, x, may cause a drop of voltage or a rise of voltage, depending on whether the..." ] }, { "section_id": "engineering-mathematics-chapter-03", "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_label": "Chapter 3: Trigonometric Series", "location": "lines 6064-15155", "status": "candidate", "occurrence_count": 34, "concepts": [ "Reactance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-03/", "snippets": [ "... starting-point of calculation of the phase of alternating currents. For instance, if a is the phase angle of a vector 98 ENGINEERING MATHEMATICS. quantity, tan a is given as the ratio of the vertical component over the horizontal component, or of the reactive component over the power component. In this case, if m . ,. . tan ex = a sin a = a and cos «...", "... : e = eo{sin ^-0.12 sin (3<9- 2. 3°) -0.23 sin (5^-1.5°) +0.13 sin (7^-6. 2°)1. . (1) In first approximation, the line capacity may be considered as a condenser shunted across the middle of the line; that is, half the line resistance and half the line reactance is in series with the line capacity. As the receiving apparatus do not utilize the higher h..." ] } ], "concordance_links": [ { "concept_id": "reactance", "label": "Reactance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/reactance/" } ] }, { "page_slug": "susceptance", "page_title": "Susceptance", "concept_ids": [ "susceptance" ], "concept_labels": [ "Susceptance" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept page through the linked source passages first. Use the dossier to locate Steinmetz's wording, then add modern, mathematical, historical, and interpretive layers only with labels.", "totals": { "occurrences": 220, "matching_sections": 38, "matching_sources": 8, "aliases": 2 }, "aliases": [ "susceptance", "susceptances" ], "sources": [ { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 68, "section_count": 9, "concepts": [ "Susceptance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 58, "section_count": 8, "concepts": [ "Susceptance" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 54, "section_count": 7, "concepts": [ "Susceptance" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 16, "section_count": 2, "concepts": [ "Susceptance" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 12, "section_count": 4, "concepts": [ "Susceptance" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 6, "section_count": 3, "concepts": [ "Susceptance" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 4, "section_count": 3, "concepts": [ "Susceptance" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 2, "section_count": 2, "concepts": [ "Susceptance" ] } ], "priority_sections": [ { "section_id": "theory-calculation-alternating-current-phenomena-chapter-10", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 10: Resistance And Reactance Of Transmission", "location": "lines 6993-9766", "status": "candidate", "occurrence_count": 26, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-10/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-10/", "snippets": [ "... s, by varying the admittance, Y = g - jh, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power - that is, upon the load on the circuit - and thus cannot be varied for the purpose of regu- lation. Its susceptance, b, however, can be changed bj' shunt- ing the circuit with a reactance, and will be in...", "... unted inductive reactance, and decreased by a shunted con- densive reactance. Hence, for the purpose of investigation, the receiver circuit can be assumed to consist of two branches, a conductance, g, - the non-inductive part of the circuit - shunted by a susceptance, h, which can be varied without expenditure of energy. The two components of current..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-09", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 9: Resistance And Reactance Of Transmission Lines", "location": "lines 5334-6956", "status": "candidate", "occurrence_count": 23, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-09/", "snippets": [ "... by varying the admittance, Y = g -f jb, of the receiver circuit. The conductance, gy of the receiver circuit depends upon the consumption of power, - that is, upon the load on the circuit, - and thus cannot be varied for the purpose of reg- ulation. Its susceptance, b, however, can be changed by shunting the circuit with a reactance, and will be incre...", "... decreased by a shunted con- densance. Hence, for the purpose of investigation, the 84 ALTERNATING-CURRENT PHENOMENA. receiver circuit can be assumed to consist of two branches, a conductance, g, - the non-inductive part of the circuit, - shunted by a susceptance, b, which can be varied without expenditure of energy. The two components of current can t..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-09", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 9: Kbsistanci: And Kbactance Of Transmission Iine8", "location": "lines 6371-8268", "status": "candidate", "occurrence_count": 20, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-09/", "snippets": [ "... by varying the admittance, Y = g + Jb, of the receiver circuit. The conductance, g, of the receiver circuit depends upon the consumption of power, - that is, upon the load on the circuit, - and thus cannot be varied for the purpose of reg- ulation. Its susceptance, by however, can be changed by shunting the circuit with a reactance, and will be increa...", "... d by a shunted con- densance. Hence, for the purpose of investigation, the 84 AL TERN A TIXG-CURRENT PHENOMENA, [§ 68 receiver circuit can be assumed to consist of two branches, a conductance, g^ - the non-inductive part of the circuit, - shunted by a susceptance, by which can be varied without expenditure of energy. The two components of current can..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 7: Admittance, Conductance, Susceptance", "location": "lines 3132-3576", "status": "candidate", "occurrence_count": 17, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-07/", "snippets": [ "CHAPTER VII. ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 38. If in a continuous-current circuit, a number of resistances, ?\\, r%, r3, . . . are connected in series, their joint resistance, R, is the sum of the individual resistances If, however, a number of resistances are connected in multiple or in parall ...", "... series connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series-connected resis- tances is equal to the sum of the individual resistances ; the ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc~ tances is equal to the sum..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-08", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 8: Admittance, Conductance, Susceptance", "location": "lines 4088-4673", "status": "candidate", "occurrence_count": 17, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-08/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-08/", "snippets": [ "CHAPTER VIII ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 48. If in a continuous-current circuit, a number of resistances, Ti, r2, ?'3, . . ., are connected in series, their joint resistance, R, is the sum of the individual resistances, K = ri + r2 + ra + . . . If, however, a number of resistances are connecte ...", "... tance of a number of series-connected resistances is equal to the sum of the individual resistances; the joint conduct- ance of a number of parallel-connected conductances is equal to the sum of the individual conductances. 64 ADMITTANCE, CONDUCTANCE, SUSCEPTANCE 55 49. In alternating-current circuits, instead of the term resist- ance we have the term..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-07", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 7: Admittance, Conductance, Susceftance", "location": "lines 3546-3871", "status": "candidate", "occurrence_count": 15, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-07/", "snippets": [ "... connection, and the use of the reciprocal term conductance in parallel connections ; therefore, The joint resistance of a number of series -connected resis- tances is equal to the sum of the individual resistances ; the § 30] ADMITTANCE, CONDUCTANCE, SUSCEPTANCE. 53 joint conductance of a number of parallel-connected conduc- tances is equal to the sum...", "... nent ^, which represents the coefficient of current in quadrature with the K.M.F., or wattless com- ponent of current, bE, g may be called the conductance^ and b the susceptanccy of the circuit. Hence the conductance, g^ is the energy component, and the susceptance, by the wattless component, of the admittance, Y = g -\\-jby while the numerical value o..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-15", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 15: Constant-Voltage Series Operation", "location": "lines 27996-29301", "status": "candidate", "occurrence_count": 14, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-15/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-15/", "snippets": [ "... on the same circuit, from constant-voltage supply. 156. Let n lamps of voltage, ei, and current, ii, thus conductance ff = j^ (1) ei be connected in series into a circuit of supply voltage, eo = nei (2) and each lamp be shunted by a reactance of susceptance, b. In each consuming device, comprising lamp and reactance, the admittance thus is, vectoriall...", "... om p = or full-load, to p = 1 or no-load, and no value of shunted reactance, 6, exists, which maintains constant current. With de- creasing load, the current, f i, decreases the slower, the higher 6 is, that is, the more current is shunted by the reactive susceptance, 6, and the poorer therefore the power-factor is. Thus shunted constant reactance can..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-11", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 11: Fouoault Or Eddy 0Ubbent8", "location": "lines 10500-11563", "status": "candidate", "occurrence_count": 10, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-11/", "snippets": [ "... and the E.M.F. induced in the primary circuit by the secon- dary current, /^ is £= ^^/; or, expanded, (V + ^V n^ + xi') ' Hence, ^ = --^ - ^- = effective conductance of mutual inductance ; r,» + jf« - »f », Xi b = - ^-^^^ - ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the s...", "... ircuit by the secon- dary current, /^ is £= ^^/; or, expanded, (V + ^V n^ + xi') ' Hence, ^ = --^ - ^- = effective conductance of mutual inductance ; r,» + jf« - »f », Xi b = - ^-^^^ - ■* = effective susceptance of mutual inductance. The susceptance of mutual inductance is negative, or of opposite sign from the susceptance of self-inductance. Or, Mutu..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-14", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 14: Dielectric Losses", "location": "lines 14334-15409", "status": "candidate", "occurrence_count": 9, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-14/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-14/", "snippets": [ "... very low) and specific capacity or permittivity k, if: I = thickness of the dielectric, A = area or cross-section, e = impressed alternating-current voltage, effective value, the dielectric capacity of the material is: JcA ^ ~~ I and the capacity susceptance: 152 ALTERNATING-CURRENT PHENOMENA hence the current passing through the dielectric as capacit...", "... r of the dielectric, and 72, k-z, h, Ao the corresponding values of the second layer. It is then : yA g = -y- = electric conductance kA C = -J- = electrostatic capacity of the layer of dielectric, hence: 2 irfk A b = 2irfC = - J - = capacity susceptance, and (1) 154 AL TERN A TING-C URREN T PHENOMENA Y = g -\\- jh = admittance, thus : Z =y = r - jx = i..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-17", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Theory Section 17: Impedance and Admittance", "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 8, "concepts": [ "Susceptance" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... impedance z - - with its components, I? the resistance and reactance, its reciprocal can be introduced. e \" z ' which is called the admittance. The components of the admittance are called the conduc- tance and the susceptance. Resolving the current i into a power component i\\ in phase with the e.m.f. and a wattless component iz in quadrature with the...", "... e.m.f., the quantity i\\_ _ power current, or current in phase with e.m.f. e e.m.f. . = 9 is called the conductance. The quantity _*2_ _ reactive current, or current in quadrature with e.m.f. e e.m.f. is called the susceptance of the circuit. The conductance represents the current in phase with the IMPEDANCE AND ADMITTANCE 101 e.m.f., or power current,..." ] } ], "concordance_links": [ { "concept_id": "susceptance", "label": "Susceptance", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/susceptance/" } ] }, { "page_slug": "symbolic-method", "page_title": "Symbolic Method", "concept_ids": [ "symbolic-method", "complex-quantities" ], "concept_labels": [ "Symbolic Method", "Complex Quantities" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as a mathematical language page: the important work is not only the formulas, but Steinmetz's translation between rotating vectors, rectangular components, and symbolic calculation.", "totals": { "occurrences": 316, "matching_sections": 70, "matching_sources": 10, "aliases": 8 }, "aliases": [ "symbolic", "symbolic expression", "symbolic method", "symbolic representation", "complex quantities", "complex quantity", "imaginary quantities", "imaginary quantity" ], "sources": [ { "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 89, "section_count": 22, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 77, "section_count": 22, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 65, "section_count": 16, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 24, "section_count": 6, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 19, "section_count": 6, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 16, "section_count": 7, "concepts": [ "Complex Quantities" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 12, "section_count": 2, "concepts": [ "Complex Quantities" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 6, "section_count": 5, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 3, "concepts": [ "Symbolic Method", "Complex Quantities" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 4, "section_count": 3, "concepts": [ "Symbolic Method", "Complex Quantities" ] } ], "priority_sections": [ { "section_id": "theory-calculation-alternating-current-phenomena-chapter-05", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 5: Symbolic Method", "location": "lines 2760-3266", "status": "candidate", "occurrence_count": 22, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-05/", "snippets": [ "CHAPTER V SYMBOLIC METHOD 25. The graphical method of representing alternating-current phenomena affords the best means for deriving a clear insight into the mutual relation of the different alternating sine waves entering into the problem. For numerical calculation, however, th ...", "... ram is shown in Fig. 21. Obviously, no exact numerical values can be taken from a parallelogram as flat as OFiFFo, and from the combination of vectors of the relative magnitudes 1 :6 :100. Hence the importance of the graphical method consists not 30 SYMBOLIC METHOD 31 so much in its usefulness for practical calculation as to aid in the simple understa...", "... eriod; that is, leading the wave by one-quarter period. Similarly - Multiplying by - j jneans lagging the wave by one-quarter period. Since j^ = - 1, it is j = v^^=n:; and j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the syste...", "... imaginary quantity or general number, a ^- jb. As the imaginary unit, j, has no numerical meaning in the system of ordinary numbers, this definition of j = V - 1 does not contradict its original introduction as a distinguishing index. For the Algebra of Complex Quantities see Appendix I. For a more complete discussion thereof see \" Engineering Mathema..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-30", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 30: Quartbr-Fhase System", "location": "lines 27501-29124", "status": "candidate", "occurrence_count": 19, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-30/", "snippets": [ "... .4, a = .1435, a = 8.2°. Impcdarice and Admittance, 283. In complex imaginary quantities, the alternating wave /* '»\\ s = £\" cos (<^ - cu) is represented by the symbol E - e (cos ci +y sin w) = c^ -\\- je^ . By an extension of the meaning of this symbolic ex- pression, the oscillating wave E=^et~^^ cos (<^ - w) can be expressed by the symbol E = e (cos...", "... . The electromotive force consumed by the inductance L of the circuit, 77 r d I o A- r if f d I Ex = /' - = 2 TT A Z = .V . lit i/ ii Hence Ej, = - xit\"*'^ {sin ( - w) + ^ cos ( - w)} = -- - - -- sin ( - (u + «)• cos tt Thus, in symbolic expression, ^x = - {- sin (w - a) +ycos (w - a)} dec a COS a = - xi {a -\\- J) (cos « + y sin w) dec...", "... ual distribution of load, but are liable to become un- balanced at unequal distribution of load ; the three-wire quarter-phase system is unbalanced in voltage and phase, even at equal distribution of load. APPENDICES APPENDIX I. ALGEBRA OF COMPLEX IMAGINARY QUANTITIES. INTRODUCTION. 267. The system of numbers, of which the science of algebra treats, f...", "... ction under any circumstances, the system of abso- lute numbers has to be expanded by the introduction of the negative number: - a = (- 1) X a, where (- 1) is the negative unit. Thereby the system of numbers is subdivided in the 270,271] COMPLEX IMAGINARY QUANTITIES. 403 positive and negative numbers, and the operation of sub- traction possible for al..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-32", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 32: Quarter-Phase System", "location": "lines 25904-27405", "status": "candidate", "occurrence_count": 19, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-32/", "snippets": [ "... have A = .4, a = .1435, a = 8.2°. Impedance and Admittance. 312. In complex imaginary quantities, the alternating wave * = e cos (* - ffl) is represented by the symbol E = e (cos w -\\-j sin w) = cos ( - w) can be expressed by the symbol E = e...", "... stance r of the circuit ^ The electromotive force consumed by the inductance L of the circuit, Ef**L-~*iNI&t = *-. dt d<$> d<$> Hence Ex = - xif.~a^> (sin ( - fy -\\- a cos (<£ - w)} xi(.~a^ . ,. „ , N = sin (^> - w -f- a). COS a Thus, in symbolic expression, £x = - °^-{- sin (w - a) +/ cos (w - a)} dec a COS a = - x i (a -f y ) (cos w + 7 sin a>) d...", "... al distribution of load, but are liable to become un- balanced at unequal distribution of load ; the three-wire quarter-phase system is unbalanced in voltage and phase, even at equal distribution of load. APPENDICES. APPENDIX I. ALGEBRA OF COMPLEX IMAGINARY QUANTITIES. INTRODUCTION. 296. The system of numbers, of which the science of algebra treats, f...", "... of subtraction under any circumstances, the system of abso- lute numbers has to be expanded by the introduction of the negative number: _ « = (_ 1) X «, .where (- 1) is the negative unit. Thereby the system of numbers is subdivided in the COMPLEX IMAGINARY QUANTITIES. 491 positive and negative numbers, and the operation of sub- traction possible for a..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-05", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 5: Symbolic Method", "location": "lines 2322-2773", "status": "candidate", "occurrence_count": 17, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-05/", "snippets": [ "CHAPTER V. SYMBOLIC METHOD. 23. The graphical method of representing alternating, current phenomena by polar coordinates of time affords the best means for deriving a clear insight into the mutual rela- tion of the different alternating sine waves entering into the problem. For n ...", "... for definition except that it is not an .ordinary number. 27. A wave of equal intensity, and differing in phase from the wave a + jb by 180°, or one-half period, is repre- sented in polar coordinates by a vector of opposite direction, and denoted by the symbolic expression, - a - jb. Or - Multiplying the symbolic expression, a + jb, of a sine wave by...", "... ing the wave through one-quarter period. Fig. 24. Similarly, - Multiplying by - j means advancing the wave through one-quarter period. since y'2 = - 1, j = V- 1 ; that is, - j is the imaginary unit, and the sine wave is represented by a complex imaginary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary num...", "... ary quantity, a -+- jb. As the imaginary unit j has no numerical meaning in the system of ordinary numbers, this definition of/ = V- 1 does not contradict its original introduction as a distinguish- ing index. For a more exact definition of this complex imaginary quantity, reference may be made to the text books of mathematics. 28. In the polar diagra..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1897-chapter-05", "source_id": "theory-calculation-alternating-current-phenomena-1897", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1897, "section_label": "Chapter 5: Symbouc Mbthod", "location": "lines 2744-3229", "status": "candidate", "occurrence_count": 16, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1897/chapter-05/", "snippets": [ "... mined analytically by two numerical quanti- ties - the length, Of, or intensity ; and the amplitude, AO/, or phase - 6), can be expressed by the symbol, JjJ...", "... e then, the e.m.f. consumed by the resistance, r, of the circuit, Er = rl dec a. The e.m.f. consumed due to the inductance, L, of the circuit, n T dl rk TT dl dl Hence E^ = - a;i€-\"*{sin (0 - ^) + a cos (0 - ^)} = sm (0 - ^ + a). cos a Thus, in symbolic expression, jFx = I - sin {B - a) - j cos (^ - a) } dec a cos a / ^ \\ /I = - xtXa - j) (cos ^ - j s...", "... lar decrement of the oscillating wave. The oscillating wave can be represented by the equation, E = e€\"***'^«cos(« - 6). In the example represented by Figs. 130 and 131, we have A = 0.4, a = 0.1435, a = 8.2°. Impedance and Admittance 184. In complex imaginary quantities, the alternating wave, z = e cos (0 - 6)^ is represented by the symbol, fl = e(cos...", "... 349 where X - tan d = 1 + a' r - ax - a 1 +a' Xe substituting ^ + 6 f or B, and e = isa we have B = ee-*^ cos (0 - ^), / = - 1-^ cos (0-^-5) . f COS 5 , . -V , sin 5 . / . .v = ee-\"^ J COS { - B) -\\ sin (0 - B) hence in complex quantities, ^ = e(cos ^ - j sin B) dec a, , r, f cos 5 . sin 5 1 J I = e\\ - J - - dec a; or, substituting, I = E r - ax -..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-12", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 12: Power, And Double Frequency Quantities In General", "location": "lines 9381-9740", "status": "candidate", "occurrence_count": 12, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-12/", "snippets": [ "... nt chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are related by multiplication...", "... The real component will be distinguished by the index 1, the imaginary or wattless component by the index/. By introducing this symbolism, the power of an alternat- ing circuit can be represented in the same way as in the direct current circuit, as the symbolic product of current and E.M.F. Just as the symbolic expression of current and E.M.F. as comp...", "... ints, these points representing the abso- lute values of potential (with regard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in...", "... egard to any reference point chosen as co-ordinate center) and their connection the dif- ference of potential in phase and intensity. Algebraically these vectors are represented by complex quantities. The impedance, admittance, etc., of the circuit is a complex quantity also, in symbolic denotation. Thus current, E.M.F., impedance, and admittance are..." ] }, { "section_id": "engineering-mathematics-chapter-01", "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "year": 1911, "section_label": "Chapter 1: The General Number", "location": "lines 915-3491", "status": "candidate", "occurrence_count": 11, "concepts": [ "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/engineering-mathematics/chapter-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/engineering-mathematics/chapter-01/", "snippets": [ "... rature with each other can be expressed by the plus si^n, and the result of combination thereby expressed by OB^-BP = 3+2j. THE GENERAL NUMBER. 17 Such a combination of an ordinary number and a quadra- ture number is called a general number or a complex quantity. The quadrature number jh thus enormously extends the field of usefulness of algebra, by a...", "... ors in space. In the quaternion calculus methods have been devised to deal with space problems. The quaternion calculus, however, has not yet found an engineering appHcation comparable with that of the general number, or, as it is frequently called, the complex quantity. The reason is that the quaternion is not an algebraic quantity, and the laws of a..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-17", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Theory Section 17: Impedance and Admittance", "location": "lines 6814-7380", "status": "candidate", "occurrence_count": 11, "concepts": [ "Symbolic Method" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-17/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-17/", "snippets": [ "... d in ohms: reactance x. The e.m.f. consumed by reactance x is in quadrature with the current, that consumed by resistance r in phase with the current. Reactance and resistance combined give the impedance, + x2; or, in symbolic or vector representation, Z = r + jx. In general in an alternating-current circuit of current i, the e.m.f. e can be resolved...", "... t is called the effective resistance. The quantity 62 _ reactive e.m.f., or e.m.f. in quadrature with the current _ i current is called the effective reactance of the circuit. And the quantity 21 = Vr!2 + x2 or, in symbolic representation, Zi = ri + jxi is the impedance of the circuit. If power is consumed in the circuit only by the ohmic resist- ance..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-24", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 24: Symbolic Representation Of General Alternating Waves", "location": "lines 22449-23642", "status": "candidate", "occurrence_count": 10, "concepts": [ "Symbolic Method", "Complex Quantities" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-24/", "snippets": [ "CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y The term, /#. El = 2/n~17 where, consists of a series of inductance factors qn of the individual harmonics. As a rule, if -350 J- > PS j / 1 i 1 1 i 1 I 0 1 0 1 0 1 Fio. 20. - Low-epecd induction motor, load c : the Elements of Electrical Engineering,\" 4th edition, difference. 39. In the synchronous machine usually the stator, in com- mutating machines the rotor is the armature, that is, the element to -which electrical power is supp..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-appendix-01-synchronous-operation", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Mathematical Appendix 5: Appendix: Synchronous Operation", "location": "PDF pages 27-68, lines 2165-5013", "status": "pdf-text-extracted-candidate", "occurrence_count": 151, "concepts": [ "Synchronizing power", "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/appendix-01-synchronous-operation/", "snippets": [ "... n a sin 2a> =- cos a cos w. 2z 2z The second term: E 2 p'Y'= - cos a. cos a> has the same sign for negative w, that is, when the machine is lagging, as for positive w when the machine is leading, thus it represents no energy transfer between the machines. The synchronizing power, or energy transfer during the synchro- nizing oscillations of two altern...", "... ts no energy transfer between the machines. The synchronizing power, or energy transfer during the synchro- nizing oscillations of two alternators, which are out of phase but in synchronism, thus is given by the expression: E 2 P=- sin a sin 2co (6) Thus, the synchronizing power p, is a maximum, and is : _E 2 . for a = 90 degrees, that is, if the resi...", "Appendix [[END_PDF_PAGE:27]] [[PDF_PAGE:28]] 22 Report of Charles P. Steinmetz APPENDIX Synchronous Operation A Consider the case of two alternators or groups of alternators such as station sections, which are running in synchronism with each other, that is, have the same frequency f, but are connected together while out of phase with each other by angle..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-11", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 12: Frequency Converter Or General Alternating Current Transformer", "location": "lines 14897-17124", "status": "candidate", "occurrence_count": 101, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-11/", "snippets": [ "... primary n r thus, if: / = primary frequency, or frequency of impressed e.m.f., sf = secondary frequency; and the e.m.f. generated per secondary turn by the mutual flux has to the e.m.f. generated per primary turn the ratio, «, s = 0 represents synchronous motion of the secondary; s < 0 represents motion above synchronism - driven by external mechanica...", "... impressed e.m.f., sf = secondary frequency; and the e.m.f. generated per secondary turn by the mutual flux has to the e.m.f. generated per primary turn the ratio, «, s = 0 represents synchronous motion of the secondary; s < 0 represents motion above synchronism - driven by external mechanical power, as will be seen; 8 = 1 represents standstill; s > 1..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-chapter-24", "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1916, "section_label": "Chapter 24: Synchronous Motor", "location": "lines 25682-29374", "status": "candidate", "occurrence_count": 95, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena/chapter-24/", "snippets": [ "CHAPTER XXIV SYNCHRONOUS MOTOR 212. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given voltage, the work done by the alternator can be either positive or negative. In the latter case the alt ...", "CHAPTER XXIV SYNCHRONOUS MOTOR 212. In the chapter on synchronizing alternators we have seen that when an alternator running in synchronism is connected with a system of given voltage, the work done by the alternator can be either positive or negative. In the latter case the alternator consumes electrical, and consequentl ..." ] }, { "section_id": "theory-calculation-alternating-current-phenomena-1900-chapter-16", "source_id": "theory-calculation-alternating-current-phenomena-1900", "source_title": "Theory and Calculation of Alternating Current Phenomena", "year": 1900, "section_label": "Chapter 16: Induction Motor", "location": "lines 13649-16361", "status": "candidate", "occurrence_count": 94, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-alternating-current-phenomena-1900/chapter-16/", "snippets": [ "... e frequency as the E.M.Fs. impressed upon the primary, but of a frequency which is the difference between the impressed frequency 238 ALTERNATING-CURRENT PHENOMENA. and the frequency of rotation, or equal to the \"slip,\" that is, the difference between synchronism and speed (in cycles). Hence, if N = frequency of main or primary E.M.F., and s = percent...", "... the motor,\" or \" Counter E.M.F.\" Since the secondary frequency is s N, the secondary in- duced E.M.F. (reduced to primary system) is El = - se. Let I0 = exciting current, or current passing through the motor, per primary circuit, when doing no work (at synchronism), and K= g -j- j 'b = orimary admittance per circuit = - . We thus have, ge = magnetic e..." ] }, { "section_id": "commonwealth-edison-generating-system-trouble-section-03-record", "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "year": 1919, "section_label": "Report Record 4: Record of Four Troubles", "location": "PDF pages 16-27, lines 1139-2164", "status": "pdf-text-extracted-candidate", "occurrence_count": 79, "concepts": [ "Synchronizing power", "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/commonwealth-edison-generating-system-trouble/section-03-record/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/commonwealth-edison-generating-system-trouble/section-03-record/", "snippets": [ "... rge a part of the entire system. It is dangerous, as Fisk B and Northwest combined give too large a power for safe handling under all emergencies. Furthermore, due to the connection between these stations being practically all resistance and no reactance, the synchronizing power between Fisk B and Northwest must be small, and when synchronism is once...", "... come back and the station section drop into step again with the rest of the system. This did not occur, but station sections remained out of step with each other at practically zero voltage for a considerable time, about a quarter of an hour. Apparently, the synchronizing power between the station sections is lower than desirable, and the speed con- t...", "... are no power limiting reactors between Fisk B and North- west Station, and the six tie cables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synch...", "... ables between these stations are of very low resistance, the Northwest Station was just as seriously affected as Fisk B, and indeed acted like a part of Fisk B. b) All the synchronous machines on Fisk Street B, and on North- west Station dropped out, and many synchronous machines on Fisk A and Quarry Street: 44 synchronous machines on Fisk B and 18 on..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-18", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 20: Single-Phase Commutator Motors", "location": "lines 23906-30087", "status": "candidate", "occurrence_count": 68, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-18/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-18/", "snippets": [ "... for single-phase railroading, and as con- stant-speed motors or adjustable-speed motors, where efficient acceleration under heavy torque is necessary. As generators, they would be of advantage for the generation of very low fre- quency, since in this case synchronous machines are uneconom- ical, due to their very low speed, resultant from the low freq...", "... es is generally the highest frequency considered for large commutating motors. High ni and low n0 means high armature reaction and low field excitation, that is, just the opposite conditions from that required for good commutator-motor design. Assuming synchronism, /o = /, as average motor speed - 750 revolutions with a four-pole 25-cyclc motor - an a..." ] }, { "section_id": "theoretical-elements-electrical-engineering-section-110", "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "year": 1915, "section_label": "Apparatus Section 4: Induction Machines: Induction Generator", "location": "lines 21158-21588", "status": "candidate", "occurrence_count": 53, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theoretical-elements-electrical-engineering/section-110/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theoretical-elements-electrical-engineering/section-110/", "snippets": [ "IV. Induction Generator 1. INTRODUCTION 163. In the range of slip from s = 0 to s = 1, that is, from synchronism to standstill, torque, power output, and power input of the induction machine are positive, and the machine thus acts as a motor, as discussed before. Substituting, however, in the equations in paragraph 1 for s values > ...", "... M CONSTANT FREQUENCY CONSTANT TERMINAL VOLTAGE OF 110 Z0- Y - 0.01 - 0.4 05 060 160 140 100. FIG. 186. - Induction machine speed curves. Substituting for s negative values, corresponding to a speed above synchronism, torque and power output and power input 342 ELEMENTS OF ELECTRICAL ENGINEERING become negative, and a load curve can be plotted for the..." ] }, { "section_id": "theory-calculation-electric-apparatus-chapter-21", "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "year": 1917, "section_label": "Chapter 23: Review", "location": "lines 32138-32819", "status": "candidate", "occurrence_count": 52, "concepts": [ "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-apparatus/chapter-21/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-apparatus/chapter-21/", "snippets": [ "... . Comprises an inductor disk of very many teeth, revolving at very high speed between two radial armatures. Used for producing very high frequencies, from 20,000 to 200,000 cycles per second. Amortisseur. - Squirrel-cage winding in the pole faces of the synchronous machine, proposed by Leblanc to oppose the hunt- ing tendency, and extensively used. Am...", "... returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. - Name used for all those types of alternating-current (single-phase or polyphase) motors or motor couples, which approach a definite synchronous speed at no-load, and slip below this speed with increasing load. 459 400 ELECTRICAL A..." ] }, { "section_id": "theory-calculation-electric-circuits-chapter-11", "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "year": 1917, "section_label": "Chapter 11: Instability Of Circuits: Induction And Syn Chronous Motors", "location": "lines 21382-22633", "status": "candidate", "occurrence_count": 50, "concepts": [ "Synchronizing power", "Synchronism" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-electric-circuits/chapter-11/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-electric-circuits/chapter-11/", "snippets": [ "... ng to the load, would be - or may ap- proximately be assumed as - proportional to the position dis- placement, p, but with reverse sign, positive for acceleration when p is negative or behind the normal position, negative or retarding when p is ahead. The synchronizing power, that is, the power exerted by the machine to return to the normal position,...", "... 1 derived by multiplying -p with v, and is shown dotted as Wj in Fig. 104. As seen, it has a double-frequency alternation with zero as average. The total resultant power or the resulting damping effect which restores stability, then, is the sum of the synchronizing power ifa and_ the damping power wi, and is shown by the dotted Fio. 104. curve v>. As...", "... zed by the central stations since the early days, and good partial load efficiencies and power-factors secured. 104. The induction motor speed-torque curve thus has on a constant-torque load a stable branch, from the maximum torque point, c. Fig. 102, to synchronism; and an unstable branch, from standstill to the maximum torque point. However, it woul...", "... \\ , V'<^< ^ ^-.ll ,. , . . . , dS - dS\" Thus, with this character of load, a torque required propor- tional to the speed, and the motor-torque curve, 2>, no instability exists, but conditions are stable from standstill to synchronism, just as in Fig. 101. That is, with increasing load, the speed de- creases and increases again with decreasing load. If..." ] } ], "concordance_links": [ { "concept_id": "synchronizing-power", "label": "Synchronizing power", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/synchronizing-power/" }, { "concept_id": "synchronism", "label": "Synchronism", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/synchronism/" } ] }, { "page_slug": "transient-phenomena", "page_title": "Transient Phenomena", "concept_ids": [ "transient-phenomena", "field-collapse" ], "concept_labels": [ "Transient Phenomena", "Field Collapse" ], "generated_at": "2026-04-29", "quality_note": "Generated concept-page dossier. Counts, snippets, and passages are OCR/PDF-text aids and require scan verification before exact quotation.", "guidance": "Read this concept as a time-domain correction to steady-state circuit thinking. The strongest pages should show where Steinmetz separates permanent terms from transient terms and then follows the stored energy.", "totals": { "occurrences": 1332, "matching_sections": 84, "matching_sources": 11, "aliases": 8 }, "aliases": [ "temporary term", "transient", "transient phenomena", "transient phenomenon", "transients", "collapse of the field", "collapsing field", "field collapse" ], "sources": [ { "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "occurrence_count": 514, "section_count": 42, "concepts": [ "Transient Phenomena" ] }, { "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 379, "section_count": 9, "concepts": [ "Transient Phenomena" ] }, { "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "occurrence_count": 355, "section_count": 9, "concepts": [ "Transient Phenomena" ] }, { "source_id": "theory-calculation-electric-circuits", "source_title": "Theory and Calculation of Electric Circuits", "occurrence_count": 49, "section_count": 7, "concepts": [ "Transient Phenomena" ] }, { "source_id": "engineering-mathematics", "source_title": "Engineering Mathematics: A Series of Lectures Delivered at Union College", "occurrence_count": 7, "section_count": 3, "concepts": [ "Transient Phenomena" ] }, { "source_id": "theory-calculation-electric-apparatus", "source_title": "Theory and Calculation of Electric Apparatus", "occurrence_count": 7, "section_count": 2, "concepts": [ "Transient Phenomena" ] }, { "source_id": "radiation-light-and-illumination", "source_title": "Radiation, Light and Illumination", "occurrence_count": 6, "section_count": 4, "concepts": [ "Transient Phenomena" ] }, { "source_id": "theoretical-elements-electrical-engineering", "source_title": "Theoretical Elements of Electrical Engineering", "occurrence_count": 6, "section_count": 2, "concepts": [ "Transient Phenomena" ] }, { "source_id": "theory-calculation-alternating-current-phenomena", "source_title": "Theory and Calculation of Alternating Current Phenomena", "occurrence_count": 5, "section_count": 4, "concepts": [ "Transient Phenomena" ] }, { "source_id": "commonwealth-edison-generating-system-trouble", "source_title": "Investigation of Some Trouble in the Generating System of the Commonwealth Edison Co.", "occurrence_count": 3, "section_count": 1, "concepts": [ "Transient Phenomena" ] }, { "source_id": "four-lectures-relativity-space", "source_title": "Four Lectures on Relativity and Space", "occurrence_count": 1, "section_count": 1, "concepts": [ "Transient Phenomena" ] } ], "priority_sections": [ { "section_id": "electric-discharges-waves-impulses-1914-lecture-04", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "location": "lines 2485-3386", "status": "candidate", "occurrence_count": 130, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-04/", "snippets": [ "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition ex ...", "... n existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the superposition of the permanent current, corresponding to the conditions after the change, and a transient current, which connects the current value before the change with that brought about by..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-04", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 4: Single-Energy Transients In Alternating Current Circuits", "location": "lines 2162-2971", "status": "candidate", "occurrence_count": 126, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-04/", "snippets": [ "LECTURE IV. SINGLE-ENERGY TRANSIENTS IN ALTERNATING- CURRENT CIRCUITS. 17. Whenever the conditions of an electric circuit are changed in such a manner as to require a change of stored energy, a transi- tion period appears, during which the stored energy adjusts itself from the condition ex ...", "... n existing before the change to the condition after the change. The currents in the circuit during the transition period can be considered as consisting of the superposition of the permanent current, corresponding to the conditions after the change, and a transient current, which connects the current value before the change with that brought about by..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-06", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 6: Double-Energy Transients", "location": "lines 3721-4369", "status": "candidate", "occurrence_count": 62, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-06/", "snippets": [ "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condi ...", "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-06", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 6: Double-Energy Transients", "location": "lines 3287-3955", "status": "candidate", "occurrence_count": 62, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-06/", "snippets": [ "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condi ...", "LECTURE VI. DOUBLE-ENERGY TRANSIENTS. 24. In a circuit in which energy can be stored in one form only, the change in the stored energy which can take place as the result of a change of the circuit conditions is an increase or decrease. The transient can be separated from the permanent condition, and then always is the representation of a gradual decrease..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-01", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 1: Nature And Origin Of Transients", "location": "lines 557-1002", "status": "candidate", "occurrence_count": 53, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-01/", "snippets": [ "LECTURE I. NATURE AND ORIGIN OF TRANSIENTS. I. Electrical engineering deals with electric energy and its flow, that is, electric power. Two classes of phenomena are met: permanent and transient phenomena. To illustrate: Let G in Fig. 1 be a direct-current generator, which over a circuit A con- n ...", "LECTURE I. NATURE AND ORIGIN OF TRANSIENTS. I. Electrical engineering deals with electric energy and its flow, that is, electric power. Two classes of phenomena are met: permanent and transient phenomena. To illustrate: Let G in Fig. 1 be a direct-current generator, which over a circuit A con- nects to a load L, as a number of lamps, etc. In the generator..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-01", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 1: Nature And Origin Of Transients", "location": "lines 460-882", "status": "candidate", "occurrence_count": 53, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-01/", "snippets": [ "LECTURE I. NATURE AND ORIGIN OF TRANSIENTS. i. Electrical engineering deals with electric energy and its flow, that is, electric power. Two classes of phenomena are met: permanent and transient, phenomena. To illustrate: Let G in Fig. 1 be a direct-current generator, which over a circuit A con- ...", "LECTURE I. NATURE AND ORIGIN OF TRANSIENTS. i. Electrical engineering deals with electric energy and its flow, that is, electric power. Two classes of phenomena are met: permanent and transient, phenomena. To illustrate: Let G in Fig. 1 be a direct-current generator, which over a circuit A con- nects to a load L, as a number of lamps, etc. In the generato..." ] }, { "section_id": "electric-discharges-waves-impulses-1914-lecture-03", "source_id": "electric-discharges-waves-impulses-1914", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1914, "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "location": "lines 1659-2484", "status": "candidate", "occurrence_count": 49, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/electric-discharges-waves-impulses-1914/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/electric-discharges-waves-impulses-1914/lecture-03/", "snippets": [ "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or osci ...", "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits ar..." ] }, { "section_id": "elementary-lectures-electric-discharges-waves-impulses-lecture-03", "source_id": "elementary-lectures-electric-discharges-waves-impulses", "source_title": "Elementary Lectures on Electric Discharges, Waves and Impulses, and Other Transients", "year": 1911, "section_label": "Lecture 3: Single-Energy Transients In Continuous Current Circuits", "location": "lines 1531-2161", "status": "candidate", "occurrence_count": 49, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/elementary-lectures-electric-discharges-waves-impulses/lecture-03/", "snippets": [ "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscil ...", "LECTURE III. SINGLE-ENERGY TRANSIENTS IN CONTINUOUS- CURRENT CIRCUITS. 13. The simplest electrical transients are those in circuits in which energy can be stored in one form only, as in this case the change of stored energy can consist only of an increase or decrease ; but no surge or oscillation between several forms of energy can exist. Such circuits ar..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-58", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 9: Inductive Discharges", "location": "lines 34897-40349", "status": "candidate", "occurrence_count": 34, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-58/", "snippets": [ "... hat throughout the entire inductive section X = 0, and current i1 therefore is constant throughout this section. Choosing now the transition point between the inductance and the transmission line as zero of distance, A = 0, the inductance 635 536 TRANSIENT PHENOMENA is massed at point ^ = 0, and the transmission line extends from X = 0 to X = V Denoti...", "... in the second expression terms of secondary order have been dropped. P qL Then substituting in (375) gives the equations of massed inductance : it = e ~M { M cos qt - N sin qt } (382) If at t = 0, £j = 0, that is, if at the beginning of the transient discharge the voltage at the inductance is zero, as for instance the inductance had been short-circuit..." ] }, { "section_id": "theory-calculation-transient-electric-phenomena-oscillations-chapter-24", "source_id": "theory-calculation-transient-electric-phenomena-oscillations", "source_title": "Theory and Calculation of Transient Electric Phenomena and Oscillations", "year": 1909, "section_label": "Chapter 2: Introduction", "location": "lines 1993-2658", "status": "candidate", "occurrence_count": 31, "concepts": [ "Transient Phenomena" ], "source_text_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/source-texts/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "workbench_url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/chapter-workbench/theory-calculation-transient-electric-phenomena-oscillations/chapter-24/", "snippets": [ "... to0. In the moment of closing the circuit of e.m.f. e0 upon the capacity C, the condenser contains no charge, that is, zero potential difference exists at the condenser terminals. If there were no resistance and no inductance in the circuit in the 18 TRANSIENT PHENOMENA moment of closing the circuit, an infinite current would exist charging the conden...", "... = 40 ohms; L = 100 mh.; C = 10 mf., and eQ = 1000 volts. In such a continuous-current circuit, containing resistance, inductance, and capacity in series to each other, the current at the moment of closing the circuit as well as the final current 20 TRANSIENT PHENOMENA is zero, but a current exists immediately after closing the circuit, as a transient..." ] } ], "concordance_links": [ { "concept_id": "transient-phenomena", "label": "Transient Phenomena", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/transient-phenomena/" }, { "concept_id": "field-collapse", "label": "Field Collapse", "url": "/Charles-Proteus-Steinmetz-Texts-AI-Decoded/concept-concordance/field-collapse/" } ] } ] }