Admittance
Steinmetz Usage
Section titled “Steinmetz Usage”Admittance is introduced as the reciprocal form of impedance, useful especially when currents divide through parallel paths. The OCR candidate gives admittance as a complex quantity with conductance and susceptance components.
Conductance is the active or power component. Susceptance is the reactive or wattless component.
Modern Equivalent
Section titled “Modern Equivalent”Modern texts often write:
The sign convention differs by author and context. The archive should preserve Steinmetz’s notation and then translate it explicitly.
Mathematical Meaning
Section titled “Mathematical Meaning”If:
then admittance depends on both r and x. Conductance is not generally just 1/r, and susceptance is not generally just 1/x.
Why It Matters
Admittance is one of the places where old AC language can save readers from a common simplification. The reciprocal of a complex quantity is not the same as taking reciprocals of its parts.
Related Pages
Section titled “Related Pages”Source-Grounded Dossier
Section titled “Source-Grounded Dossier”Generated evidence layer: this dossier is built from the processed concept concordance. Counts and snippets are OCR/PDF-text aids, not final quotations. Verify against scans before making exact claims.
Candidate occurrences tracked for this page.
Sources with at least one hit.
Sections, lectures, chapters, or report divisions to review.
What The Current Corpus Shows
Section titled “What The Current Corpus Shows”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.
The strongest current source concentration is Theory and Calculation of Alternating Current Phenomena with 136 candidate hits across 17 sections.
The dossier is meant to turn a concept page into a research workbench: begin with Steinmetz’s source wording, then add modern interpretation, mathematical reconstruction, historical context, and any ether-field reading as separate layers.
Terms And Aliases Tracked
Section titled “Terms And Aliases Tracked”admittance, admittances
Concordance Records
Section titled “Concordance Records”Source Distribution
Section titled “Source Distribution”| Source | Candidate Hits | Sections | Concepts represented |
|---|---|---|---|
| Theory and Calculation of Alternating Current Phenomena | 136 | 17 | Admittance |
| Theory and Calculation of Alternating Current Phenomena | 109 | 15 | Admittance |
| Theory and Calculation of Alternating Current Phenomena | 73 | 13 | Admittance |
| Theory and Calculation of Electric Apparatus | 68 | 9 | Admittance |
| Theoretical Elements of Electrical Engineering | 55 | 9 | Admittance |
| Theory and Calculation of Electric Circuits | 16 | 5 | Admittance |
| Theory and Calculation of Transient Electric Phenomena and Oscillations | 9 | 4 | Admittance |
| Engineering Mathematics: A Series of Lectures Delivered at Union College | 7 | 3 | Admittance |
Priority Passages To Read
Section titled “Priority Passages To Read”Chapter 16: Induction Motor - 28 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1900)
Location: lines 13649-16361 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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 ;...Chapter 20: Single-Phase Induction Motors - 23 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 21538-22301 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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...Apparatus Section 3: Induction Machines: Single -phase Induction Motor - 22 candidate hits
Source: Theoretical Elements of Electrical Engineering (1915)
Location: lines 20428-21157 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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...Chapter 17: The Alternating-Current Transformer - 21 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 16521-17716 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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...Chapter 12: Effective Resistance And Reactance - 20 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1916)
Location: lines 10718-13483 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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...Chapter 10: Effective Resistance And Reactance - 18 candidate hits
Source: Theory and Calculation of Alternating Current Phenomena (1900)
Location: lines 6957-8383 - Tracked concepts: Admittance
Open source text - Open chapter workbench
... 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...Reading Layers To Build Out
Section titled “Reading Layers To Build Out”| Layer | What to add next |
|---|---|
| Steinmetz wording | Pull exact source passages only after scan verification; keep OCR text labeled until then. |
| Modern engineering reading | Translate the source usage into present electrical-engineering or physics language without erasing the older vocabulary. |
| Mathematical layer | Link equations, variables, diagrams, and worked examples when the concept has formula candidates. |
| Historical layer | Identify whether the term is still used, renamed, absorbed into modern theory, or historically obsolete. |
| Ether-field interpretation | Keep interpretive readings separate from Steinmetz’s explicit claim and from modern physics. |
| Open questions | Record places where the concordance suggests a lead but the scan or edition has not yet been checked. |
Next Editorial Actions
Section titled “Next Editorial Actions”- Open the highest-priority source-text passages above and verify the wording against scans.
- Promote exact definitions, equations, diagrams, and hidden-gem passages into this page with source references.
- Add related concept links, equation pages, and diagram pages once the evidence is scan checked.
- Keep speculative or Wheeler-style readings in explicitly labeled interpretation blocks.