Alternating Current And Symbolic Method Evidence
Alternating Current And Symbolic Method
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What This Theme Gathers
Section titled “What This Theme Gathers”Passages involving alternating current, vectors, phasors, complex quantities, imaginary quantities, the symbolic method, harmonics, wave shape, and power factor.
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Modern Reading Prompt
Read for the historical bridge from rotating vectors and symbolic notation into the phasor language used in modern AC engineering.
Interpretive Boundary
Do not treat symbolic notation as a metaphysical claim by itself. Interpretive readings must first preserve the mathematical role of the symbols.
Matched Aliases
Section titled “Matched Aliases”| Alias | Hits |
|---|---|
alternating current | 1505 |
alternating-current | 1505 |
power factor | 586 |
harmonics | 580 |
harmonic | 468 |
vector | 385 |
wave shape | 181 |
a.c. | 86 |
complex quantities | 76 |
symbolic expression | 72 |
vectors | 70 |
imaginary quantities | 39 |
complex quantity | 35 |
symbolic method | 31 |
symbolic representation | 22 |
wattless current | 14 |
imaginary quantity | 6 |
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Section titled “Representative Source-Located Passages”Chapter 25: Distortion Of Wave-Shape And Its Causes - 135 hit(s)
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CHAPTER XXV DISTORTION OF WAVE-SHAPE AND ITS CAUSES 232. In the preceding chapters we have considered the alter- nating currents and alternating e.m.fs. as sine waves or as replaced by their equivalent sine waves. While this is sufficiently exact in most cases, under certain circumstances the deviation of the wave from sine sha ...... the equivalent sine wave becomes indefinite. Thus it becomes desirable to investi- gate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be repre- sented by a series of sine functions of odd orders, the inves- tigation of distortion of wave-shape resolves itself in the in- vestigation of the higher harmonics of the alternating wave. In general we have to distinguish between higher harmonics of e.m.f. and higher harmonics of current. Both depend upon each other in so far as with a sine wave of impressed e.m.f. a distorting effect will ...Chapter 20: Single-Phase Commutator Motors - 101 hit(s)
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CHAPTER XX SINGLE-PHASE COMMUTATOR MOTORS I. General 189. Alternating-current commutating machines have so far become ef industrial importance mainly as motors of the series or varying-speed type, 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 woul ...... - tion and thus subtract; that is, the field magnetism of the alter- nating-current motor must be in phase with the armature cur- rent, or nearly so. This is inherently the case with the series type of motor, in which the same current traverses field coils and armature windings. Since in the alternating-current transformer the primary and secondary currents and the primary voltage and the secondary voltage are proportional to each other, the different circuits of the alternating-current commutator motor may be connected with each other directly (in shunt or in series, according to the type of the mot ...Chapter 3: Trigonometric Series - 92 hit(s)
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... a or cot a resubstituted in the final result, if the latter contains sin a . . - , or its reciprocal. cos a In electrical engineering tan a or cot a frequently appears as the 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 « = Va^ + h^ cot a = c "d' sin ...... racy required. The problem then is, from the numerical values of the wave, to determine its equation. While the oscillograph shows the shape of the wave, it obviously is not possible therefrom to calculate other quantities, as from the voltage the current under given circuit conditions, if the wave shape is not first represented by a mathematical expression. . It therefore is of importance in engineering to translate thejicite or the table "^ of numerical values of a periodic function into a mathematical expression thereof. • ' , (B) If one of the engineering quantities, as the e.m.f. of an ...Chapter 24: Symbolic Representation Of General Alternating Waves - 92 hit(s)
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CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y<zu = a (cos a -\-j sin d) of the alternating wave, A — a0 cos (<£ — a) applies to the sine wave only. The general alternating wave, however, contains an in- finite series of terms, of odd frequencies, A = Al cos ...CHAPTER XXIV. SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES. 253. The vector representation, A = a1 +y<zu = a (cos a -\-j sin d) of the alternating wave, A — a0 cos (<£ — a) applies to the sine wave only. The general alternating wave, however, contains an in- finite series of terms, of odd frequencies, A = Al cos (<£ — #1) 4- Az cos (3 <£ — #3) + A& cos (5 <£ — ...Chapter 21: Regulating Pole Converters - 91 hit(s)
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... etween the eiuimjuia- tor brushes and the resultant magnetic flux, so that the direct voltage between the brushes is not the maximum diametrical alternating voltage but only a part thereof. Or by changing the maximum diametrical alternating voltage, at constant effective impressed voltage, by wave-shape distortion by the superposition of liigher harmonics. In the former case, only a reduction of the direct voltage lx*- low the normal value can lie produced, while in the latter case an increase as well as a reduction can be produced, an increase if the higher harmonies are in phase, and a red ...... gnetic flux, so that the direct voltage between the brushes is not the maximum diametrical alternating voltage but only a part thereof. Or by changing the maximum diametrical alternating voltage, at constant effective impressed voltage, by wave-shape distortion by the superposition of liigher harmonics. In the former case, only a reduction of the direct voltage lx*- low the normal value can lie produced, while in the latter case an increase as well as a reduction can be produced, an increase if the higher harmonies are in phase, and a reduction if the higher harmonics are in opposition to t ...Chapter 14: Constant-Potential Constant-Current Trans Formation - 91 hit(s)
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CHAPTER XIV CONSTANT-POTENTIAL CONSTANT-CURRENT TRANS- FORMATION 127. The generation of alternating-current electric power prac- tically always takes place at constant voltage. For some pur- poses, however, as for operating series arc circuits, and to a lim- ited extent also for electric furnaces, a constant, or approximately constant alternating current is required. While constant alter- nating-cur ...... ENT TRANS- FORMATION 127. The generation of alternating-current electric power prac- tically always takes place at constant voltage. For some pur- poses, however, as for operating series arc circuits, and to a lim- ited extent also for electric furnaces, a constant, or approximately constant alternating current is required. While constant alter- nating-current arcs have largely come out of use and their place taken by constant direct-current luminous arc circuits, or incan- descent lamps, the constant direct current is usually derived by rectification of constant alternating-current supply circuits. ...Chapter 27: Symbolic Representation Of General Alternating Waves - 83 hit(s)
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CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of terms, of odd frequencies, A = Aic ...CHAPTER XXVII SYMBOLIC REPRESENTATION OF GENERAL ALTERNATING WAVES 259. The vector representation, A — a'^ -{- ja^'^ = a (cos d -\- j sin 6) of the alternating wave, A = tto cos {(f) — 6) apphes to the sine wave only. The general alternating wave, however, contains an infinite series of terms, of odd frequencies, A = Aicos( 0- ^i) + ^3 cos (3 (^ - 63) + As cos (5 <^ - ...Chapter 7: Shaping Of Waves : General - 81 hit(s)
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CHAPTER VII SHAPING OF WAVES : GENERAL 69. In alternating-current engineering, the sine wave, as shown in Fig. 46, is usually aimed at as the standard. This is not duo to any inherent merit of the sine wave. For all those pm-poses, where the energy developed by the cur- rent in a resistance is the object, as for incandescent lighting, heating, etc., any wav ...... ^vke Fig. 47, when impressed upon a transformer, would give a ^^^ed wave of magnetism and thereby an increased hyHteresis Ill 112 ELECTRIC CIRCUITS The advantage of the sine wave is, that it remains unch&nged in shape under most conditions, while this is not the case with any- other wave shape, and any other wave shape thus introduces the danger, that under certain conditions, or in certain parts of the circuit, it may change to a shape which is undesirable or even Figs. 46 to 49. dangerous. Voltage, e, and current, i, are related to each other \>y proportionality, by differentia ...Chapter 1: The General Number - 74 hit(s)
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... C we are again 2 steps distant from the starting point, just as in Fig. 2. That is, 5-3 = 2 (Fig. 2), 5-7 = 2 (Fig. 3). In the case where we can subtract 7 from 5, we get the same distance from the starting point as when we subtract 3 from 5, 4 ENGINEERING MATHEMATICS. but the distance AC in Fig. 3, while the same, 2 steps, as in Fig. 2, is different in character, the one is toward the left, the other toward the right. That means, we have two kinds of distance units, those to the right and those to the left, and have to find some way to distinguish them. The distance 2 in Fig. ...... nd some way to distinguish them. The distance 2 in Fig. 3 is toward the left of the starting point A, that is, in that direction, in which we step when subtracting, and it thus appears natural to distinguish it from the distance 2 in Fig. 2, by calling the former— 2, while we call the distance AC in Fig. 2: +2, since it is in the direction from A, in which we step in adding. This leads to a subdivision of the system of absolute numbers, 1, 2, 3, . . . into two classes, positive numbers, + 1, +2, +3, ...: and negative numbers, -1,-2, -3, ...; and by the introduction of negative ...Chapter 16: Induction Motor - 68 hit(s)
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CHAPTER XVI. INDUCTION MOTOR. 151. A specialization of the general alternating-current transformer is the induction motor. It differs from the stationary alternating-current transformer, which is also a specialization of the general transformer, in so far as in the stationary transformer only the transfer of electrical energy from primary to secondary is used, but not the mechan ...CHAPTER XVI. INDUCTION MOTOR. 151. A specialization of the general alternating-current transformer is the induction motor. It differs from the stationary alternating-current transformer, which is also a specialization of the general transformer, in so far as in the stationary transformer only the transfer of electrical energy from primary to secondary is used, but not the mechanical force acting between the two, and therefore primary and secondary coils are held r ...Lecture 6: Higher Harmonics Of The Generator Wave - 65 hit(s)
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SIXTH LECTURE HIGHER HARMONICS OF THE GENERATOR WAVE mHE open circuit reactance of the transformer is the only reactance high enough to give resonance with the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance de ...... the line capacity at fundamental frequency. All other reactances are too low for this. Since, however, the inductive reactance increases and the capacity reactance decreases proportionally to the frequency, the two reactances come nearer together for higher frequency; that is, for the higher harmonics of the generator wave, and for some of the higher harmonics of the generator wave resonance rise of voltage so may occur between the line capacity and the circuit inductance. The origin and existence of higher harmonics therefore bears investigation in transformers, transmlission lines and c ...Chapter 7: Higher Harmonics In Induction Motors - 65 hit(s)
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CHAPTER VII HIGHER HARMONICS IN INDUCTION MOTORS 88. The usual theory and calculation of induction motors, .■is discussed in '* Theoretical Elements of Electrical Enginccr- ing" and in "Theory and Calculation of Alternating-current Phenomena," is based on the assumption of the sine wave. That U, it is assumed that the vo ...CHAPTER VII HIGHER HARMONICS IN INDUCTION MOTORS 88. The usual theory and calculation of induction motors, .■is discussed in '* Theoretical Elements of Electrical Enginccr- ing" and in "Theory and Calculation of Alternating-current Phenomena," is based on the assumption of the sine wave. That U, it is assumed that the voltage impressed upon the motor per phase, and therefore the magnetic flux and the current, KM sine waves, and it is further assumed, that the distribution of the winding on the circumference of the armatu ...Chapter 4: Induction Motor With Secondary Excitation - 62 hit(s)
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CHAPTER IV INDUCTION MOTOR WITH SECONDARY EXCITATION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, 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 always lagging, the more so, the larger a part o ...... TION 38. While in the typical synchronous machine and eommu- tating machine the magnetic field is excited by a direct current, 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 always lagging, the more so, the larger a part of the total current is given by the magnetizing current. To secure good power-fact ...Chapter 23: Effects Of Higher Harmonics - 61 hit(s)
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CHAPTER XXIII. EFFECTS OF HIGHER HARMONICS. 244. To elucidate the variation in the shape of alternat- ing waves caused by various harmonics, in Figs. 175 and Fig. 175. Effect of Triple Harmonic. 176 are shown the wave-forms produced by the superposi- tion of the triple and the quintuple harmonic upon the fundamental sine wave. ...CHAPTER XXIII. EFFECTS OF HIGHER HARMONICS. 244. To elucidate the variation in the shape of alternat- ing waves caused by various harmonics, in Figs. 175 and Fig. 175. Effect of Triple Harmonic. 176 are shown the wave-forms produced by the superposi- tion of the triple and the quintuple harmonic upon the fundamental sine wave. EFFECTS OF HIGHER HARMONICS. 399 In Fig. 175 is shown the fundamental sine wave and the complex ...Chapter 26: Effects Of Higher Harmonics - 59 hit(s)
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CHAPTER XXVI EFFECTS OF HIGHER HARMONICS 251. To elucidate the variation in the shape of alternating waves caused by various harmonics, in Figs. 185 and 186 are shown the wave-forms produced by the superposition of the P44S4t 4i' Fig. 185. triple and the quintuple harmonic upon the fundamental sine wave. In Fig. 185 is s ...CHAPTER XXVI EFFECTS OF HIGHER HARMONICS 251. To elucidate the variation in the shape of alternating waves caused by various harmonics, in Figs. 185 and 186 are shown the wave-forms produced by the superposition of the P44S4t 4i' Fig. 185. triple and the quintuple harmonic upon the fundamental sine wave. In Fig. 185 is shown the fundamental sine wave and the com- plex waves produced by the superposition of a triple ...Chapter 22: Distortion Of Wave-Shape And Its Causes - 58 hit(s)
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CHAPTER XXII. DISTORTION OF WAVE-SHAPE AND ITS CAUSES. 233. In the preceding chapters we have considered the alternating currents and alternating E.M.Fs. as sine waves or as replaced by their equivalent sine waves. While this is sufficiently exact in most cases, under certain circumstances the deviation of the wave from sine sha ...... nt of the equivalent sine wave becomes indefinite. Thus it becomes desirable to investigate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be represented by a series of sine functions of odd orders, the investigation of distortion of wave-shape resolves itself in the investigation of the higher harmonics of the alternating wave. In general we have to distinguish between higher har- monics of E.M.F. and higher harmonics of current. Both depend upon each other in so far as with a sine wave of impressed E.M.F. a distorting effect will ...Chapter 4: Vector Representation - 56 hit(s)
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CHAPTER IV VECTOR REPRESENTATION 16. While alternating waves can be, and frequently are, rep- resented graphically in rectangular coordinates, with the time as abscissae, and the instantaneous values of the wave as ordinates, the best insight with regard to the mutual relation of different alternating waves is ...... ating waves can be, and frequently are, rep- resented graphically in rectangular coordinates, with the time as abscissae, and the instantaneous values of the wave as ordinates, the best insight with regard to the mutual relation of different alternating waves is given by their representation as vectors, in the so-called crank diagram. A vector, equal in length to the maximum value of the alternating wave, revolves at uniform speed so as to make a complete revolution per period, and the pro- jections of this revolving vector on the horizontal then denote the instantaneous values of the wave. ...Chapter 20: Ri - 53 hit(s)
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CHAPTER XXri. XFFBCTB OF HIOHXilt BAAHONICS. 223. To elucidate the variation in the shape of alternat- ing waves caused by various harmonics, in Figs. 159 and rig. reo. £jr«t •/ wp/. ho™ 160 are shown the wave-forms produced by the superposi- tion of the triple and the quintuple harmonic upon the fimdamental sine wave. § 223] EFFECTS OF JIIGHER HARMONICS. 335 In Fig. 159 is shown the fundamental sine wave and the co ...CHAPTER XXri. XFFBCTB OF HIOHXilt BAAHONICS. 223. To elucidate the variation in the shape of alternat- ing waves caused by various harmonics, in Figs. 159 and rig. reo. £jr«t •/ wp/. ho™ 160 are shown the wave-forms produced by the superposi- tion of the triple and the quintuple harmonic upon the fimdamental sine wave. § 223] EFFECTS OF JIIGHER HARMONICS. 335 In Fig. 159 is shown the fundamental sine wave and the complex waves produced by the superposition of a triple harmonic of 30 per cent the amplitude of the fundamental, under the relative phase displacements of ...Chapter 24: Synchronous Motor - 51 hit(s)
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... 01 of the polar diagram. (Fig. 145.) Ji I = i = current, and Z = impedance, r = effective resist- ance, X = effective reactance, and z = \/r^ -{- x^ = absolute value of impedance, then the e.m.f. consumed by the resistance is £'11 = ri, and is in phase with the current; hence represented by vector OEn] and the e.m.f. consumed by the reactance is E2 = xi, and 90° ahead of the current; hence the e.m.f. consumed 301 302 ALTERNATING-CURRENT PHENOMENA by the impedance hE = ViEuY" + (£'2)^ or = i -s/r"^ -\- x- = iz, X and ahead of the current by the angle 8, where tan 8 = ~. We have ...... nd z = \/r^ -{- x^ = absolute value of impedance, then the e.m.f. consumed by the resistance is £'11 = ri, and is in phase with the current; hence represented by vector OEn] and the e.m.f. consumed by the reactance is E2 = xi, and 90° ahead of the current; hence the e.m.f. consumed 301 302 ALTERNATING-CURRENT PHENOMENA by the impedance hE = ViEuY" + (£'2)^ or = i -s/r"^ -\- x- = iz, X and ahead of the current by the angle 8, where tan 8 = ~. We have now acting in circuit the e.m.fs., E, Ei, E^; or Ei and E are components of E^, that is, E^i is the diagonal of a parallelo- gram, with El and E a ...Chapter 19: Alternating- Current Motors In General - 47 hit(s)
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CHAPTER XIX ALTERNATING- CURRENT MOTORS IN GENERAL 171. The starting point of the theory of the polyphase and single-phase induction motor usually is the general alternating- current transformer. Coining, however, to the commutator motors, this method becomes less suitable, and the following more general method preferable. ...CHAPTER XIX ALTERNATING- CURRENT MOTORS IN GENERAL 171. The starting point of the theory of the polyphase and single-phase induction motor usually is the general alternating- current transformer. Coining, however, to the commutator motors, this method becomes less suitable, and the following more general method preferable. In its general form the alternating-current motor consists of one or more stationary electric circuits magnetically related to one or more rotating ele ...Theory Section 9: Vector Diagrams - 45 hit(s)
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9. VECTOR DIAGRAMS 42. The best way of graphically representing alternating-cur- rent phenomena is by a vector diagram. The most frequently used vector diagram is the crank diagram. In this, sine waves of alternating currents, voltages, etc., are represented as pr ...9. VECTOR DIAGRAMS 42. The best way of graphically representing alternating-cur- rent phenomena is by a vector diagram. The most frequently used vector diagram is the crank diagram. In this, sine waves of alternating currents, voltages, etc., are represented as projec- tions of a revolving vector on the horizontal. That is, a vector equal in length to the ma ...Chapter 21: Dibtobtiox Of Wavs-Shafe And Its Causes - 45 hit(s)
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... nt of the equivalent sine wave becomes indefinite. Thus it becomes desirable to investigate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be represented by a series of sine functions of odd orders, the investigation of distortion of wave-shape resolves itself in the investigation of the higher harmonics of the alternating wave. In general we have to distinguish between higher har- monic^ of E.M.F. and higher harmonics of current. Both depend upon each other in so far as with a sine wave of impressed E.M.F. a distorting effect will ...... comes desirable to investigate the distortion of the wave, its causes and its effects. Since, as stated before, any alternating wave can be represented by a series of sine functions of odd orders, the investigation of distortion of wave-shape resolves itself in the investigation of the higher harmonics of the alternating wave. In general we have to distinguish between higher har- monic^ of E.M.F. and higher harmonics of current. Both depend upon each other in so far as with a sine wave of impressed E.M.F. a distorting effect will cause distortion of the current wave, while with a sine wave ...Chapter 12: Frequency Converter Or General Alternating Current Transformer - 44 hit(s)
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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 ...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 corresponding amount of electric power is produced; or i ...Chapter 23: Review - 42 hit(s)
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... d most extensively used arc machines were: Brush Arc Machine. — 141-144. A quarter-phase constant- current alternator with rectifying commutators. Thomson-Houston Arc Machine. — 141-144. A three-phase F-connected constant-current alternator with rectifying commu- tator. The development of alternating-current series arc lighting by constant-current transformers greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting returned to direct current, the development of the mercury-arc rectifier superseded the arc machine. Asynchronous Motor. — Name used for all thos ...... lighting by constant-current transformers greatly reduced the importance of the arc machine, and when in the magnetite lamp arc lighting 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 APPARATUS Brush Arc Machine. — (Sec1 "Are Machines.'1} Compound Alternator. — 138. Alternator with rectifying ...Chapter 12: Effective Resistance And Reactance - 39 hit(s)
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... The resistance of an electric circuit is determined : 1. By direct comparison with a known resistance (Wheat- stone bridge method, etc.). This method gives what may be called the true ohmic resist- ance of the circuit. 2. By the ratio: Volts consumed in circuit Amperes in circuit In an alternating-current circuit, this method gives, not the resistance of the circuit, but the impedance, z = \/f^ + x^. 3. By the ratio: Power consumed, (Current) 2 where, however, the "power" does not include the work done by the circuit, and the counter e.m.fs. representing it, as, for instance, in the case o ...... resistance of the circuit, but the impedance, z = \/f^ + x^. 3. By the ratio: Power consumed, (Current) 2 where, however, the "power" does not include the work done by the circuit, and the counter e.m.fs. representing it, as, for instance, in the case of the counter e.m.f. of a motor. In alternating-current circuits, this value of resistance is the power coefficient of the e.m.f.. Power component 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 ...Chapter 17: The Alternating-Current Transformer - 39 hit(s)
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CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. ...CHAPTER XVII THE ALTERNATING-CURRENT TRANSFORMER 141. The simplest alternating-current apparatus is the trans- former. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed e.m.f., while in the secondary circuit an e.m.f. is generated. Thus, in the primary circuit power is consumed, and ...Chapter 18: Oscillating Currents - 39 hit(s)
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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; and is called a pulsating cur- rent if the arithmetic mean value differs from zero. Assuming the wave as a sine curve, or replacing it by the equivalent sine wave, the alternating current is characterized by the period or the time of one complete cycl ...... n equal time intervals repeating the same values — is called an alternating current if the arithmetic mean value equals zero; and is called a pulsating cur- rent if the arithmetic mean value differs from zero. Assuming the wave as a sine curve, or replacing it by the equivalent sine wave, the alternating current is characterized by the period or the time of one complete cyclic change, and the amplitude or the maximum value of the current. Period and amplitude are constant in the alternating current. A very important class are the currents of constant period, but geometrically varying amplitude; that ...Chapter 14: The Alternating-Current Transformer - 38 hit(s)
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CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thu ...CHAPTER XIV. THE ALTERNATING-CURRENT TRANSFORMER. 126. The simplest alternating-current apparatus is the transformer. It consists of a magnetic circuit interlinked with two electric circuits, a primary and a secondary. The primary circuit is excited by an impressed E.M.F., while in the secondary circuit an E.M.F. is induced. Thus, in the primary circuit power is consumed, and in ...Chapter 2: Long-Distance Transmission Line - 38 hit(s)
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... e, or by condensers in the middle and at the two ends of the line, the former of four times the capacity of either of the two latter (the first approximation giving linear, the second a para- bolic distribution). For further investigation of these approximations see "Theory and Calculation of Alternating-Current Phenomena/' 4th edition, pages 225 to 233. If, however, the wave of impressed e.m.f. contains appreciable higher harmonics, some of the latter, may approach resonance frequency and thus cause trouble. For instance, with a line of 150 miles length, the resonance frequency is /0 = 313 cycles pe ...... he first approximation giving linear, the second a para- bolic distribution). For further investigation of these approximations see "Theory and Calculation of Alternating-Current Phenomena/' 4th edition, pages 225 to 233. If, however, the wave of impressed e.m.f. contains appreciable higher harmonics, some of the latter, may approach resonance frequency and thus cause trouble. For instance, with a line of 150 miles length, the resonance frequency is /0 = 313 cycles per second, or between the 5th harmonic and the 7th harmonic, 300 and 420 cycles of a 60-cycle system; fairly close to the 5th ...Chapter 37: Quarter-Phase System - 37 hit(s)
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... ad of the same phase displacement, nevertheless the system becomes unbalanced, and the two e.m.fs. at the end of the hne are neither equal in magnitude, nor in quadrature with each other. B. One Branch Loaded, One Unloaded Zi = Z2 = Z, Z -^• (a) Fi = 0, F2 = F, {b) Fi = Y, Y, = 0. 464 ALTERNATING-CURRENT PHENOMENA Substituting these values in (4), gives: (a) (b) 1 + YZ E\ = E 1 + V2 - i V2 i + rz^ + ^"2 V2 = ^ 1 = ^ I 1 1 + V2 + V2 YZ 2.414 + 1.414 E'2 = jE 1 1 + YZ = jE 1 + \/2 V~2 1 E\ = E 1 + 1.707 YZ 1 1 -\-YZ 1 + \/2 V2 ...... re balanced with regard to voltage and phase at equal distribution of load, but are liable to become unbalanced at unequal distribution of load; the three-wire, quarter-phase system is unbalanced in voltage and phase, even at equal dis- tribution of load. 30 APPENDIX ALGEBRA OF COMPLEX IMAGINARY QUANTITIES ("See Engineering Mathematics") INTRODUCTION 312. The system of numbers, of which the science of algebra treats, finds its ultimate origin in experience. Directly derived from experience, however, are only the absolute integral numbers; fractions, for instance, are not directly derived from ...