AC Theory Textbook PDF
Preview AC Theory Textbook
Sixth Edition, last update July 25, 2007 2 Lessons In Electric Circuits, Volume II – AC By Tony R. Kuphaldt Sixth Edition, last update July 25, 2007 i c⃝2000-2013, Tony R. Kuphaldt This book is published under the terms and conditions of the Design Science License. These terms and conditions allow for free copying, distribution, and/or modification of this document by the general public. The full Design Science License text is included in the last chapter. As an open and collaboratively developed text, this book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Design Science License for more details. Available in its entirety as part of the Open Book Project collection at: openbookproject.net/electricCircuits PRINTING HISTORY • First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer readability. • Second Edition: Printed in September of 2000. Illustrations reworked in standard graphic (eps and jpeg) format. Source files translated to Texinfo format for easy online and printed publication. • Third Edition: Equations and tables reworked as graphic images rather than plain-ASCII text. • Fourth Edition: Printed in November 2001. Source files translated to SubML format. SubML is a simple markup language designed to easily convert to other markups like LATEX, HTML, or DocBook using nothing but search-and-replace substitutions. • Fifth Edition: Printed in November 2002. New sections added, and error corrections made, since the fourth edition. • Sixth Edition: Printed in June 2006. Added CH 13, sections added, and error corrections made, figure numbering and captions added, since the fifth edition. ii Contents 1 BASIC AC THEORY 1 1.1 What is alternating current (AC)? . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 AC waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Measurements of AC magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Simple AC circuit calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 AC phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6 Principles of radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2 COMPLEX NUMBERS 27 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.2 Vectors and AC waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3 Simple vector addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 Complex vector addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5 Polar and rectangular notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Complex number arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.7 More on AC ”polarity” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.8 Some examples with AC circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3 REACTANCE AND IMPEDANCE – INDUCTIVE 57 3.1 AC resistor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.2 AC inductor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Series resistor-inductor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Parallel resistor-inductor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.5 Inductor quirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.6 More on the “skin effect” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4 REACTANCE AND IMPEDANCE – CAPACITIVE 81 4.1 AC resistor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 AC capacitor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.3 Series resistor-capacitor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Parallel resistor-capacitor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 iii iv CONTENTS 4.5 Capacitor quirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5 REACTANCE AND IMPEDANCE – R, L, AND C 99 5.1 Review of R, X, and Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2 Series R, L, and C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 5.3 Parallel R, L, and C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.4 Series-parallel R, L, and C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.5 Susceptance and Admittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 5.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6 RESONANCE 121 6.1 An electric pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.2 Simple parallel (tank circuit) resonance . . . . . . . . . . . . . . . . . . . . . . . . 126 6.3 Simple series resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 6.4 Applications of resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 6.5 Resonance in series-parallel circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6.6 Q and bandwidth of a resonant circuit . . . . . . . . . . . . . . . . . . . . . . . . 145 6.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 7 MIXED-FREQUENCY AC SIGNALS 153 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 7.2 Square wave signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 7.3 Other waveshapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.4 More on spectrum analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.5 Circuit effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 7.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 8 FILTERS 189 8.1 What is a filter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8.2 Low-pass filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 8.3 High-pass filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.4 Band-pass filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 8.5 Band-stop filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 8.6 Resonant filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 8.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 8.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 9 TRANSFORMERS 217 9.1 Mutual inductance and basic operation . . . . . . . . . . . . . . . . . . . . . . . . 218 9.2 Step-up and step-down transformers . . . . . . . . . . . . . . . . . . . . . . . . . 232 9.3 Electrical isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 9.4 Phasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 9.5 Winding configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 9.6 Voltage regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248 CONTENTS v 9.7 Special transformers and applications . . . . . . . . . . . . . . . . . . . . . . . . . 251 9.8 Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268 9.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 10 POLYPHASE AC CIRCUITS 283 10.1 Single-phase power systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 10.2 Three-phase power systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 10.3 Phase rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 10.4 Polyphase motor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 10.5 Three-phase Y and Delta configurations . . . . . . . . . . . . . . . . . . . . . . . . 306 10.6 Three-phase transformer circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 10.7 Harmonics in polyphase power systems . . . . . . . . . . . . . . . . . . . . . . . . 318 10.8 Harmonic phase sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 10.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 11 POWER FACTOR 347 11.1 Power in resistive and reactive AC circuits . . . . . . . . . . . . . . . . . . . . . . 347 11.2 True, Reactive, and Apparent power . . . . . . . . . . . . . . . . . . . . . . . . . . 352 11.3 Calculating power factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 11.4 Practical power factor correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 11.5 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 12 AC METERING CIRCUITS 367 12.1 AC voltmeters and ammeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 12.2 Frequency and phase measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 374 12.3 Power measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 12.4 Power quality measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 12.5 AC bridge circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 12.6 AC instrumentation transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 12.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 13 AC MOTORS 407 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408 13.2 Synchronous Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 13.3 Synchronous condenser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 13.4 Reluctance motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421 13.5 Stepper motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 13.6 Brushless DC motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 13.7 Tesla polyphase induction motors . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 13.8 Wound rotor induction motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 13.9 Single-phase induction motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464 13.10 Other specialized motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 13.11 Selsyn (synchro) motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 13.12 AC commutator motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 vi CONTENTS Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 14 TRANSMISSION LINES 483 14.1 A 50-ohm cable? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 14.2 Circuits and the speed of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 14.3 Characteristic impedance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 14.4 Finite-length transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 14.5 “Long” and “short” transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . 499 14.6 Standing waves and resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 14.7 Impedance transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 14.8 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 529 A-1 ABOUT THIS BOOK 537 A-2 CONTRIBUTOR LIST 541 A-3 DESIGN SCIENCE LICENSE 549 INDEX 552 Chapter 1 BASIC AC THEORY Contents 1.1 What is alternating current (AC)? . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 AC waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Measurements of AC magnitude . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Simple AC circuit calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 AC phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6 Principles of radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.1 What is alternating current (AC)? Most students of electricity begin their study with what is known as direct current (DC), which is electricity flowing in a constant direction, and/or possessing a voltage with constant polarity. DC is the kind of electricity made by a battery (with definite positive and negative terminals), or the kind of charge generated by rubbing certain types of materials against each other. As useful and as easy to understand as DC is, it is not the only “kind” of electricity in use. Certain sources of electricity (most notably, rotary electro-mechanical generators) naturally produce voltages alternating in polarity, reversing positive and negative over time. Either as a voltage switching polarity or as a current switching direction back and forth, this “kind” of electricity is known as Alternating Current (AC): Figure 1.1 Whereas the familiar battery symbol is used as a generic symbol for any DC voltage source, the circle with the wavy line inside is the generic symbol for any AC voltage source. One might wonder why anyone would bother with such a thing as AC. It is true that in some cases AC holds no practical advantage over DC. In applications where electricity is used to dissipate energy in the form of heat, the polarity or direction of current is irrelevant, so long as there is enough voltage and current to the load to produce the desired heat (power dissipation). However, with AC it is possible to build electric generators, motors and power 1 2 CHAPTER 1. BASIC AC THEORY I I DIRECT CURRENT (DC) ALTERNATING CURRENT (AC) I I Figure 1.1: Direct vs alternating current distribution systems that are far more efficient than DC, and so we find AC used predominately across the world in high power applications. To explain the details of why this is so, a bit of background knowledge about AC is necessary. If a machine is constructed to rotate a magnetic field around a set of stationary wire coils with the turning of a shaft, AC voltage will be produced across the wire coils as that shaft is rotated, in accordance with Faraday’s Law of electromagnetic induction. This is the basic operating principle of an AC generator, also known as an alternator: Figure 1.2 N S + - Load I I N S Load no current! no current! Load N S N Load S - + I I Step #1 Step #2 Step #3 Step #4 Figure 1.2: Alternator operation 1.1. WHAT IS ALTERNATING CURRENT (AC)? 3 Notice how the polarity of the voltage across the wire coils reverses as the opposite poles of the rotating magnet pass by. Connected to a load, this reversing voltage polarity will create a reversing current direction in the circuit. The faster the alternator’s shaft is turned, the faster the magnet will spin, resulting in an alternating voltage and current that switches directions more often in a given amount of time. While DC generators work on the same general principle of electromagnetic induction, their construction is not as simple as their AC counterparts. With a DC generator, the coil of wire is mounted in the shaft where the magnet is on the AC alternator, and electrical connections are made to this spinning coil via stationary carbon “brushes” contacting copper strips on the rotating shaft. All this is necessary to switch the coil’s changing output polarity to the external circuit so the external circuit sees a constant polarity: Figure 1.3 Load N S N S - + + - I N S S N Load Step #1 Step #2 N S S N Load N S Load S N - - I + + Step #3 Step #4 Figure 1.3: DC generator operation The generator shown above will produce two pulses of voltage per revolution of the shaft, both pulses in the same direction (polarity). In order for a DC generator to produce constant voltage, rather than brief pulses of voltage once every 1/2 revolution, there are multiple sets of coils making intermittent contact with the brushes. The diagram shown above is a bit more simplified than what you would see in real life. The problems involved with making and breaking electrical contact with a moving coil should be obvious (sparking and heat), especially if the shaft of the generator is revolving at high speed. If the atmosphere surrounding the machine contains flammable or explosive 4 CHAPTER 1. BASIC AC THEORY vapors, the practical problems of spark-producing brush contacts are even greater. An AC gen- erator (alternator) does not require brushes and commutators to work, and so is immune to these problems experienced by DC generators. The benefits of AC over DC with regard to generator design is also reflected in electric motors. While DC motors require the use of brushes to make electrical contact with moving coils of wire, AC motors do not. In fact, AC and DC motor designs are very similar to their generator counterparts (identical for the sake of this tutorial), the AC motor being dependent upon the reversing magnetic field produced by alternating current through its stationary coils of wire to rotate the rotating magnet around on its shaft, and the DC motor being dependent on the brush contacts making and breaking connections to reverse current through the rotating coil every 1/2 rotation (180 degrees). So we know that AC generators and AC motors tend to be simpler than DC generators and DC motors. This relative simplicity translates into greater reliability and lower cost of manufacture. But what else is AC good for? Surely there must be more to it than design details of generators and motors! Indeed there is. There is an effect of electromagnetism known as mutual induction, whereby two or more coils of wire placed so that the changing magnetic field created by one induces a voltage in the other. If we have two mutually inductive coils and we energize one coil with AC, we will create an AC voltage in the other coil. When used as such, this device is known as a transformer: Figure 1.4 Transformer AC voltage source Induced AC voltage Figure 1.4: Transformer “transforms” AC voltage and current. The fundamental significance of a transformer is its ability to step voltage up or down from the powered coil to the unpowered coil. The AC voltage induced in the unpowered (“secondary”) coil is equal to the AC voltage across the powered (“primary”) coil multiplied by the ratio of secondary coil turns to primary coil turns. If the secondary coil is powering a load, the current through the secondary coil is just the opposite: primary coil current multiplied by the ratio of primary to secondary turns. This relationship has a very close mechanical analogy, using torque and speed to represent voltage and current, respectively: Figure 1.5 If the winding ratio is reversed so that the primary coil has less turns than the secondary coil, the transformer “steps up” the voltage from the source level to a higher level at the load: Figure 1.6 The transformer’s ability to step AC voltage up or down with ease gives AC an advantage unmatched by DC in the realm of power distribution in figure 1.7. When transmitting electrical power over long distances, it is far more efficient to do so with stepped-up voltages and stepped- down currents (smaller-diameter wire with less resistive power losses), then step the voltage back down and the current back up for industry, business, or consumer use. Transformer technology has made long-range electric power distribution practical. Without 1.1. WHAT IS ALTERNATING CURRENT (AC)? 5 + + Large gear Small gear (many teeth) (few teeth) AC voltage source Load high voltage low current low voltage high current many turns few turns Speed multiplication geartrain "Step-down" transformer high torque low speed low torque high speed Figure 1.5: Speed multiplication gear train steps torque down and speed up. Step-down trans- former steps voltage down and current up. + + Large gear Small gear (many teeth) (few teeth) AC voltage source Load low voltage high current high voltage low current few turns many turns Speed reduction geartrain "Step-up" transformer low torque high speed high torque low speed Figure 1.6: Speed reduction gear train steps torque up and speed down. Step-up transformer steps voltage up and current down. Step-up Step-down Power Plant low voltage high voltage low voltage . . . to other customers Home or Business Figure 1.7: Transformers enable efficient long distance high voltage transmission of electric energy. 6 CHAPTER 1. BASIC AC THEORY the ability to efficiently step voltage up and down, it would be cost-prohibitive to construct power systems for anything but close-range (within a few miles at most) use. As useful as transformers are, they only work with AC, not DC. Because the phenomenon of mutual inductance relies on changing magnetic fields, and direct current (DC) can only produce steady magnetic fields, transformers simply will not work with direct current. Of course, direct current may be interrupted (pulsed) through the primary winding of a transformer to create a changing magnetic field (as is done in automotive ignition systems to produce high-voltage spark plug power from a low-voltage DC battery), but pulsed DC is not that different from AC. Perhaps more than any other reason, this is why AC finds such widespread application in power systems. • REVIEW: • DC stands for “Direct Current,” meaning voltage or current that maintains constant po- larity or direction, respectively, over time. • AC stands for “Alternating Current,” meaning voltage or current that changes polarity or direction, respectively, over time. • AC electromechanical generators, known as alternators, are of simpler construction than DC electromechanical generators. • AC and DC motor design follows respective generator design principles very closely. • A transformer is a pair of mutually-inductive coils used to convey AC power from one coil to the other. Often, the number of turns in each coil is set to create a voltage increase or decrease from the powered (primary) coil to the unpowered (secondary) coil. • Secondary voltage = Primary voltage (secondary turns / primary turns) • Secondary current = Primary current (primary turns / secondary turns) 1.2 AC waveforms When an alternator produces AC voltage, the voltage switches polarity over time, but does so in a very particular manner. When graphed over time, the “wave” traced by this voltage of alternating polarity from an alternator takes on a distinct shape, known as a sine wave: Figure 1.8 In the voltage plot from an electromechanical alternator, the change from one polarity to the other is a smooth one, the voltage level changing most rapidly at the zero (“crossover”) point and most slowly at its peak. If we were to graph the trigonometric function of “sine” over a horizontal range of 0 to 360 degrees, we would find the exact same pattern as in Table 1.1. The reason why an electromechanical alternator outputs sine-wave AC is due to the physics of its operation. The voltage produced by the stationary coils by the motion of the rotating magnet is proportional to the rate at which the magnetic flux is changing perpendicular to the coils (Faraday’s Law of Electromagnetic Induction). That rate is greatest when the magnet poles are closest to the coils, and least when the magnet poles are furthest away from the coils.
The list of books you might like
