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Summary of Equations to Accompany INTRODUCTORY CIRCUIT ANALYSIS, Eleventh Edition, by Robert L. Boylestad © Copyright 2007 by Prentice Hall. All Rights Reserved. dc Introduction 12 Conversions 1 meter 100 cm 39.37 in., 1 in. 2.54 cm, C Q/V eA/d 8.85 10 er A/d farads (F), 1 yd 0.914 m 3 ft, 1 mile 5280 ft, °F 9/5°C 32, °C C erCo Electric field strength V/d Q/eA (/meter) 12 t/t t/t 5/9(°F 32), K 273.15 °C Scientific notation 10 Transients (charging) iC (E/R)e , t RC, uC E(1 e ), 9 6 3 3 t/t t/RC tera T, 10 giga G, 10 mega M, 10 kilo k, 10 (discharge) uC Ee , iC (E/R)e iC iCav C(DuC /Dt) 6 9 12 milli m, 10 micro m, 10 nano n, 10 pico p Series QT Q1 Q2 Q3, 1/CT (1/C1) (1/C2) (1/C3) n n n n n m nm Powers of ten 1/10 10 , 1/10 10 , (10 )(10 ) 10 , (1/CN), CT C1C2/(C1 C2) Parallel QT Q1 Q2 Q3, n m nm n m nm 2 10 /10 10 , (10 ) 10 CT C1 C2 C3 Energy WC (1/2)CV and Current 2 9 2 2 2 Coulomb’s law F kQ1Q2/r , k 9 10 Nm /C , Self- L N mA/l (henries), L mr Lo Q coulombs (C), r meters (m) Current I Q/t (), Induced voltage eLav L(Di/Dt) Transients (storage) iL 19 t/t t/t t seconds (s), Qe 1.6 10 C Voltage V W/Q (volts), Im(1 e ), Im E/R, t L/R, uL Ee (decay), uL t/t ′ t/t ′ W joules (J) [1 (R2/R1)]Ee , t′ L/(R1 R2), iL Ime , Im E/R1 Series LT L1 L2 L3 LN Parallel 1/LT (1/L1) Resistance (1/L2) (1/L3) (1/LN), LT L1L2/(L1 L2) 2 Circular wire R rl/A (), r resistivity, l feet, Energy WL 1/2(LI ) 2 2 ACM (dmils) , r(Cu) 10.37 Metric units l cm, A cm , 6 Magnetic Circuits r(Cu) 1.724 10 -cm Temperature (T T1)/R1 2 ( T T2)/R2, R1 R20[1 a20(T1 20°C)], a20(Cu) 0.00393 Flux density B F/A (webers/m ) Permeability m mrmo Color code Bands 1–3: 0 black, 1 brown, 2 red, 3 orange, (Wb/Am) Reluctance l/mA (rels) Ohm’s law F / 4 yellow, 5 green, 6 blue, 7 violet, 8 gray, 9 white, (webers) Band 3: 0.1 gold, 0.01 silver, Band 4: 5% gold, 10% silver, Magnetomotive force NI (-turns) Magnetizing 20% no band, Band 5: 1% brown, 0.1% red, 0.01% orange, force H /l NI/l Ampère’s circuital law 0 0.001% yellow Conductance G 1/R siemens (S) 5 Flux Fentering Fleaving Air gap Hg 7.96 10 Bg Ohm’s Law, Power, and Energy Ohm’s law I E/R, E IR, R E/I Power P W/t VI I 2R V 2/R (watts), 1 hp 746 W Greek Alphabet Efficiency h% (Po /Pi) 100%, hT h1 h2 h3 hn Energy W Pt, W (kWh) [P(W) t(h)]/1000 Letter Capital Lowercase Letter Capital Lowercase

Series Circuits Alpha AaNu Nn

RT R1 R2 R3 RN, RT NR, I E/RT, V IR Beta BbXi Yy Kirchhoff’s voltage law V 0, Vrises Vdrops Gamma GgOmicron Oo rule Vx RxE/RT Delta DdPi Pp Parallel dc Circuits Epsilon EeRho Rr Zeta ZzSigma j RT 1/(1/R1 1/R2 1/R3 1/RN), RT R/N, Eta HhTau Tt R R R R R I EG E/R T 1 2/( 1 2), T T Theta VvUpsilon Uu Kirchhoff’s current law I I entering leaving Iota IiPhi Ff Current divider rule I (R /R )I, (Two parallel elements): x T x Kappa KkChi Xx I1 R2I/(R1 R2), I2 R1I/(R1 R2) Lambda LlPsi Ww Series-Parallel Circuits Mu M m Omega q

Potentiometer loading RL >> RT Ammeter Rshunt RmICS /(Imax ICS) Voltmeter Rseries (Vmax VVS)/ICS Prefixes Ohmmeter Rs (E/ICS) Rm zero-adjust/2 Methods of Analysis and Selected Topics (dc) Multiplication SI SI Factors Prefix Symbol Source conversions E IRp, Rs Rp, I E/Rs a b 18 Determinants D 1 1 a b a b 1 000 000 000 000 000 000 10 exa E ⏐⏐a b 1 2 2 1 2 2 1 000 000 000 000 000 1015 peta P ′ Bridge networks R1/R3 R2/R4 -Y conversions R 1 000 000 000 000 1012 tera T R R R , R R R /R′, R R R /R′, R R R /R′, R R /3 A B C 3 A B 2 A C 1 B C Y D 1 000 000 000 109 giga G Y- conversions R″ R R R R R R , R R″/R , R R″/R , 1 2 1 3 2 3 C 3 B 2 1 000 000 106 mega M RA R″/R1, RD 3RY 1 000 103 kilo k Network Theorems 0.001 103 milli m 6 Superposition Voltage sources (short-circuit equivalent), current 0.000 001 10 micro M sources (open-circuit equivalent) 0.000 000 001 10 9 nano n 12 Thévenin’s Theorem RTh: (all sources to zero), ETh: (open-circuit 0.000 000 000 001 10 pico p terminal voltage) 0.000 000 000 000 001 1015 femto f 18 Maximum power transfer theorem RL RTh RN, Pmax 2 2 0.000 000 000 000 000 001 10 atto a E Th /4RTh IN RN /4 boy30444_formulacard.qxd 3/24/06 2:04 PM Page 2

Summary of Equations to Accompany INTRODUCTORY CIRCUIT ANALYSIS, Eleventh Edition, by Robert L. Boylestad © Copyright 2007 by Prentice Hall. All Rights Reserved. ac

2 2 Sinusoidal Alternating Waveforms R-C filters (high-pass) fc 1/(2pRC), Vo /Vi R/RXC tan1(X /R) (low-pass) f 1/(2pRC), V /V X /R2 X2 Sine wave u Vm sin a, a qt 2pft, f 1/T, 1 radian 57.3°, C c o i C C R radians (p/180°) (degrees), degrees (180°/p) (radians) tan 1 Identities sin(qt 90°) cos qt, sin qt cos[qt (p/2)], XC sin(a) sin a, cos(a) cos a Average value G Octave 2 1, 6 dB/octave Decade 10 1, 20 dB/decade algebraic sum of areas/length of curve Effective (rms) value Irms 0.707Im, Im 2Irms, 2 Irms area[i(t)]/T Mutual inductance M k LpLs Iron-core Ep 4.44fNpFm, Es 4.44fNsFm, Ep /Es Np /Ns, a Np /Ns, Ip /Is Ns/Np, The Basic Elements and 2 Zp a ZL, Ep Ip Es Is, Pi Po(ideal) 2 R: Im Vm /R, in phase L: XL qL, uL leads iL by 90° Air-core Zi Zp [qM) /(Zs ZL)] C: XC 1/qC, iC leads uC by 90° Power P (Vm Im /2) cos v Polyphase Systems V I cos v R: P V I I2 R V 2 /R Power rms rms rms rms rms rms factor F cos v P/V I Rectangular form C A jB Y-Y system Ifg IL IfL, Vf Ef, EL 3 Vf Y-D system p rms rms Polar form C Cv Conversions C A2 B2, v Vf EL, IL 3If D-D system Vf EL Ef, IL 3If 1 tan (B/A), A C cos v, B C sin v Operations j 1, D-Y system EL 3Vf, If IL, EL Ef Power PT 3Pf, 2 j 1, 1/j j, C1 C2 (A1 A2) j(B1 B2), QT 3Qf, ST 3Sf 3ELIL, Fp PT /ST C1 C2 C1C2 (v1 v2), C1/C2 (C1/C2) (v1 v2) Pulse Waveforms and the R-C Response

Series and Parallel ac Circuits % tilt [(V1 V2)/V] 100% with V (V1 V2)/2 Elements R X X Pulse repetition frequency (prf) 1/T 0°, L 90°, C 90° Duty cycle (tp/T) 100% Series ZT Z1 Z2 Z3 ZN, Is E/ZT, Fp R/ZT Vav (duty cycle)(peak value) (1 duty cycle) (Vb) Voltage divider rule Vx ZxE/ZT Parallel YT Y1 Y2 t/RC R-C circuits uC Vi (Vf Vi)(1 e ) Y3 YN, ZT Z1Z2/(Z1 Z2), G 0°, BL 90°, Compensated attenuator RpCp RsCs BC 90°, Fp cos vT G/YT Current divider rule I1 Z2IT/(Z1 Z2), I2 Z1IT /(Z1 Z2) Equivalent circuits Rs Nonsinusoidal Circuits 2 2 2 2 2 2 2 2 Rp Xp /(Xp Rp ), Xs Rp Xp/(Xp Rp ), Rp (Rs Xs )/Rs, Fourier series f(a) A0 A1 sin qt A2 sin 2qt 2 2 Xp (Rs Xs )/Xs An sin nqt B1 cos qt B2 cos 2qt Bn cos nqt Even function f(a) f(a), no B terms Odd function f(a) Series-Parallel ac Networks: n f(a), no An terms, no odd harmonics if f(t) f [(T/2) t], no even Employ block impedances and obtain general solution for reduced harmonics if f(t) f [(T/2) t] network. Then substitute numerical values. General approach similar Effective (rms) value V(rms) to that for dc networks. 2 2 2 ′2 ′2 V 0 (Vm1 V mn V m1 V mn)/2 2 2 Methods of Analysis and Selected Topics (ac) Power PT V0 I0 V1I1 cos v Vn In cos vn Irms R Vrms /R Source conversions E IZp, Zs Zp, I E/Zs Bridge Standard Values networks Z1/Z3 Z2/Z4 D-Y, Y-D conversions See dc coverage, replacing R by Z. Ohms Kilohms Megohms Network Theorems ()(k)(M) Review dc content on other side. 0.10 1.0 10 100 1000 10 100 1.0 10.0 Thévenin’s theorem (dependent sources) Eoc ETh, ZTh Eoc /Isc, Z E /I Norton’s theorem (dependent sources) I I , 0.11 1.1 11 110 1100 11 110 1.1 11.0 Th g g sc N 0.12 1.2 12 120 1200 12 120 1.2 12.0 ZN Eoc/Isc, ZN Eg/Ig Maximum power transfer theorem 2 0.13 1.3 13 130 1300 13 130 1.3 13.0 ZL ZTh, vL vTh , Pmax E Th/4RTh Z 0.15 1.5 15 150 1500 15 150 1.5 15.0 Power (ac) 0.16 1.6 16 160 1600 16 160 1.6 16.0 2 2 R: P VI VmIm /2 I R V /R Apparent power S VI, 0.18 1.8 18 180 1800 18 180 1.8 18.0 P S cos v, Fp cos v P/S Reactive power Q VI sin v 0.20 2.0 20 200 2000 20 200 2.0 20.0 2 2 2 2 L: QL VI I XL V /XL, C: QC VI I XC V /XC, 0.22 2.2 22 220 2200 22 220 2.2 22.0 2 2 ST PT Q T, Fp PT /ST 0.24 2.4 24 240 2400 24 240 2.4 Resonance 0.27 2.7 27 270 2700 27 270 2.7 0.30 3.0 30 300 3000 30 300 3.0 Series XL XC, fs 1/(2p LC), ZTs R, Ql XL/Rl, Qs XL/R 0.33 3.3 33 330 3300 33 330 3.3 (1/R) L/C, VLs QsE, VCs QsE, PHPF (1/2)Pmax, f1 2 0.36 3.6 36 360 3600 36 360 3.6 (1/2p)[R/2L (1/2)(R/L) 4/LC], f2 (use R/2L), BW f2 f1 2 2 0.39 3.9 39 390 3900 39 390 3.9 R/2pL f /Q Parallel X X , X (R X )/X , s s Lp C Lp l L L 0.43 4.3 43 430 4300 43 430 4.3 f [1/(2pLC)]1(R2C/L), Z R R , R (R2 X2)/R p l Tp s p p l L l 0.47 4.7 47 470 4700 47 470 4.7 Q (R R )X , BW f f f /Q Q 6 10: Z R Q2R , p s p LP 2 1 p p Tp s l 0.51 5.1 51 510 5100 51 510 5.1 X X , X X , f 1/(2pLC), Q Q , I I QI , Lp L L C p p l L C T 0.56 5.6 56 560 5600 56 560 5.6 BW f Q R pL p/ p l /2 0.62 6.2 62 620 6200 62 620 6.2 Decibels, Filters, and Bode Plots 0.68 6.8 68 680 6800 68 680 6.8 x 0.75 7.5 75 750 7500 75 750 7.5 Logarithms N b , x logb N, loge x 2.3 log10 x, log10 ab n log10a log10b, log10a/b log10a log10b, log10 a nlog10a, 0.82 8.2 82 820 8200 82 820 8.2 dB 10log10 P2/P1, dBu 20log10 V2/V1 0.91 9.1 91 910 9100 91 910 9.1 boy30444_indx.qxd 3/27/06 2:31 PM Page 1149

Index

A ampere, 3 applications (continued) absolute zero, 72-73 defined, 39-41 low-voltage compensation, 1018-19 ac circuits Ampère, André-Marie, 3-5, 40, 461 magnetic reed switch, 533-34 angular velocity, 548-59 Ampère’s circuital law, 461, 520-21 magnetic resonance imaging, 534 applications, 575-77 ampere-hour rating, 48-51 microwave oven, 116-18, 167-68 average value, 559-66 ampere-turns, 464 noise filters, 975-78 capacitance, 591-94 amplitude parallel computer bus connections, 228 complex numbers, 608-23 pulse waveform, 1068 parallel configurations, 223-28 computer analysis, 577-81, 628-32 sinusoidal waveform, 541 phase-shift power control, 695-97 definitions, 541-43, 546 analogies portable power generator, 859-61 effective value, 566-70 parallel elements, 194 safety concerns (high voltage and dc frequency, 542, 545-46 series elements, 134, 138 versus ac), 576-77 frequency response, 597-602 angular velocity, 548-49 schematic with nodal , 330-32 frequency spectrum, 543-46 anode, 47 series alarm circuit, 167-68 generation, 540-41 apparent power, 838-40, 1043, 1045-46 series control, 164-65 generator, 540 appendices speakers and microphones, 531-32, inductance, 590-91 conversion factors, 1120-22 692-95 instrumentation, 571-75 determinants, 1128-35 strain gauges, 94-95 introduction, 131, 539-81 Greek alphabet, 1136 stray resonance, 902 lagging, 555 magnetic parameter conversions, 1137 surge protector (line conditioner), leading, 555 maximum power transfer conditions, 446-49 oscilloscope, 558-59 1138-39 TV or PC monitor yolk, 496-99 parallel, 663-701 PSpice, Multisim, and Mathcad, TV remote, 1085-88 period, 542 1126-27 Wheatstone bridge smoke detector, phase relations, 554-59 solutions to selected odd-numbered 329-30 phasors, 623-28 exercises, 1140-47 Armstrong, Edwin, 6 power, 567, 603-7, 835-64 TI-86 calculator, 1123-25 atomic structure, 33-35, 64 power factor, 607-8 applications attenuators, 973-75 radians, 546-48 12 V car battery charger, 56-58 auditory response, 924-25 reactance, 591 (120 V at 60 Hz) versus (220 V at autotransformer, 1014 resistance, 589 50 Hz), 575-76 average induced voltage, 487-89 rms value, 570 attenuators, 973-75 average power, 603-7, 837, 1043-45 series, 637-63 ballast , 1019-21 average value series-parallel, 713-37 boosting a car battery, 269-72 fundamentals, 559-66 sinusoidal ac voltage, 540-43, 546-59 camera flash lamp, 493 nonsinusoidal waveforms, 1096-97 ac generator, 540 car system, 224-26 pulse waveforms, 1074-75 accuracy, 11, 23 constant current alarm system, 327-29 AWG, 67-69 active filter, 927 crossover networks, 972-73 admittance, 663-65 dimmer control in an automobile, B admittance diagram, 665 93-94 Babbage, Charles, 6 Ah rating, 48-51 electric baseboard heating element, Baird, John, 6 air gap, 525-27 90-93 balance conditions air trimmer , 411-12 electronic systems, 272-73, 816-20 ac networks, 765-69 air-core transformer, 1009-12 flash lamp, 443-46 dc networks, 321 alkaline battery, 42-43 flashlight, 54-56 ballast transformer, 1019-21 , 539 GFCI, 728-30 band frequencies alternator 224-25, 540 graphic and parametric equalizers, parallel resonance, 889-90 aluminum, 67 902-5 series resonance, 878-80 ammeter, 53-54, 200-201, 247-48, 258, sensor, 532-33 bandwidth 360-63 holiday lights, 165-67 parallel resonance, 889-91, 894 design 266-67 household dimmer switch, 494-96 series resonance, 878-80 loading effect, 161-62 household wiring, 118-20, 226-28, Bardeen, John, 6 series dc circuit, 139-40 691-92 base-line voltage, 1069 1149 boy30444_indx.qxd 3/27/06 2:31 PM Page 1150

1150 INDEX

battery, 38-39, 41-45, 55, 131-32, 142-43, ceramic trimmer capacitor, 412 contributors (continued) 214-15, 224-26 CGS system, 8-11 Watt, James, 106 Bednorz, George, 76 charger, 56-58 Weber, Wilhelm Eduard, 463 bel, 921-22 chassis ground, 725 controlled sources, 743-44 block diagram approach chip , 79-80 conventional flow, 41, 131-32 ac, 713-25 chokes, 473 conversion factors, Appendix A dc, 248-51 chopper network, 445 conversions Bode, Hendrick Wade, 944 Chu, Paul, 76 dc sources, 285-87 Bode plots, 943-72 circuit breakers, 115,119-20 dependent and independent sources, branch current analysis, 289-94 circular mils, 64-66 744-47 Brattain, Walter H., 6 clamp meter, 573 Cooper effect, 76 breadboard, 162-64, 222-23 closed loop, 144 copper, 34-35, 51, 67 breakdown strength, 52 coefficient of coupling, 990-92 core-type transformer, 1013-14 breakdown voltage, 403 coercive force, 517 corner frequency, 878-80 bridge networks coil See coulomb, 36-38, 397-98, 400-401, 439 ac, 764-69 color coding, 82-85 Coulomb, Charles Augustin, 4, 35 dc, 318-21 common logarithm, 918-20 Coulomb’s law, 35, 398 bubbles, 520 compensated attenuator probe, 1085 coupled coils, 1006-9 complex configurations, 243 critical temperature, 77 C complex conjugate, 612 crossover networks, 972-73 C++, 27 complex numbers, 608-23 current, 33, 38-41 Calculator See TI-86 or TI-89 addition, 613 current divider rule calculus, 567-68 calculator, 618-20 ac, 675 calibration factor, 571 conversions between forms, 610-12 dc, 208-12 capacitance, 399-403 division, 616-18 current sensitivity, 266-69 capacitance comparison bridge, 769 imaginary axis, 608-9 current sources capacitors, 5, 59, 397-453, 493, 495, Mathcad, 620-23 dependent, 749-50 591-97, 695-96 multiplication, 615-16 independent, 283-89, 743-44 ac response, 591-94, 640-42 phasors, 623-28 series connection, 289 applications, 443-49 polar form, 609-10 cutoff frequencies breakdown voltage, 403 real axis, 608-9 parallel resonance, 889-91 capacitance, 399-403 rectangular form, 609 series resonance, 878-80 charging, 415-22 subtraction, 613-14 cycle, 542 construction, 403-15 computer analysis

current iC, 436-38 introduction, 26-28 D , 401-3, 408 Mathcad See Mathcad -connected generator, 1039-40 discharging, 422-28 Multisim See Multisim - system, 1040-41 , 397-99, 401-2 PSpice See PSpice -Y system, 1040-42 energy, 442 software packages, 27-28 -Y,Y- conversion farad, 400 computer bus connections, 228 ac circuits, 769-74 initial conditions, 429-31 computers, 6 d’Arsonval movement, 266-69, 571 instantaneous values, 431-32 conductance, 86-87, 186-88, 220-21 dB, 921-26 labeling, 413-14 conductor, 38, 51, 63-64, 71-72 dB measurements, 925-26 leakage current, 412-13 constant current alarm system, 327-29 dc circuits measurements, 414-15 contributors analogies, 194 parallel, 438-39 Bode, Hendrick Wade, 944 complex, 243 relative , 402-7 Coulomb, Charles Augustin, 35 introduction, 131-32 series, 438-39 Faraday, Michael, 400 instrumentation, 194-95 standard values, 415 Fourier, Baron Jean, 1096 methods of analysis, 283-334 temperature effects, 413 Henry, Joseph, 466 parallel, 185-231 Thévenin equivalent, 433-36 Hertz, Heinrich Rudolph, 542 series, 131-71 , 416-420, 424-25 Joule, James Prescott, 109 series-parallel, 243-74 transients, 415-36 Kirchhoff, Gustav Robert, 143 theorems, 345-88 types, 407-12 Norton, Edward L., 363 dc current (defined), 41 camera flash lamp, 493 Ohm, George Simon, 102 dc-dc converter, 445 car system, 224-26 Siemens, Werner von, 86 decibels, 921-26 carbon composition resistor, 78 Steinmetz, Charles Proteus, 625-26 DeForest, Lee, 6 CAT scan, 534 Tesla, Nikola, 464 dependent sources cell, 4, 42 Thévenin, Leon-Charles, 353 conversion, 744-46 ceramic capacitors, 410, 413 Volta, Count Alessandro, 37 introduced, 743-44 boy30444_indx.qxd 3/27/06 2:31 PM Page 1151

INDEX 1151

dependent sources (continued) electron flow, 41, 131-32 fuel cell, 47-48 mesh analysis, 749-50 electronic systems, 816-20 full-wave rectified waveform, 571, 1095 nodal analysis, 757, 758-59 emf, 41 function generator, 540-41 Norton’s theorem, 810-12 EMI, 446-48 fundamental component, 1096 superposition, 792-94 energy, 106, 108-14, 116-18, 442, 449, fuse, 115, 214-15, 224-26 Thévenin’s theorem, 799-806 492-93, 837, 842, 845 derivative engineering notation, 16-17, 23 G capacitor, 436, 592 ENIAC, 6 gage, 67-69 inductor, 487, 590 equivalent circuit, 682-84, 1002-5 gallium arsenide, 52 sinusoidal function, 587-89 even function, 1097-98 gauss, 465 determinants, 290, 292, Appendix D exponential function, 415-16 Gauss, Karl Friedrich, 461-62 DIAC, 695-96 generators, 46 diamagnetic, 464 F germanium, 52 dielectric, 5, 401-3, 408 fall time, 1069-70 GFCI breaker, 41, 115, 728-30 dielectric constant, 402-7 farad, 400 gilbert, 464 dielectric strength, 403 Faraday, Michael, 5, 400, 461 Gilbert, William, 3 difference engine, 6 Faraday’s law, 472-74, 540, 857, 989-92 gold, 67 differential transformer, 1002 ferrite inductor, 469 graphic and parametric equalizers, 902-5 differentiation, 590-93 ferromagnetic materials, 465, 467, 514 Gray, Stephen, 4 digital meter, 54, 218-20 filament, 165-66, 214-15 Greek alphabet, Appendix E dimmer, 494-96 film resistors, 78-80 ground fault circuit interrupter, 41, 115, dimmer control, 93-94 filtering, 46 728-30 diode, 56-59, 105-6 filters, 59, 926-43 grounding, 120, 227-28, 574, 725-28 dipole, 401 active, 927 Grove, Sir William, 47 dipped capacitors, 411 applications, 973-78 Guericke, Otto von, 3-4 , 41, 131 Bode plots, 943-72 H disc capacitors, 410-11 computer analysis, 979-81 half-power frequencies DMM, 54, 88, 564, 573, 1107-8 double-tuned, 942-43 parallel resonance, 889-90 domain theory, 518, 520 high-pass, 927-28, 932-36, 944-49 series resonance, 878-80 dot convention, 1008-9 low-pass, 927-32, 949-51 half-wave rectification, 1095-96, 1104-5, double subscript notation, 152-56 pass-band, 927-28, 936-40 1109-11 double-tuned filter, 942-43 passive, 926 half-wave symmetry, 1098-99 duality, 220-21, 513 stop-band, 927-28, 940-42 Hall effect sensor, 532-33 ductility, 67 fixed capacitors, 407-11 harmonic terms, 1096 duty cycle, 1071-72, 1074-75 fixed inductors, 468-69 Hay bridge, 765-67 fixed resistors, 78-80 heat sink, 58 E fixed-point notation, 16-17 helium, 34 earth ground, 725-26 flash lamp, 443-46 henry, 466-68 eddy currents, 857 Fleming, John Ambrose, 5-6 Henry, Joseph, 466 Edison effect, 5 Fleming’s valve, 5-6 hertz, 542 Edison, Thomas, 5 floating-point notation, 16-17 Hertz, Heinrich Rudolph, 5, 542 effective resistance, 856-59 fluorescent light, 1019-21 high-pass filter, 927-28, 932-36, 944-49 effective value, 566-70 flux density, 464, 513-14 history, 1-7 efficiency, 112-14, 117, 370-71 flyback, 446, 493 horsepower, 106 Einstein’s theory of relativity, 75 FORTRAN, 27 house wiring, 118-20, 226-28, 691-92 electric baseboard heating element, 90-93 Fourier analyzer, 1100 household dimmer switch, 494-96 electric field, 397-99 Fourier series, 1096-1105 hydrogen, 33, 47-48 electric field strength, 398, 401-2 Fourier, Baron Jean, 1096 hysteresis, 516-20, 857-58 lines, 397-99 Franklin, Benjamin, 4 electrodynamometer movement, 572 free electron, 64 I , 47-48 frequency counter, 573 ICs, 1-2, 6-7, 59, 207 electrolyte, 42, 47-48 frequency, 542, 545-46 ideal pulse, 1067-68 electrolytic capacitor, 407-10, 412 frequency response imaginary axis, 608-10 , 463, 513-14, 523-24 capacitors, 598-99, 601-2 impedance electromagnetic induction, 5 inductors, 598, 600-601 capacitors, 640-42 electromagnetic interference, 446-48 parallel ac circuits, 675-82 inductors, 639-40 electromagnetic theory, 5 resistors, 597-600 resistors, 640-42 , 4, 462-63 series ac circuits, 653-63 impedance diagram, 642-43 , 41 frequency spectrum, 543-46 impedance matching, 998-1001 electron, 33-41 fringing, 401, 525 incandescent lamp, 575 boy30444_indx.qxd 3/27/06 2:31 PM Page 1152

1152 INDEX

independent sources, 743-44 internal resistance, 156-60, 286 magnetic circuits (continued) conversions, 744-46 inverter, 541 Ampere’s circuital law, 520-21 induced voltage, 472-74, 487-89 ion, 36, 48 applications, 531-34 inductance, 466-68, 989-92 iron-core transformer, 992-1006 domain theory, 518, 520 inductors isolation, 1001-2 electromagnet, 513-14, 523-24 ac response, 590-91, 639-40 ferromagnetic materials, 514 applications, 493-99 J flux density, 513-14 average induced voltage, 487-89 joule, 36-37, 106-9, 492-93 flux paths, 521 computer analysis, 499-504 Joule, James Prescott, 109 fringing, 525 construction, 466-68 hysteresis, 516-20 energy, 492-93 , 513-14 K henry, 466-68 lines, 513-15 kilowatthour, 109-12 induced voltage, 472-74 magnetizing force, 515-20 kilowatthour meter, 109 inductance, 466-68 magnetomotive force, 513-15, Kirchhoff, Gustav Robert, 5, 143 initial conditions, 477-79 520-21 Kirchhoff’s current law instantaneous value, 487 normal curve, 518-20 ac circuits, 669-75 labeling, 471-72 Ohm’s law, 514-15 dc circuits, 203-8 Lenz’s law, 473 permeability, 514 Kirchhoff’s voltage law magnetic effects, 461-65 relative permeability, 514 ac circuits, 644 measurement, 472 reluctance, 514 dc circuits, 143-47 parallel, 489-90 residual flux density, 517 practical equivalent, 470-71 saturation, 520 series, 489-90 L series configurations, 521-27 steady-state conditions, 490-92 labeling series-parallel configurations, 527-29 Thévenin equivalent, 484-86 capacitors, 413-14 table approach, 522-25 time constant, 476 inductors, 471-72 transformer, 524-25 transients, 474-84 resistors, 82-86 magnetic field, 461-65, 513-14 types, 468-70 ladder networks magnetic flux density, 464-65, 513-14 inferred absolute temperature, 72-74 ac, 724-25 magnetic flux lines, 462-65, 472-73, 515, initial conditions dc, 258-61 992-94 capacitive networks, 429-31 lagging, 555 magnetic parameter conversions, inductive networks, 477-79 languages, 27 Appendix F instantaneous values, 431-32, 487, 541 lead-acid secondary cell, 43-44 magnetic reed switch, 533-34 instrumentation leading, 555 magnetic resonance imaging, 534 ac measurements, 571-75 leakage current, 412-13 , 461-65 ammeter, 200-201 leakage flux, 1003 magnetizing force, 515-20 capacitors, 414-15 LED, 446-47 magnetomotive force, 464, 513-15, dB, 925-26 Leibniz wheel, 6 520-21 digital, 218-20 Leibniz, Gottfried Wilhelm von, 6 magnetron, 117 DMM, 219, 564-66, 1107-8 Lenz’s law, 473 malleability, 67 LCR meter, 472 Leyden jar, 4 Marconi, Guglielmo, 5 loading effects, 161-62 lithium battery, 43 Mathcad nonsinusoidal circuits, 1100 logarithms, 917-26 branch-current analysis, 292-93 Norton’s theorem, 366 common, 918 complex numbers, 620-23 ohmmeters, 81, 87-88, 134, 194-95, decibels, 921-26 exponential function, 432-33 414-15, 472 log-log plot, 918-20 introduction, 28, 95-97 oscilloscopes, 558-59, 564-66, 687-90, natural, 918 ladder network, 260-61 1084-85 properties, 920-21 mesh analysis, 305, 752 parallel circuits, 194-95, 200-201 scale, 88-89 nodal analysis, 317, 756-57 power, 855-56 semilog paper, 918-20 parallel resistors, 199-200 pulse waveforms, 1075 log scale, 88-89 system requirements, Appendix C series circuits, 138-40 logic probe, 331-32 total impedance, 722-23 series supplies, 142-43 log-log plots, 918-20 maximum power transfer theorem series-parallel circuits, 247-48, 258 Lorentz, Hendrick, 532 ac circuits, 812-16 Thévenin’s theorem, 360-63 low-pass filter, 927-32, 949-51 dc circuits, 367-76 voltmeters, 200-201, 218-20 low-voltage compensation, 1018-19 derivation (ac networks), Appendix G VOM, 219-20 Maxwell, James Clerk, 5, 462 , 51-52, 63, 71-72 M Maxwell bridge, 768 integrated circuit, 1-2, 6-7, 207 , 461-63 Maxwell’s equations, 5 integration, 563, 567-68, 593, magnetic circuits, 513-34 megohmmeter, 269 1099-1100 air gap, 525-27 menu, 27 boy30444_indx.qxd 3/27/06 2:31 PM Page 1153

INDEX 1153

mesh analysis, 295-306, 747-54 negative-going pulse, 1069 P ac circuits neutral, 119 parallel circuits format approach, 750-54 neutrons, 34 ac, 663-701 general approach, 747-50 newtons, 35 admittance diagram, 665 dc circuits NiCAD battery, 45 applications, 691-97 format approach, 301-6 nickel hydrogen battery, 45 computer analysis, 697-701 general approach, 295-301 nickel-cadmium battery, 45 current divider rule, 675 supermesh, 299-301 nickel-metal hydride secondary cell, frequency response, 675-82 metal-oxide varistor, 448-49 44-45 Ohm’s law, 668 meters Ni-H battery, 45 phase measurements, 687-90 kilowatt-hour meter, 109 NiMH battery, 44-45 power, 669 methods of analysis Nipkow, Paul, 6 R-C network, 671-73 ac circuits, 743-77 nodal analysis R-L network, 669-71 bridge networks, 764-69 ac circuits R-L-C network, 673-75 mesh analysis, 747-54 format approach, 759-64 source current, 668 nodal analysis, 754-64 general approach, 754-59 summary table, 682 dc circuits, 283-334 dc circuits susceptance, 665 branch-current analysis, 289-94 format approach, 313-18 total impedance, 664 mesh analysis, 295-306 general approach, 306-11 dc, 185-232 nodal analysis, 306-18 supernode, 311-13 analogies, 194 mica capacitor, 411, 413 node, 290 applications, 223-28 microbar, 924-25 noise filters, 975-78 capacitors, 438-39 microwave oven, 116-18, 167 nonsinusoidal circuits, 1095-1114 computer analysis, 228-31 mil, 64 addition and subtraction, 1111-12 current divider rule, 208-12 milliohmmeter, 269 average value, 1096-97 current sources, 287-89 Millman’s theorem, 376-79 circuit response, 1105-11 inductors, 489-90 mirror symmetry, 1098-99 computer analysis, 1112-14 instrumentation, 194-95, 200-201 MKS system, 8-11 even function, 1097-98 Kirchhoff’s current law, 203-8 molded carbon composition Fourier series, 1096-1100 Ohm’s law, 195 potentiometer, 81 half-wave symmetry, 1098-99 power distribution, 201-3 MOV, 448-49 instrumentation, 1100, 1107-8 protoboard, 222-23 MRI, 534 mirror symmetry, 1098-99 summary table, 220-21 Muller, Alex, 76 odd function, 1097 voltage sources, 213-14 multiple-load transformer, 1015-16 square wave, 1102-4 parallel resonance, 885-902 Multisim normal magnetization curve, 518-20 bandwidth, 889-91, 894 ac sources, 578-81 normalization, 929 cutoff frequencies, 889-91 high-pass filter, 981 Norton, Edward L., 363 examples, 896-902 introduction, 28 Norton’s theorem maximum impedance, 887-88, ladder network, 735-37 ac circuits, 806-12 892-95 mesh analysis, 333-34 dc circuits, 363-66 quality factor, 888-89, 891-95 Ohm’s law, 124-27 notation, 151-56 selectivity, 888-91 parallel dc circuits, 230-31 double-subscript, 152-56 summary table, 895-96 parallel resonance, 909-11 single-subscript, 153-56 unity power factor, 886-87, parallel R-L network, 700-701 nucleus, 33-34 891-92 series dc circuits, 170-71 paramagnetic, 464 series R-L response, 630-32 O Pascal, 27 superposition, 387-88, 824-25 odd function, 1097 Pascal, Blaise, 6 system requirements, Appendix C Oerstad, Hans Christian, 4, 461 pass-band, 927-28, 936-40 transformer, 1024-25 ohm, 3, 63 passive filter, 926-27 transient R-L response, 503-4 Ohm, Georg Simon, 3, 102 PC monitor, 496-99 Musschenbroek, Pieter van, 4 ohmmeter, 81, 87-88, 194-95, 268-69, peak amplitude, 541 mutual inductance, 989-92, 1006-9 360-62, 414-15, 472, 575, 687 peak value, 541 ohm/ rating, 219-20 peak-to-peak value, 541 N Ohm’s law, 2, 5, 101-7, 120-27, 135-38, period, 542 nameplate data, 1012-13 195, 514-15, 589-90, 644 periodic pulse train, 1071 nanotechnology, 1-2 oil capacitor, 411 periodic waveform, 542 National Electric Code, 120 open circuits, 214-15, 217-18, 419 permanent magnet, 461-63, 520 natural frequency, 872 oscilloscope, 558-59, 564-66, 573-74, permeability, 464-65, 514 natural logarithm, 918, 920 687-90, 1001-2, 1084-85 phase measurements, 687-90 negative temperature coefficient, 53, 72, overshoot, 1070 phase relationship, 554-59 88-89 oxygen, 47-48 phase sequence, 1033-34, 1040 boy30444_indx.qxd 3/27/06 2:31 PM Page 1154

1154 INDEX

phase sequence indicator, 1055 PSpice (continued) reciprocal, 612-13 phase-shift power control, 695-97 ac sources, 577-78 reciprocity theorem, 381-82 diagram, 624, 639-40, 642 average capacitive current, 451-53 rectangular form, 609-12 phasors, 623-28, 638 capacitors and the ac response, 628-30 rectification, 46 phenolic inductor, 469 current-controlled , 775-77 rectified ac waveform, 1095-96 phosphorescent coating, 497-99 dc bridge network, 332-33 reed switch, 533-34 photoconductive cell, 89 double-tuned filter, 979-81 reflected impedance, 996-98 photons, 540-41 Fourier series, 1112-14 regulator, 56-57 pixel, 498-99 introduced, 28 relative permeability, 465, 514 point symmetry, 518 maximum power transfer, 383-87 relative permittivity, 402-7 polar form, 609-12 nodal analysis, 774-75 release phase, 479-84 polarized, 401-2 Ohm’s law, 120-24 rels, 514 polyester film capacitor, 407-10 parallel dc networks, 228-30 reluctance, 514, 992 polyphase systems, 1029-56 parallel resonance, 907-9 residual flux density, 517 -connected generator, 1039-40 power curves, 861-64 resistance, 63-97, 104-6, 589, 637-39, - system, 1040-41 R-C response, 1088-90 856-59 phase sequence, 1033-34, 1040 series ac circuit, 697-700 applications, 90-95 phase sequence indicator, 1055 series circuits, 168-70 circular mils, 64-66 power, 1042-48 series resonance, 905-7 circular wires, 64-71 single-phase, 1029 system requirements See Appendix C coefficient of resistance, 74 three-phase, 1030-42 Thévenin’s theorem, 382-83, 820-24 color coding, 82-85 three-wattmeter method, 1048-49 transformer, 1021-24 conductance, 86-87 two-wattmeter method, 1049-52 transient R-C response, 449-51 inferred absolute temperature, 72-74 unbalanced systems, 1052-56 transient response with initial Mathcad, 95-97 Y-connected generator, 1031-39 conditions, 501-2 metric units, 69-71 Y- system, 1037-39 transient R-L response, 499-501 photoconductive cell, 89 Y-Y system, 1035-37 voltage divider supply, 273-74 ppm/°C, 75 Popov, Aleksandr, 5 voltage-controlled , resistivity, 64, 66, 70-71 positive temperature coefficient, 72 822-24 superconductors, 75-77 positive-going pulse, 1069 pulse repetition rate, 1071-72 symbol, 63 potential difference, 38, 101 pulse train, 1071 temperature effects, 71-75 potential energy, 38 pulse transformer, 1014 thermistor, 88-89 potentiometer, 80-81, 695-96 pulse waveforms, 1067-90 types, 78-82 potentiometer loading, 264-66 average value, 1074-75 varistors, 89-90 power, 567 computer analysis, 1088-90 resistivity, 64, 66, 70-71 ac, 118-20, 603-7, 644, 835-64 definitions, 1068-70 resistors dc, 106-8, 140-41, 201-3 duty cycle, 1071-72, 1074-75 parallel, 185-95 efficiency, 112-14 ideal, 1067-68 series, 132-34 nonsinusoidal functions, 1107 instrumentation, 1075, 1084-85 resonance, 871-911 three-phase systems, 1042-48 pulse repetition rate, 1071-72 parallel, 885-902 transformer, 997-98 pulse width, 1068 series, 872-84 power factor, 607-8, 646, 648, 650, 670, stray, 902 672, 674, 839, 841, 845, 874, Q RFI, 446-48, 494 1044, 1046 quality factor rheostat, 80 power factor correction, 851-55 parallel resonance, 891-95 right-hand rule, 462-63 power generator, 859-60 series resonance, 874-76 rise time, 1069-70 power meters, 855-56 QBASIC, 27 rms value, 566-70, 1106 power supplies, 46-47, 142-43, 156-60 Röntgen, Wilhelm, 5 power triangle, 845-47 R rotor, 224, 540, 1029 powers of ten, 12-16, 18-19, 25-26 radian, 546-48 ppm/°C, 75, 413 radiation losses, 856 S prefixes, 17-18 radio, 5-6 safety concerns, 576-77 preshoot, 1070 radio frequency interference, 447-48 saturation, 520 primary cell, 42-43 R-C response, 1074-84 sawtooth waveform, 1095 primary winding, 989-92 reactance schematic with nodal voltages, programs, 27 capacitors, 593, 640 330-32 protoboards, 162-64, 222-23 inductors, 591, 639 scientific notation, 16-17 proton, 33-35 reactive power, 840-41, 844, 1043-45 SCR, 445-46, 493-96 PSpice real axis, 608-10 secondary cell, 42-45 ac bridge network, 730-35 real power, 603-7, 837 secondary winding, 989-92 boy30444_indx.qxd 3/27/06 2:31 PM Page 1155

INDEX 1155

selectivity siemen, 86-87 systems of units (continued) parallel resonance, 888-91 Siemens, Werner von, 86 MKS, 8-11 series resonance, 878-80 significant figures, 11-12 SI, 9-11 semiconductors, 52-53, 71-72 silicon, 52 semilog paper, 918-20 silicon-controlled rectifier See SCR T series capacitors, 438-39 silver, 67 tantalum capacitor, 407-8, 413 series circuits single subscript notation, 153-56 tapped transformer, 1015-16 ac, 637-63 single-phase generator, 1029 television, 6 computer analysis, 697-700 single-phase, 859, 1029-30 temperature coefficient of resistance, 74 frequency response, 653-63 single-pole, double-throw relay, 329-30 temperature effects impedance diagram, 642-44 sinusoidal ac voltage, 540-43, 546-59 capacitors, 413 Ohm’s law, 644 sinusoidal alternating current, 131 resistance, 71-75 power, 644 sinusoidal waveforms, 546-559 tesla, 464 R-C circuit, 646-48 skin effect, 856-57 Tesla, Nikola, 464 R-L circuit, 645-46 smart remote, 1087 theorems R-L-C circuit, 648-50 software packages, 27-28 ac networks, 787-825 source current, 644 solar cell, 42, 45-46, 540-41 maximum power transfer theorem, summary table, 663 source conversions 812-16 voltage divider rule, 650-51 ac Norton’s theorem, 806-12 dc, 131-71 dependent, 746-47 superposition, 787-94 ammeter, 139-40 independent, 744-46 Thévenin’s theorem, 794-806 current, 135 dc, 285-89 dc networks, 345-88 Kirchhoff’s voltage law, 143-47 speaker system, 531-32, 692-95, 1000-1001 maximum power transfer theorem, notation, 151-56 specific gravity, 44 367-76 Ohm’s law, 135-38 spectrum analyzer, 1100 Millman’s theorem, 376-79 power, 140-41 speed of light, 75 Norton’s theorem, 363-66 resistors, 132-34 square wave, 539, 1077-83, 1095, 1102-4 reciprocity theorem, 381-82 supplies, 141-43 static , 3 substitution theorem, 379-81 voltage, 136-37 stator, 540 superposition, 345-52 voltage divider rule, 148-51 steady-state solution, 429, 490-92 Thévenin’s theorem, 353-63 voltmeter, 139 Steinmetz, Charles Proteus, 625-26 thermistor, 88-89 magnetic, 521-27 step-down transformer, 994-95 Thévenin, Leon-Charles, 353 series inductors, 489-90 step-up transformer, 994 Thévenin’s theorem series-parallel networks stop band, 927-28, 940-42 ac circuits, 794-806 ac, 713-37 strain gauges, 94-95 attenuator probe, 1084 applications, 728-30 stray capacitance, 442-43 capacitive networks, 433-36 block impedances, 713-25 stray resonance, 902 dc circuits, 353-63 computer analysis, 730-37 substitution theorem, 379-81 inductive networks, 484-86 examples, 713-24 summary tables three-phase generator, 1030-42 dc, 243-74 Bode plots, 970-72 three-phase systems See polyphase systems block diagram approach, 248-51 parallel ac circuits, 682 three-wattmeter method, 1048-49 examples, 251-58 parallel dc circuits, 220-21 TI-86 calculator, Appendix B ladder networks, 258-61 parallel resonance, 895-96 TI-89 calculator Mathcad, 260-61 series ac circuits, 663 basic operations, 23-26 reduce and return approach, 244-51 series dc circuits, 220-21 complex numbers, 618-20, 752 magnetic, 527-29 superconductors, 75-77 determinants, 293, 305-6, 319-20 series resistors, 132-34 supermesh current, 299-301 exponential function, 420-21, 432 series resonance, 872-84 supernode, 311-13 logarithms, 921 bandwidth, 878-80 superposition theorem nodal analysis (ac), 761 cutoff frequencies, 878-80 ac circuits, 787-94 Norton’s theorem (ac), 809 examples, 882-84 dc circuits, 345-52 sinusoidal functions, 552-53 quality factor, 874-76 surface mount resistors, 85-86 superposition (ac), 792 selectivity, 878-80 surge protector (line conditioner), 446-49 total admittance, 720-21 total impedance, 876-78 susceptance, 665 total impedance, 723 sheet resistance, 70 swinging choke, 1020 voltage divider rule (ac), 650-53 shells, 34-35 symbols, 22 tilt, 1070 shell-type transformer, 1013 symmetrical lattice, 318-19 time constant Shockley, William, 6 systems of units, 8-11, 19-22 capacitive networks, 416-20, 424-36 short circuits, 214-18, 419 CGS, 8-11 inductive networks, 476 SI system, 9-11, 463-65, 513 English, 8-11 transformation ratio, 994-1000 boy30444_indx.qxd 3/27/06 2:31 PM Page 1156

1156 INDEX

transformers, 56-59, 216, 524-25, 575, true rms meter, 571, 1107-8 voltaic cell, 4 989-1025 tube, 5-6 voltmeter, 53-54, 139, 161-62, 200-201, air-core, 1009-12 tuned networks, 871-72 218-20, 247-48, 258, 267-68, applications, 1017-21 turns ratio, 57 360-63 coefficient of coupling, 990-92 TV monitor, 496-99 VOM, 54, 88, 219-20, 571 computer analysis, 1021-25 TV remote, 1085-88 differential, 1002 tweeter, 692-95 W dot convention, 1008-9 two-wattmeter method, 1049-52 watt, 106-8 equivalent circuit, 1002-5 Watt, James, 106 frequency considerations, 1005-6 U wattsecond, 109 impedance matching, 998-1001 unbalanced three-phase system, 1052-56 wave analyzer, 1100 iron-core, 992-1006 units of measurement, 7-11 waveforms, 541 isolation, 1001-2 weber, 463-64 mutual inductance, 989-92 V Weber, Wilhelm Eduard, 463 mutually coupled, 1006-9 VA, 838-39, 844 Wheatstone bridge smoke detector, nameplate data, 1012-13 vacuum tube, 6 329-30 power, 996-98 VAR, 841, 844 wire tables, 67-69 primary winding, 989-1006 variable capacitors, 411-12 wire-wound resistors, 78-79 reflected impedance, 996-98 variable inductors, 469-70 woofer, 692-95 secondary winding, 989-1006 variable resistors, 80-82 Wu, Man Kven, 76 step-down, 994-95 varistors, 89-90, 448-49 step-up, 994 volt, 3, 36-37 X transformation ratio, 994-1000 Volta, Count Alessandro, 3-4, 37 x-rays, 5, 498 types, 1013-17 voltage, 33, 35-38 transients volt-ampere, 838-39 Y capacitive networks, 415-36 volt-ampere-reactive, 841, 844 Y- system, 1037-39 inductive networks, 474-79 voltage divider rule Y- and -Y conversions transistor, 6, 717-18, 763-64, 798-99, ac circuits, 650-51 ac circuits, 769-74 803-6, 816-20 dc circuits, 148-51 dc circuits, 321-27 TRIAC, 494-96, 695-96 voltage divider supply, 261-64 Y-connected generator, 1031-39 triangular wave, 539, 1095 voltage regulation, 156-60 yolk, 496-99 trigger network, 445 voltage sensitivity, 267-68 Y-Y system, 1035-37 trimmer, 81-82 voltage sources, 141-43, 213-14, 743-44, troubleshooting, 221-22 749