Index

Page references with “t” denote tables; “f” denotes figures

A

AC
definition of, 3
resistor application, 145
voltage, 5–6
AC circuits
capacitive reactance, 188–191
capacitors in, 185
parallel inductors in, 289–290
RC. See RC AC circuits resistors
description of, 150, 184
parallel, 154–155
power dissipation, 159–161
series, 151–153
series-parallel. See Series-parallel resistive AC circuit
RL. See RL AC circuit
series inductors in, 288–289
total current, 439–440
AC generator
description of, 7
output waveform, 10–11
rotating, 42–45
voltage, 42–45
AC waveform
DC waveforms and, 6–7, 37–38
generation of, 3–4, 7
oscilloscope measurement of, 91–93
plotting of, 4–5
sine function and, 41
Air capacitors, 183
Amplitude, of sinusoidal waveform
peak, 33–34, 147–148
peak-to-peak, 33–34, 93, 147–148
phase relationships and, 123
root-mean-square, 34
Arctangent, 231
Autotransformers, 281–282

B

Bandwidth, 463–465
Beam controls, for oscilloscope
astigmatism, 73
focus, 72
intensity, 72
position, 73

C

Capacitance
definition of, 173
in parallel, 195–196
in series, 193–195
Capacitance unit, 178
Capacitance values
abbreviations, 178
calculation of, 179
standard, 178
Capacitive circuits
parallel
analysis of, 198–199
power in, 200–201
phase relationships in, 185–186
series
analysis of, 196–198
power in, 200
Capacitive reactance
in AC circuit, 188–191
definition of, 186
equation, 188
in parallel circuit, 193
in series circuit, 192
in series RC circuit, 227
Capacitors
in AC circuit, 185
air, 183
ceramic disc, 180, 514
charging of, 174–175, 337
color codes, 510–514
in DC circuit, 184
description of, 173
discharging of, 175
electrolytic, 181–183
impedance, 186
leakage current, 183, 184t
mica, 512
paper, 181
plates, 176, 179
schematic symbol of, 173
tubular, 513
types of, 174, 180–183
values of, 176–180
variable resistance, 192
voltage ratings of, 180
Ceramic disc capacitors, 180
Charge cycle, 337–340
Charging, of capacitor, 174–175
Chassis wiring color code, 515
Circuits. See Parallel circuits; Resistors; Series circuit
Coefficient of coupling, 272–273
Coil
cross-sectional area calculations, 265
illustration of, 262f
inductance of
physical properties that determine, 264–265
principles, 263
internal resistance of, 267
North–South magnetic field of, 262–263
Q of
calculation of, 326
definition of, 325
equation, 326
factors that affect, 327
principles of, 325–326
Color codes
capacitors, 510–514
chassis, 515
resistors, 510
transformer, 282, 515
Complex numbers
definition of, 400
in polar form
converting to rectangular form, 409, 411–412
description of, 409
math operations, 433–434
in rectangular form
conversion to polar from, 409–413
description of, 409
math operations, 431–433
RC circuit, 408
RL circuit, 407–408
Complex problem analysis, 413–415
Constant 0.707, 34–37
Coordinates of the point, 398
Cosine, 41, 48–49, 499
Counter EMF, 263
Coupling, coefficient of, 272–273
Coupling control, of oscilloscope, 86–87
Current
change of, 266–267
universal time constant chart for solving, 348–349
Current flow, 10

D

DC circuit
capacitors in, 184
power dissipation in, 159–160
resistors, 184
RL
opposing current decrease, 354–356
opposing current increase, 352–354
universal time constant chart application, 357–360
DC heating effect, 34
DC waveform
AC waveform and, 6–7, 37–38
definition of, 6
voltages, 6, 35f
Dielectric, 173
Dielectric constant, 179–180
Dielectric strength, 180

E

Electrical degrees, 111–113
Electrolytic capacitors, 181–183
Electromagnetic induction, 8–10
Electromagnetic properties
Faraday’s discoveries regarding, 259–260
Oersted’s discoveries regarding, 260
Electron current flow, 259
Electron gun, of oscilloscope, 69–70
Equations
AC electricity, 496–497
DC electricity, 495

F

Farad, 176–178
Faraday, Michael, 259–260
Frequency of waveforms
calculations, 31–32
capacitance impedance and, 186–187
definition of, 14, 31
phase difference determinations, 122
prefixes, 15
units, 14–15

G

Greek characters, 493

H

Half-power points, 465
Hertz, 14–15
Hypotenuse
finding of, when sides of triangle are given, 50–52
finding sides of triangle when given, 50

I

Imaginary axis, 400
Impedance
calculation of, 408–409
definition of, 222
j-operators for writing, 429–431
in polar form
converting to rectangular form, 409, 411–412
description of, 409
Pythagorean theorem application to, 224–225
RC, in parallel RL circuit, 319
in rectangular form
conversion to polar from, 409–413
description of, 409
RC circuit, 408
RL circuit, 407–408
RL, 407–408
in RLC circuits, 437–439
in series circuit, 434–436
in series RL circuit, 306–308
Inductance
in circuit, 266–269
of coil, 263
mutual
calculation of, 273
definition of, 271
description of, 271–272
parallel-connected inductors with, 273–274
series-connected inductors with, 273
principles of, 261
units of, 264
of wire, 261–262
Inductive circuits
parallel, 291
power in, 290
series, 290–291
Inductive reactance
definition of, 283
derivation of, 284–285
equation, 283–284, 287
frequency change effects on, 285–287
inductance change effects on, 285–287
Inductors
changing circuit effects, 266–267
illustration of, 259f
parallel
in AC circuits, 289–290
description of, 270–271
mutual inductance with, 274–275
schematic symbol of, 259f
series
in AC circuits, 288–289
description of, 270
mutual inductance with, 274
variable, 265–266
In-phase, 120, 149
Instantaneous current, 113–114
Instantaneous values
calculation of, 146
sine wave, 109–110
time intervals, 115–117
Instantaneous voltage
calculation of, 145–147
at radian rotation, 119
at specific times, 117
universal time constant chart for solving, 348–349

J

j-operators
circuit analysis using, 434–442
description of, 403–404
impedances written using, 429–431
math operations using, 431
rotations, 404–407
vector application of, 404–407

K

Kirchhoff’s voltage law
description of, 229
RC time constants related to, 351

L

L/C ratio, 466–467
Leakage current, 183, 184t
Left-hand rule for generators, 260

M

Magnetic lines of force, 8
Metric prefixes, 504
Multiple-secondary transformers, 282
Mutual inductance
calculation of, 273
definition of, 271
description of, 271–272
parallel-connected inductors with, 273–274
series-connected inductors with, 273

N

Negative numbers, square roots of, 399–400

O

Oersted, Hans Christian, 260
Ohm’s law, 146, 228
Oscilloscope
AC waveform measurement using, 91–93
analog
digital oscilloscope and, comparisons between, 89
illustration of, 67f, 91f
beam controls
astigmatism, 73
focus, 72
intensity, 72
position, 73–74
calibration of, 73
control circuits of, 71
digital
controls of, 90
description of, 89
displays, 91
illustration of, 68f
outputs, 91, 92f
display system, 69
electron gun of, 69–70
functions, 67
holdoff control of, 88
horizontal controls
coupling, 86–87
positioning, 80–81
illumination control, 74
level control of, 88
mainframe controls of, 71–74
overview of, 67–68
rotation control, 73
screen
graticules, 74
properties of, 70–71
segments of, 68–71
slope control of, 87–88
sweep of
definition of, 80
sweep time, 81–82
triggering, 81
variable sweep time, 83
triggering
control functions, 83–84
definition of, 80–81
external sources, 86
internal sources, 84–85
level control, 88
line sources, 85–86
slope control, 87–88
sources, 84–86
vertical controls for
functions of, 74
illustration of, 74f
positioning, 74–75
voltage measurements, 75–77
vertical coupling control, 79–80
vertical deflection
AC voltage, 76
DC voltage, 75–76
example of, 78–79
volts per division, 77–79
Out-of-phase, 120

P

Paper capacitors, 181
Parallel circuits
RC
alternative solution method, 244–245
analysis of, 242–245
branch current, 242
description of, 237
illustration of, 237f
impedance vectors, 239–240
phase angle, 241, 243–244
phase relationships, 237–241
power calculations in, 245–247
power phasor relationships, 246–247
total current, 243
total impedance, 243
RL
alternative solution method, 323–324
branch currents, 320–321
example, 319
impedance of, 319, 321
phase angle, 320, 322
phase relationships, 317–318
phasor addition, 318–319
power calculations, 324–325
solution, 320
total currents, 321
RLC
analysis of, 384–386
branch currents, 284, 381
calculations, 382–383, 385
circuit phase diagram, 381f
current phasor comparisons and diagram, 382f, 384f
description of, 380
impedance in, 436
phase angle, 383, 385
power, 383, 385
Parallel inductors
in AC circuits, 289–290
description of, 270–271
mutual inductance with, 274–275
Parallel resistive AC circuit, 154–155
Parallel resonance
current magnification, 470–471
example, 472–474
frequency, 468, 475–476
impedance, 469–470
Q of a circuit, 470
total current, 468–469
Peak amplitude
conversions
overview of, 148–149
from peak-to-peak amplitude, 39, 508
from root-mean-square amplitude, 38, 508
definition of, 33, 147–148
Peak-to-peak amplitude
conversions
overview of, 148–149
to peak amplitude, 39, 508
from root-mean-square amplitude, 38, 508
to root-mean-square amplitude, 39, 508
definition of, 33–34, 147–148
determination of, 33–34, 93
Period of waveform
calculations, 15, 31–32
converting to frequency of waveform, 16
definition of, 15, 31
equation, 15–16
Phase angle
negative, 233
in parallel RL circuit, 320, 322
in RC circuits
parallel, 241, 243–244
series, 230
in RLC circuits, 375–376, 379–380
in series RL circuit, 311–314
tangent function for solving, 231–233
Phase difference
conventional specification, 123
definition of, 120
determining of, 121–122
Phase relationships
amplitude versus phase, 123
in capacitive circuits, 185–186
current, 149–150
definition of, 119–120
in-phase, 120, 149
out-of-phase, 120, 149
in parallel RL circuit, 317–318
phasor notation for representing. See Phasor notation
in RC circuits
parallel, 237–241
series, 219–220
in RL AC circuit
parallel, 317–318
series, 305–306
in series RL circuit, 305–306
voltage, 149–150
Phasor algebra
complex numbers, 400
description of, 397
polar coordinates
circuit analysis and, 403
definition of, 403
description of, 401–402
real and imaginary axis, 400
square roots of negative numbers, 399–400
vectors
j-operator application to, 404
location of, 398–399
rotation of, 399
X–Y coordinates, 397–398
Phasor magnitude, 126
Phasor notation
definition of, 124
description of, 123–124
examples of, 126–129
for multiple vectors, 128–129
for two vectors, 126–127
uses of, 124–125
Phosphorescence, 70
Polar coordinates
circuit analysis and, 403
definition of, 403
description of, 401–402
Polar form, complex numbers in
converting to rectangular form, 409, 411–412
description of, 409
math operations, 433–434
Power
apparent
calculation of, 235–236
definition of, 235
in parallel RC circuit, 246
in parallel RLC circuits, 383
in parallel RL circuit, 324
in series RC circuits, 235–236
in series RLC circuits, 377
in series RL circuit, 316
dissipation of, 159–161
in inductive circuits, 290
in parallel capacitive circuits, 200–201
in parallel inductive circuits, 291
in RC circuits
parallel, 245–247
series, 234–236
reactive
calculation of, 199
in parallel RC circuit, 246
in parallel RL circuit, 324
in series RC circuit, 235
in series RL circuit, 316
real
calculation of, 235
definition of, 159
in parallel RC circuit, 245
in parallel RL circuit, 324
in series RC circuit, 235
in series RL circuit, 316
in RLC circuits
parallel, 383, 386
series, 376–377, 380
in RL circuit
parallel, 324–325
series, 315–317
in series capacitive circuits, 200
in series inductive circuits, 290–291
Pure reactance polar form, 440
Pure resistance polar form, 440
Pythagorean theorem
description of, 224
impedance solutions using, 224–225
voltage solutions using, 225–226

Q

Q
of a circuit
description of, 459
measurement of, 460
parallel-resonant circuit, 470
voltage magnification, 459–460
of a coil
calculation of, 326
definition of, 325
equation, 326
factors that affect, 327
principles of, 325–326
Quadrants
definition of, 46, 498
sine of, 46–48
sine wave and, 46f

R

Radians, 117–119
Rate-of-change equation, 268–269
RC AC circuits
parallel
alternative solution method, 244–245
analysis of, 242–245
branch current, 242
description of, 237
illustration of, 237
impedance vectors, 239–240
phase angle, 241, 243–244
phase relationships, 237–241
power calculations in, 245–247
power phasor relationships, 246–247
total current, 243
total impedance, 243
series
alternative solution method, 233–234
analysis of, 226–234
capacitive reactance, 227
phase angle in, 230, 233
phase relationships in, 219–220
power in, 234–236
tangent function, 230–231
RC DC circuits
charge cycle, 337–340
discharge cycle, 340–342
RC time constant
calculation, 343–344
converting of time to, 347–348
defined, 342
Kirchhoff’s voltage law and, 351
Reactance
capacitive
in AC circuit, 188–191
definition of, 186
description of, 455
equation, 188
in parallel, 193
in series, 192
in series RC circuit, 227
inductive
definition of, 283
derivation of, 284–285
description of, 455
equation, 283–284, 287
frequency change effects on, 285–287
inductance change effects on, 285–287
of RLC circuits, 374
vector addition, 222–223
Reactive power, 199
Real axis, 400
Rectangular form, complex numbers in
conversion to polar from, 409–413
description of, 409
math operations, 431–433
RC circuit, 408
RL circuit, 407–408
Resistance vector addition, 222–223
Resistors
in AC circuit, 145
description of, 150, 185
parallel, 154–155
power dissipation, 159–161
series, 151–153
series-parallel
branch currents, 157–158
current chart, 158–159
simplified, 156
total current, 157
total resistance, 157
voltage chart, 158
voltage drops, 157
color codes, 510
in DC circuit, 184
Resonance
equivalent equations, 456–457
frequency
bandwidth and, 464–465
change of, 466–468
definition of, 456
parallel
current magnification, 470–471
description of, 509
example, 472–474
frequency, 468, 475–476
impedance, 469–470
Q of a circuit, 470
total current, 468–469
series
description of, 509
example, 460–462
impedance, 457
phase angle, 458
Q of a circuit, 459–460
voltage phase relationships, 458
Right triangle
quadrants, 498
sides and angles of
how to find when theta and hypotenuse are given, 50
relationship between, 39–40
trigonometric functions, 41, 498–499
RL AC circuit
impedance of, 306–308, 319, 321, 407–408
parallel
alternative solution method, 323–324
branch currents, 320–321
example, 319
impedance of, 319, 321
phase angle, 320, 322
phase relationships, 317–318
phasor addition, 318–319
power calculations, 324–325
solution, 320
total currents, 321
series
alternative solution method, 314–315
impedance, 306–308
phase angle, 311–314
phasor addition, 306
phase relationships, 305–306
power calculations, 315–317
solution of, 309–310
voltages, 308
RLC circuits
impedance in, 437–439
parallel
analysis of, 384–386
branch currents, 284, 381
calculations, 382–383, 385
circuit phase diagram, 381f
current phasor comparisons and diagram, 382f, 384f
description of, 380
phase angle, 383, 385
power, 383, 385
series
analysis of, 378–380
calculations, 372–375, 378–379
circuit voltage values, 373–374
phase angle, 375–376, 379–380
phase differences, 371
phasor diagram, 371f–372f
power values, 376–377, 380
reactance, 374
voltage phasor comparisons, 372
RL DC circuit
opposing current decrease, 354–356
opposing current increase, 352–354
universal time constant chart application, 357–360
RL time constants
calculation of, 356
defined, 356
Root-mean-square amplitude
conversions
overview of, 148–149
peak amplitude from RMS, 38, 39f, 508
from peak-to-peak amplitude, 39, 508
peak-to-peak amplitude from RMS, 38, 39f, 508
definition of, 34
notation for, 38

S

Schematic symbols, 494
Scientific notation, 504
Scope. See Oscilloscope
Screen, of oscilloscope
graticules, 74
properties of, 70–71
Self-inductance, 263
Series circuit
impedance for, 434–436
RC
alternative solution method, 233–234
analysis of, 226–234
capacitive reactance, 227
phase angle in, 230, 233
phase relationships in, 219–220
power in, 234–236
tangent function, 230–231
RL
alternative solution method, 314–315
impedance, 306–308
phase angle, 311–314
phasor addition, 306
phase relationships, 305–306
power calculations, 315–317
solution of, 309–310
voltages, 308
Series inductors
in AC circuits, 288–289
description of, 270
mutual inductance with, 274
Series-parallel resistive AC circuit
branch currents, 157–158
current chart, 158–159
simplified, 156
total current, 157
total resistance, 157
voltage chart, 158
voltage drops, 157
Series resistive AC circuit, 151–153
Series resonance
example, 460–462
impedance, 457
phase angle, 458
Q of a circuit, 459–460
voltage phase relationships, 458
Sine function
AC waveform and, 41
definition of, 39, 499
description of, 41, 410
Sine wave, 45
instantaneous values, 109–110
period of, 115
plotting of, 111–113
Sinusoidal voltage, 35f
Sinusoidal waveform
characteristics of, 114–115, 146
description of, 11
instantaneous values of, 111–113
non-sinusoidal waveform and, 114–115
repetitious, 13
Square roots
calculator for extracting, 503
how to use, 500–502
of negative numbers, 399–400
Square waves, 13

T

Tangent, 41, 49–50, 499
Tangent function
definition of, 230
phase angle solutions using, 231–233
in series RC circuits, 230–231
Theta
definition of, 42
finding sides of triangle when given, 50
tangent of, 49–50
Time constants
RC
calculation of, 343–344
conversion of time to, 347–348
defined, 342
Kirchhoff’s voltage law and, 351
RL
calculation of, 356
defined, 356
universal time constant chart. See Universal time constant chart
Transformers
audio, 283
autotransformers, 281–282
construction of, 275
efficiency of, 280
filament, 283
illustration of, 275f
isolation, 280–281
lead color code, 282
multiple-secondary, 282
power ratings of, 279–280
primary-to-secondary current relationship, 279
schematic representation of, 275f
specifications, 282–283
turns ratio versus voltage, 276–278
variable-output, 282
wiring color code, 515
Trigonometry
definition of, 39
functions, 41, 46–48, 498–499
right-triangle side and angle relationships, 39–40
Turns ratio, 276–278

U

Unit conversion charts, 490–492
Universal time constant chart
circuit current and, 345–346
description of, 344
EC and, 344–345
ER and, 345–346
example of, 505–507
exponential characteristic of, 345
RL circuit currents and voltages, 357–360
uses of
converting time to time constant, 347–348
current values
charging, 348–349
discharging, 350–351
description of, 346–347
instantaneous voltage values
charging, 348–349
discharging, 350–351

V

Variable inductors, 265–266
Variable-output transformers, 282
Vector
definition of, 124
location of, 398–399
in phasor algebra, 398–399
phasor notation for, 126–129
rotation of, 399
Vector addition
definition of, 220
parallelogram method, 221
phasor diagram, 221f
reactance, 222–223
resistance, 222–223
voltage, 222
Vector solutions
description of, 223
Pythagorean theorem application, 224–226
Voltage drop
calculation of, 440
description of, 157
series-parallel resistive AC circuit, 157

W

Waveform cycles
alternations, 11–12
definition of, 13
identification of, 11–12, 13
nonstandard, 12–13
voltage considerations, 14
Waveform frequency
calculations, 31–32
converting time to, 16
definition of, 14, 31
prefixes, 15
units, 14–15
Waveform period
calculations, 15, 31–32
definition of, 15, 31
equation, 15–16
Waveforms
AC
DC waveforms and, 6–7, 37–38
generation of, 3–4, 7
oscilloscope measurement of, 91–93
plotting of, 4–5
sine function and, 41
DC
definition of, 6
voltages, 6, 35f
sinusoidal
characteristics of, 114–115, 146
description of, 11
instantaneous values of, 111–113
non-sinusoidal waveform and, 114–115
repetitious, 13

X

X–Y coordinates, 397–398

Z

Z. See Impedance
0.707 constant, 34–37
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