Bird J. Electrical Circuit Theory and Technology
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Standard electrical quantities—their symbols and units 969
Resistance, temperature
coefficient of
˛ per degree Celsius
or per kelvin
/
°
Cor/K
Resistivity * ohm metre m
Slip s per unit or per cent p.u. or %
Standing wave ratio s
–
–
Susceptance B siemen S
Temperature coefficient
of resistance
˛ per degree Celsius
or per kelvin
/
°
Cor/K
Temperature,
thermodynamic
T kelvin K
Time t second s
Torque T newton metre Nm
Velocity
v metre per second m/s
Velocity, angular ω radian per second rad/s
Volume V cubic metres m
3
Wavelength . metre m
(Note that m/s may also be written as ms
1
,C/m
2
as Cm
2
,/KasK
1
, and so on.)
Greek alphabet
LETTER UPPER CASE LOWER CASE
Alpha A ˛
Beta B ˇ
Gamma
Delta υ
Epsilon E ε
Zeta Z
Eta H
Theta
Iota I
Kappa K
Lambda
Mu M
Nu N
Xi
Omicron O o
Pi
Rho P
Sigma
Tau T
Upsilon
Phi
Chi X
Psi
Omega !ω
Common prefixes
PREFIX NAME MEANING:
multiply by
E exa 10
18
Ppeta 10
15
T tera 10
12
G giga 10
9
Mmega 10
6
k kilo 10
3
h hecto 10
2
da deca 10
1
d deci 10
1
c centi 10
2
m milli 10
3
micro 10
6
nnano 10
9
p pico 10
12
f femto 10
15
a atto 10
18
Resistor colour coding
and ohmic values
Colour code for fixed
resistors
COLOUR SIGNIFICANT MULTIPLIER TOLERANCE
FIGURES
Silver – 10
2
š 10%
Gold – 10
1
š 5%
Black 0 1 –
Brown 1 10 š 1%
Red 2 10
2
š 2%
Orange 3 10
3
–
Yellow 4 10
4
–
Green 5 10
5
š 0.5%
Blue 6 10
6
š 0.25%
Violet 7 10
7
š 0.1%
Grey 8 10
8
–
White 9 10
9
–
None – – š 20%
Thus, for a four-band fixed resistor (i.e. resistance values with two
significant figures):
yellow-violet-orange-red indicates 47 k with a tolerance of š 2%
orange-orange-silver-brown indicates 0.33 with a tolerance of š 1%
and brown-black-brown indicates 100 with a tolerance of š 20%
(Note that the first band is the one nearest the end of the resistor).
For a five-band fixed resistor (i.e. resistance values with three significant
figures):
red-yellow-white-orange-brown indicates 249 k with a tolerance of
š 1%
(Note that the fifth band is 1.5 to 2 times wider than the other bands).
Resistor colour coding and ohmic values 973
Letter and digit code
for resistors
RESISTANCE MARKED AS:
VALUE
0.47 R47
1 1R0
4.7 4R7
47 47R
100 100R
1k 1K0
10 k 10K
10 M 10M
Tolerance is indicated as follows:
F Dš1%,GDš2%,J Dš5%,K Dš10% and M Dš20%
Thus, for example, R33M D 0.33 š 20%
4R7K D 4.7 š 10%
390RJ D 390 š 5%
6K8F D 6.8k š 1%
68KK D 68 k š 10%
4M7M D 4.7M š 20%
Index
Absolute permeability, 77, 689
permittivity, 59
A.c. bridges, 130, 476, 585
generator, 193, 666
values, 195
Acceptor circuit, 226
Active power, 232, 238, 464
Admittance, 444
Alkaline cell, 38
Alternating current, 193
waveforms, 194
Ammeter, 13, 115
Ampere, 3, 4
Amplifier gain, 285
Amplitude, 121, 195
Analogue instrument, 113
-to-digital conversion, 293
Anderson bridge, 608
Anode, 32
Antinode, 892
Apparent power, 232, 238,
464, 466
Argand diagram, 415
Argument, 421
Armature, 352
reaction, 353
Assymetrical -section, 875
T-section, 875
Atom, 11, 690
Attenuation, 128, 758, 763
bands, 790
coefficient, 816, 883
constant, 874
Attenuators, 758
assymetrical , 775
assymetrical T, 775
cascade, 782
L-section, 779
symmetrical , 760, 767
symmetrical T, 759, 764
Attraction type of m.i. instrument,
113
Auto transformers, 337
Auxiliary equation, 911, 912
Avalanche effect, 143
Average value, 196
Avometer, 118
Back e.m.f., 364
Band-pass filter, 792
-stop filter, 792
Bandwidth, 229, 280, 504
Base, 145
Battery, 35
Bell, electric, 20, 91
B-H curves, 77, 78
Bipolar junction transistor, 145
Bridge, a.c., 130, 476
rectifier, 208
Brush contact loss, 363
Brushes, 351
Buffer amplifier, 286
Calibration accuracy, 131
Candela, 3
Capacitance, 57, 61, 711, 722
between concentric cylinders,
725
of isolated twin line, 773, 870
Capacitive reactance, 214, 430
Capacitors, 55, 57
discharging, 70, 266
in parallel 63
in series 64
parallel plate 61, 711
practical types 69, 715
Car ignition, 20
Cartesian complex numbers, 415
Cathode, 32
ray oscilloscope, 13, 121
double beam, 122
Cell, 32, 36
capacity, 39
Ceramic capacitor, 69
Characteristicimpedance,759,875
of filters, 792
976 Index
Characteristics, d.c. generator, 358
d.c. machines, 369
transistor, 150
Charge, 4, 12, 58
density, 59
Charged particles, 31
Charging of cell, 34, 38
capacitor, 260, 901
Chemical effect of electric
current, 20, 31
Choke, 106
Circuit magnification factor, 497
Closed-loop gain, 283
Coaxial cable, 721
Coefficient of coupling, 843
Coercive force, 84, 692
Cofactor, 534
Coils in series, cumulatively
coupled, 845
differentially coupled, 846
Collector, 145
Combination of waveforms, 204
Commercial bridge, 131
Common-mode rejection ratio,
281
Commutation, 351
Commutator, 351, 352
Complex conjugate, 417
equations, 419
Complex frequency, 931
Complex numbers, 415
applications to parallel
networks, 444, 448
applications to series circuits,
429
Cartesian form, 415
De Moivres theorem, 423
determination of power, 465
equations, 419
operations involving, 417
polar form, 421
Complex wave, 124, 631
form factor, 648
general equation, 632
harmonics in single-phase
circuits, 653
mean value, 648
power associated with, 650
resonance due to harmonics,
664
r.m.s. value, 645
sources of harmonics, 666
waveform considerations, 683
Composite filters, 833
Compound winding, 353
wound generator, 360
motor, 372
Concentric cable, 725
field plotting, 731
Conductance, 6, 444, 870
Conductor, 12, 16, 137
Constant-current source, 181
Constant-k high-pass filter, 811
low-pass filter, 801
Contact potential, 140, 141
Continuity tester, 118
Continuous loading, 884
Cooker, 20
Copper loss, 330, 362
Core loss, 362
component, 319
Corrosion, 33
Coulomb, 4, 12
Coulomb’s law, 56
Coupled circuits, 849
dot rule, 857
Coupling coefficient, 843
Crest value, 195
Critically damped circuit, 911,
947
Cumulative compound motor, 372
Curie temperature, 692
Current, 3, 4, 11
division, 48, 449
magnification, 249, 519
main effects of, 20
transformer, 342
Curvilinear squares, 720, 721
Cut-off frequency, 790
Cycle, 194
Damping, 98, 946
device, 113
D.c. circuit theory, 167, 174
generators, 350, 356
machine construction, 352
Index 977
machine losses, 362
machines, 350
motors, 96, 364, 368
motor starter, 376
potentiometer, 130
transients, 259
Decibel, 126, 761
meter, 127
Delta connection, 298, 302,
603
-star transformation, 603
De Moivre’s theorem, 423
Depletion layer, 140
De Sauty bridge, 130, 482
Design impedance, 799
Detector types, a.c. bridges,
478
Determinants, 532, 538
Deviation from resonant
frequency, 509
Diamagnetism, 690
Dielectric, 57, 60, 711
hysteresis, 715
liquid, 715
loss, 715, 717
strength, 67, 712
stress, 727
Differential amplifier, 288, 289
compound motor, 373
voltage amplifier, 279
Differential equation solution,
921, 925
Differentiator circuit, 275
Diffusion, 141
Digital voltmeter, 117
Dimensions of most economical
cable, 728
Dirac function, 919
Discharging of capacitors, 70, 904
cells, 34, 38
Dissipation factor, 716
Distortion on transmission line,
882
Diverter, 379
Domains, 692
Doping, 138
Dot rule for coupled circuits, 857
Double beam oscilloscope, 122
cage induction motor, 405
Dust core, 698, 706
Dynamic current gain, 153, 156
resistance, 248, 517
Eddy current loss, 330, 696
Effective value, 196
Efficiency of d.c. generator, 363
d.c. motor, 373
induction motor, 395
transformer, 330
Electrical energy, 7, 18
power, 7, 16
symbols, 10, 910
measuring instruments and
measurements, 112
Electric bell, 20, 91
cell, 32
field strength, 57, 711
fire, 20
flux density, 59, 711
potential, 6
Electrochemical series, 32
Electrodes, 32
Electrolysis, 31
Electrolyte, 31, 37
Electrolytic capacitors, 70
Electromagnetic induction, 100
laws of, 101
Electromagnetic wave, 870
Electromagnetism, 89
Electromagnets, 91
Electron, 11, 31
Electronic instruments, 117
Electroplating, 20, 32
Electrostatic field, 55
E.m.f., 6, 34
equation of transformer, 320
in armature winding, 353
Emitter, 145
Energy, 5
associated with travelling wave,
886
electrical, 7, 18
stored in capacitor, 68
electric field, 737, 738
electromagnetic field, 750
magnetic field of inductor, 107,
750
Equipotential lines, 721
978 Index
Errors, measurement, 131
Exponential growth and decay
curves, 260
Even function, 683
Farad, 57
Faraday’s laws of electromagnetic
induction, 101
Ferrites, 692, 698, 706
Ferromagnetic-cored coils, 667
materials, 80, 691
Field plotting, 720, 731
theory, 620
Filter networks, 790
band-pass, 792
band-stop, 792
composite, 833
high-pass, 791, 807
low-pass, 791, 797
‘m derived’, 825
time delay, 822
Final value theorem, 920, 921
Fleming’s left-hand rule, 94
right-hand rule, 101
Flux density, 75, 688
linkage, 741
magnetic, 75, 688
Force, 4
on a charge, 98
current-carrying conductor,
90
Forced magnetization, 669
resonant frequency, 519
Form factor, 196, 648
Formulae, 164, 409, 960
Forward bias, 140, 145
characteristics, 140, 142
Free magnetization, 668
Frequency, 121, 194, 201
resonant, 247
Friction and windage losses, 362
Fourier series, 633
Full wave rectification, 208
Fundamental, 124, 631
Furnace, 20
Fuse, 20
Galvanometer, 129
Gas insulation, 715
Generator, 20
a.c., 102, 193
efficiency of, 363
Germanium, 138
Gravitational force, 4
Greek alphabet, 971
Grip rule, 90
Half-power points, 230, 508
-wave rectification, 208
-wave rectifier, 643
Harmonic analysis, 124, 633, 678
numerical method, 678
resonance, 664
synthesis, 633
Harmonics, 124, 631
in single phase circuits, 653
sources of, 666
Hay bridge, 130, 480
Heating effect of electric current,
20
Heaviside bridge, 130
Henry, 104, 741
Hertz, 121, 194
High-pass filter, 791, 807
ladder, 796
‘m derived’, 831
Hole, 138
Hysteresis, 84, 692, 693
loop, 84, 692, 693
loss, 84, 330, 693
Image impedance, 775
Imaginary numbers, 415
Impedance, 216, 220
matching, 623
triangle, 216, 220
Impulse, 919
Incident wave, 885
Induced e.m.f., 102, 741
Inductance, 104, 741, 841, 872
mutual, 104, 108
of a coil, 107
of a concentric cylinder, 741
of an isolated twin line, 746,
870
Induction motor, three-phase, 386
construction, 390
copper loss, 395
double cage, 405
impedance and current, 394
Index 979
losses and efficiency, 395
principle of operation, 390
production of rotating magnetic
field, 387
rotor e.m.f. and frequency, 393
starting, 403
torque equation, 397
-speed characteristic, 401
uses, 405
Inductive circuit, switching, 275
reactance, 214, 430
Inductors, 106
Initial conditions, 949
value theorem, 920
Initial slope and three-point
method, 261
Input bias current, 280
impedance, 283, 285
offset current, 280
voltage, 281
Insertion loss, 772
Instantaneous values, 195
Instrument ‘loading’ effect, 118
Insulation resistance tester, 118
Insulator, 12, 16, 137
Integrator circuit, 275
op amp, 288
Internal resistance of a cell, 34
Interpoles, 352
Inverse Laplace transform, 921
Inverting op amp, 282
Ion, 12, 31
Iron, 20
Iron loss, 330, 362
Isolating transformer, 340
Iterative impedance, 759, 775
Joule, 5, 7, 18, 68, 107
Kelvin, 3
Kettle, 20
Kilo-, 4, 14
Kilowatt-hour, 7, 18
Kirchhoff’s laws, 167, 531
in the s-domain, 932
network analysis, 535
Ladder network, 795
Lag, angle of, 201
Lamps in series and parallel, 52
Lap winding, 352, 353
Laplace transforms, 901, 914
by partial fractions, 923
capacitor, 930
definition of, 915
elementary functions, 915
inductor, 930
initial
conditions, 949
value theorem, 920
inverse, 921
L–R–C c
ircuit, 944
of derivatives, 920
resistor, 930
to solve differential equations,
925
Laws of electromagnetic
induction, 101
L–C parallel network, 241
Lead, angle of, 201
Lead-acid cell, 37
Leakage currents, 715
Leclanch
´
e cell, 36
Lenz’s law, 101
Level compounded machine, 361
Lifting magnet, 20, 92
Liquid dielectrics, 715
Linear device, 14
scale, 113
Loading effect, 118, 132
Load line, 154
Local action, 32, 33
Logarithmic ratios, 126, 761
Long shunt compound motor, 373
Loop currents, 545
inductance, 748
Loss angle, 484, 715
Losses in d.c. machines, 362
induction motor, 395
transformers, 330
Loudspeaker, 93
Low-pass filter, 791, 797
ladder, 795
‘m derived’, 828
LR–C parallel network, 243, 516
resonance, 516
LR–CR parallel network
resonance, 517
L–R–C circuit using Laplace
transforms, 944