John Bird
1 Units associated with basic electrical quantities........................................ 1
SI units .......................................................................................................................... 1
Charge........................................................................................................................... 4
Force ............................................................................................................................. 4
Work .............................................................................................................................. 5
Power ............................................................................................................................ 5
Electrical potential and e. m. f. ...................................................................................... 6
Resistance and conductance ........................................................................................ 6
Electrical power and energy .......................................................................................... 7
Summary of terms, units and their symbols .................................................................. 8
Further problems on units associated with basic electrical quantities........................... 9
2 An introduction to electric circuits .............................................................. 10
Standard symbols for electrical components................................................................. 10
Electric current and quantity of electricity ...................................................................... 11
Potential difference and resistance ............................................................................... 13
Basic electrical measuring instruments ......................................................................... 13
Linear and non- linear devices ...................................................................................... 13
Ohms law ..................................................................................................................... 14
Multiples and sub- multiples .......................................................................................... 14
Conductors and insulators............................................................................................. 16
Electrical power and energy .......................................................................................... 16
Main effects of electric current ...................................................................................... 20
Fuses............................................................................................................................. 20
Further problems ........................................................................................................... 13
3 Resistance variation .................................................................................. 23
Resistance and resistivity.............................................................................................. 23
Temperature coefficient of resistance ........................................................................... 26
Further problems on resistance variation ...................................................................... 29
4 Chemical effects of electricity .................................................................... 31
Introduction.................................................................................................................... 31
Electrolysis .................................................................................................................... 31
Electroplating................................................................................................................. 32
The simple cell .............................................................................................................. 32
Corrosion ....................................................................................................................... 33
E.m.f. and internal resistance of a cell .......................................................................... 34
Primary cells .................................................................................................................. 36
Secondary cells ............................................................................................................. 37
Cell capacity .................................................................................................................. 39
Further problems on the chemical effects of electricity ................................................. 39
Assignment 1................................................................................................ 41
5 Series and parallel networks ..................................................................... 42
Series circuits ................................................................................................................ 42
Potential divider............................................................................................................. 44
Parallel networks ........................................................................................................... 45
Current division ............................................................................................................. 48
Wiring lamps in series and in parallel ............................................................................ 52
Further problems on series and parallel networks ........................................................ 53
6 Capacitors and capacitance ...................................................................... 55
Electrostatic field ........................................................................................................... 57
Electric field strength ..................................................................................................... 57
Capacitance .................................................................................................................. 57
Capacitors ..................................................................................................................... 57
Electric flux density........................................................................................................ 59
Permittivity..................................................................................................................... 59
The parallel plate capacitor ........................................................................................... 61
Capacitors connected in parallel and series.................................................................. 63
Dielectric strength.......................................................................................................... 67
Energy stored ................................................................................................................ 68
Practical types of capacitor ........................................................................................... 69
Discharging capacitors .................................................................................................. 70
Further problems on capacitors and capacitance ......................................................... 70
7 Magnetic circuits........................................................................................ 74
Magnetic fields .............................................................................................................. 74
Magnetic flux and flux density ....................................................................................... 75
Magnetomotive force and magnetic field strength......................................................... 76
Permeability and B Ò H curves ....................................................................................... 77
Reluctance .................................................................................................................... 80
Composite series magnetic circuits ............................................................................... 81
Comparison between electrical and magnetic quantities .............................................. 84
Hysteresis and hysteresis loss ...................................................................................... 84
Further problems on magnetic circuits .......................................................................... 85
Assignment 2................................................................................................ 87
8 Electromagnetism...................................................................................... 89
Magnetic field due to an electric current........................................................................ 89
Electromagnets ............................................................................................................. 91
Force on a current- carrying conductor ......................................................................... 92
Principle of operation of a simple d. c. motor ................................................................ 96
Principle of operation of a moving coil instrument ......................................................... 97
Force on a charge ......................................................................................................... 98
Further problems on electromagnetism......................................................................... 98
9 Electromagnetic induction ......................................................................... 100
Introduction to electromagnetic induction ...................................................................... 100
Laws of electromagnetic induction ................................................................................ 101
Inductance..................................................................................................................... 104
Inductors........................................................................................................................ 106
Energy stored ................................................................................................................ 107
Inductance of a coil ....................................................................................................... 107
Mutual inductance ......................................................................................................... 108
Further problems on electromagnetic induction ............................................................ 109
10 Electrical measuring instruments and measurements............................. 113
Introduction.................................................................................................................... 113
Analogue instruments.................................................................................................... 113
Moving-iron instrument .................................................................................................. 113
The moving-coil rectifier instrument .............................................................................. 114
Comparison of moving- coil, moving- iron and moving- coil rectifier instruments ......... 114
Shunts and multipliers ................................................................................................... 115
Electronic instruments ................................................................................................... 117
The ohmmeter ............................................................................................................... 117
Multimeters .................................................................................................................... 118
Wattmeters .................................................................................................................... 118
Instrument ˛ loadingÌ effect ............................................................................................ 118
The cathode ray oscilloscope ........................................................................................ 121
Waveform harmonics .................................................................................................... 124
Logarithmic ratios .......................................................................................................... 126
Null method of measurement ........................................................................................ 129
Wheatstone bridge ........................................................................................................ 129
D.c. potentiometer ......................................................................................................... 130
A.c. bridges ................................................................................................................... 130
Measurement errors ...................................................................................................... 131
Further problems on electrical measuring instruments and measurements.................. 133
11 Semiconductor diodes ............................................................................. 137
Types of materials ......................................................................................................... 137
Silicon and germanium.................................................................................................. 138
n-type and p-type materials ........................................................................................... 138
The p-n junction............................................................................................................. 139
Forward and reverse bias.............................................................................................. 140
Semiconductor diodes................................................................................................... 140
Rectification ................................................................................................................... 143
Further problems on semiconductor diodes .................................................................. 143
12 Transistors............................................................................................... 145
The bipolar junction transistor ....................................................................................... 145
Transistor action............................................................................................................ 147
Transistor symbols ........................................................................................................ 149
Transistor connections .................................................................................................. 149
Transistor characteristics .............................................................................................. 150
The transistor as an amplifier ........................................................................................ 152
The load line .................................................................................................................. 154
Current and voltage gains ............................................................................................. 155
Thermal runaway........................................................................................................... 158
Further problems on transistors .................................................................................... 159
Assignment 3................................................................................................ 162
Main formulae for Part 1............................................................................... 164
General.......................................................................................................................... 164
Capacitors and capacitance .......................................................................................... 164
Magnetic circuits............................................................................................................ 164
Electromagnetism.......................................................................................................... 164
Electromagnetic induction ............................................................................................. 164
Measurements............................................................................................................... 164
Part 2 Electrical Principles and Technology ....................................... 165
13 D.c. circuit theory..................................................................................... 167
Introduction.................................................................................................................... 167
Kirchhoffs laws ............................................................................................................. 167
The superposition theorem............................................................................................ 171
General d.c. circuit theory ............................................................................................. 174
Th · evenins theorem.................................................................................................... 176
Constant-current source ................................................................................................ 181
Nortons theorem........................................................................................................... 181
Th · evenin and Norton equivalent networks ................................................................. 184
Maximum power transfer theorem................................................................................. 187
Further problems on d. c. circuit theory ......................................................................... 189
14 Alternating voltages and currents............................................................ 193
Introduction.................................................................................................................... 193
The a.c. generator ......................................................................................................... 194
Waveforms .................................................................................................................... 194
A.c. values..................................................................................................................... 195
The equation of a sinusoidal waveform......................................................................... 200
Combination of waveforms ............................................................................................ 204
Rectification ................................................................................................................... 208
Further problems on alternating voltages and currents................................................. 209
Assignment 4................................................................................................ 212
15 Single-phase series a.c. circuits .............................................................. 213
Purely resistive a.c. circuit ............................................................................................. 214
Purely inductive a.c. circuit ............................................................................................ 214
Purely capacitive a. c. circuit ......................................................................................... 214
R … L series a.c. circuit ................................................................................................... 215
R … C series a.c. circuit .................................................................................................. 220
R … L … C series a.c. circuit ............................................................................................. 221
Series resonance .......................................................................................................... 225
Q-factor ......................................................................................................................... 227
Bandwidth and selectivity .............................................................................................. 229
Power in a.c. circuits ..................................................................................................... 230
Power triangle and power factor.................................................................................... 232
Further problems on single- phase series a. c. circuits ................................................. 234
16 Single-phase parallel a. c. circuits ........................................................... 238
Introduction.................................................................................................................... 238
R … L parallel a.c. circuit ................................................................................................. 238
R … C parallel a.c. circuit ................................................................................................ 240
L … C parallel a.c. circuit ................................................................................................. 241
LR … C parallel a.c. circuit .............................................................................................. 243
Parallel resonance and Q- factor ................................................................................... 247
Power factor improvement ............................................................................................ 252
Further problems on single- phase parallel a. c. circuits ............................................... 256
17 D.c. transients ......................................................................................... 259
Introduction.................................................................................................................... 259
Charging a capacitor ..................................................................................................... 260
Time constant for a C … R circuit .................................................................................... 260
Transient curves for a C … R circuit ................................................................................ 261
Discharging a capacitor ................................................................................................. 266
Current growth in an L … R circuit ................................................................................... 268
Time constant for an L … R circuit ................................................................................... 269
Transient curves for an L … R circuit............................................................................... 269
Current decay in an L … R circuit .................................................................................... 272
Switching inductive circuits............................................................................................ 275
The effects of time constant on a rectangular waveform............................................... 275
Further problems on d. c. transients.............................................................................. 276
18 Operational amplifiers ............................................................................. 278
Introduction to operational amplifiers ............................................................................ 278
Some op amp parameters ............................................................................................. 280
Op amp inverting amplifier ............................................................................................ 282
Op amp non- inverting amplifier .................................................................................... 285
Op amp voltage- follower .............................................................................................. 286
Op amp summing amplifier ........................................................................................... 286
Op amp voltage comparator .......................................................................................... 288
Op amp integrator ......................................................................................................... 288
Op amp differential amplifier ......................................................................................... 289
Digital to analogue ( D/ A) conversion........................................................................... 291
Analogue to digital ( A/ D) conversion ........................................................................... 293
Further problems on operational amplifiers................................................................... 294
Assignment 5................................................................................................ 296
19 Three phase systems .............................................................................. 297
Introduction.................................................................................................................... 297
Three-phase supply....................................................................................................... 298
Star connection ............................................................................................................. 298
Delta connection............................................................................................................ 302
Power in three- phase systems ..................................................................................... 303
Measurement of power in three- phase systems .......................................................... 306
Comparison of star and delta connections .................................................................... 312
Advantages of three- phase systems ............................................................................ 312
Further problems on three- phase systems................................................................... 312
20 Transformers ........................................................................................... 315
Introduction.................................................................................................................... 315
Transformer principle of operation ................................................................................ 316
Transformer no- load phasor diagram........................................................................... 319
E.m.f. equation of a transformer .................................................................................... 320
Transformer on- load phasor diagram........................................................................... 324
Transformer construction .............................................................................................. 325
Equivalent circuit of a transformer ................................................................................. 326
Regulation of a transformer ........................................................................................... 329
Transformer losses and efficiency................................................................................. 330
Resistance matching ..................................................................................................... 334
Auto transformers .......................................................................................................... 337
Isolating transformers.................................................................................................... 340
Three-phase transformers ............................................................................................. 340
Current transformers ..................................................................................................... 342
Voltage transformers ..................................................................................................... 343
Further problems on transformers................................................................................. 344
Assignment 6................................................................................................ 349
21 D.c. machines.......................................................................................... 350
Introduction.................................................................................................................... 350
The action of a commutator ........................................................................................... 351
D.c. machine construction ............................................................................................. 352
Shunt, series and compound windings.......................................................................... 353
E.m.f. generated in an armature winding ...................................................................... 353
D.c. generators .............................................................................................................. 356
Types of d.c. generator and their characteristics .......................................................... 356
D.c. machine losses ...................................................................................................... 362
Efficiency of a d.c. generator ......................................................................................... 363
D.c. motors .................................................................................................................... 364
Torque of a d.c. machine............................................................................................... 365
Types of d.c. motor and their characteristics................................................................. 368
The efficiency of a d. c. motor ....................................................................................... 373
D.c. motor starter........................................................................................................... 376
Speed control of d. c. motors ........................................................................................ 377
Motor cooling................................................................................................................. 381
Further problems on d. c. machines .............................................................................. 381
22 Three-phase induction motors................................................................. 386
Introduction.................................................................................................................... 386
Production of a rotating magnetic field .......................................................................... 387
Synchronous speed....................................................................................................... 388
Construction of a three- phase induction motor ............................................................ 390
Principle of operation of a three- phase induction motor ............................................... 390
Slip ................................................................................................................................ 391
Rotor e.m.f. and frequency ............................................................................................ 393
Rotor impedance and current ........................................................................................ 394
Rotor copper loss .......................................................................................................... 395
Induction motor losses and efficiency ........................................................................... 395
Torque equation for an induction motor ........................................................................ 397
Induction motor torque - speed characteristics ............................................................. 401
Starting methods for induction motors........................................................................... 403
Advantages of squirrel- cage induction motors ............................................................. 404
Advantages of wound rotor induction motor .................................................................. 405
Double cage induction motor......................................................................................... 405
Uses of three-phase induction motors........................................................................... 405
Further problems on three- phase induction motors ..................................................... 406
Assignment 7................................................................................................ 408
Main formulae for Part 2............................................................................... 409
A.c. theory: .................................................................................................................... 409
Single-phase circuits: .................................................................................................... 410
D.c. transients: .............................................................................................................. 410
Operational amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
Three-phase systems: ................................................................................................... 411
Transformers: ................................................................................................................ 411
D.c. machines:............................................................................................................... 411
Three-phase induction motors:...................................................................................... 411
Part 3 Advanced Circuit Theory and Technology ............................... 413
23 Revision of complex numbers ................................................................. 415
Introduction.................................................................................................................... 415
Operations involving Cartesian complex numbers ........................................................ 417
Complex equations........................................................................................................ 419
The polar form of a complex number ............................................................................ 421
Multiplication and division using complex numbers in polar form.................................. 421
De Moivres theorem „ powers and roots of complex numbers ..................................... 423
Further problems on complex numbers ......................................................................... 424
24 Application of complex numbers to series a. c. circuits........................... 429
Introduction.................................................................................................................... 429
Series a.c. circuits ......................................................................................................... 429
Further problems on series a. c. circuits ....................................................................... 440
25 Application of complex numbers to parallel a. c. networks...................... 25
Introduction.................................................................................................................... 25
Admittance, conductance and susceptance.................................................................. 25
Parallel a.c. networks .................................................................................................... 448
Further problems on parallel a. c. networks .................................................................. 454
26 Power in a.c. circuits ............................................................................... 459
Introduction.................................................................................................................... 459
Determination of power in a. c. circuits ......................................................................... 459
Power triangle and power factor.................................................................................... 464
Use of complex numbers for determination of power .................................................... 465
Power factor improvement ............................................................................................ 470
Further problems on power in a. c. circuits ................................................................... 472
Assignment 8................................................................................................ 475
27 A.c. bridges ............................................................................................. 476
Introduction.................................................................................................................... 476
Balance conditions for an a. c. bridge ........................................................................... 476
Types of a.c. bridge circuit ............................................................................................ 478
Further problems on a. c. bridges ................................................................................. 488
28 Series resonance and Q- factor .............................................................. 491
Introduction.................................................................................................................... 491
Series resonance .......................................................................................................... 491
Q-factor ......................................................................................................................... 495
Voltage magnification .................................................................................................... 498
Q-factors in series ......................................................................................................... 502
Bandwidth...................................................................................................................... 504
Small deviations from the resonant frequency .............................................................. 509
Further problems on series resonance and Q- factor.................................................... 512
29 Parallel resonance and Q- factor............................................................. 515
Introduction.................................................................................................................... 516
The LR … C parallel network ........................................................................................... 516
Dynamic resistance ....................................................................................................... 517
The LR … CR parallel network ........................................................................................ 517
Q-factor in a parallel network ........................................................................................ 519
Further problems on parallel resonance and Q- factor.................................................. 527
Assignment 9................................................................................................ 530
30 Introduction to network analysis .............................................................. 531
Introduction.................................................................................................................... 531
Solution of simultaneous equations using determinants ............................................... 532
Network analysis using Kirchhoffs laws ....................................................................... 535
Further problems on Kirchhoffs laws............................................................................ 542
31 Mesh-current and nodal analysis ............................................................ 545
Mesh-current analysis ................................................................................................... 545
Nodal analysis ............................................................................................................... 550
Further problems on mesh- current and nodal analysis ................................................ 559
32 The superposition theorem...................................................................... 562
Introduction.................................................................................................................... 562
Using the superposition theorem................................................................................... 562
Further problems on the superposition theorem ........................................................... 573
33 Thevenins and Nortons theorems ......................................................... 5755
Introduction.................................................................................................................... 575
Thevenins theorem....................................................................................................... 575
Nortons theorem........................................................................................................... 587
Thevenin and Norton equivalent networks .................................................................... 593
Further problems on Thevenins and Nortons theorem................................................ 598
Assignment 10.............................................................................................. 602
34 Delta-star and star-delta transformations ................................................ 603
Introduction.................................................................................................................... 603
Delta and star connections ............................................................................................ 603
Delta-star transformation............................................................................................... 603
Star-delta transformation............................................................................................... 611
Further problems on delta-star and star-delta transformations ..................................... 614
35 Maximum power transfer theorems and impedance matching................ 617
Maximum power transfer theorems ............................................................................... 617
Impedance matching ..................................................................................................... 623
Further problems on maximum power transfer theorems and impedance matching .... 626
Assignment 11.............................................................................................. 629
36 Complex Waveforms ............................................................................... 631
Introduction.................................................................................................................... 631
The general equation for a complex waveform ............................................................. 632
Harmonic synthesis ....................................................................................................... 633
Rms value, mean value and the form factor of a complex wave................................... 645
Power associated with complex waves ......................................................................... 650
Harmonics in single- phase circuits ............................................................................... 653
Resonance due to harmonics........................................................................................ 664
Sources of harmonics.................................................................................................... 666
Further problems on complex waveforms ..................................................................... 671
37 A numerical method of harmonic analysis............................................... 678
Introduction.................................................................................................................... 678
Harmonic analysis on data given in tabular or graphical form....................................... 683
Complex waveform considerations ............................................................................... 683
Further problems on a numerical method of harmonic analysis.................................... 685
38 Magnetic materials .................................................................................. 688
Revision of terms and units used with magnetic circuits ............................................... 688
Magnetic properties of materials ................................................................................... 690
Hysteresis and hysteresis loss ...................................................................................... 692
Eddy current loss........................................................................................................... 696
Separation of hysteresis and eddy current losses......................................................... 701
Nonpermanent magnetic materials ............................................................................... 704
Permanent magnetic materials...................................................................................... 706
Further problems on magnetic materials ....................................................................... 707
Assignment 12.............................................................................................. 710
39 Dielectrics and dielectric loss .................................................................. 711
Electric fields, capacitance and permittivity................................................................... 711
Polarization.................................................................................................................... 711
Dielectric strength.......................................................................................................... 712
Thermal effects.............................................................................................................. 714
Mechanical properties ................................................................................................... 714
Types of practical capacitor ........................................................................................... 715
Liquid dielectrics and gas insulation .............................................................................. 715
Dielectric loss and loss angle ........................................................................................ 715
Further problems on dielectric loss and loss angle ....................................................... 719
40 Field theory.............................................................................................. 720
Field plotting by curvilinear squares .............................................................................. 720
Capacitance between concentric cylinders ................................................................... 725
Capacitance of an isolated twin line .............................................................................. 733
Energy stored in an electric field ................................................................................... 737
Induced e.m.f. and inductance ...................................................................................... 741
Inductance of a concentric cylinder ( or coaxial cable).................................................. 741
Inductance of an isolated twin line ................................................................................ 746
Energy stored in an electromagnetic field ..................................................................... 750
Further problems on field theory ................................................................................... 753
41 Attenuators .............................................................................................. 758
Introduction.................................................................................................................... 758
Characteristic impedance.............................................................................................. 759
Logarithmic ratios .......................................................................................................... 761
Symmetrical T-and p- attenuators ................................................................................. 764
Insertion loss ................................................................................................................. 772
Asymmetrical Tand p- sections ..................................................................................... 775
The L-section attenuator ............................................................................................... 779
Two-port networks in cascade....................................................................................... 782
Further problems on attenuators ................................................................................... 785
Assignment 13.............................................................................................. 789
42 Filter networks ......................................................................................... 790
Introduction.................................................................................................................... 791
Basic types of filter sections .......................................................................................... 791
The characteristic impedance and the attenuation of filter sections.............................. 792
Ladder networks............................................................................................................ 795
Low-pass filter sections ................................................................................................. 797
High-pass filter sections ................................................................................................ 807
Propagation coefficient and time delay in filter sections................................................ 815
˛m-derivedÌ filter sections .............................................................................................. 825
Practical composite filters.............................................................................................. 833
Further problems on filter networks ............................................................................... 837
43 Magnetically coupled circuits................................................................... 841
Introduction.................................................................................................................... 841
Self-inductance.............................................................................................................. 841
Mutual inductance ......................................................................................................... 842
Coupling coefficient ....................................................................................................... 843
Coils connected in series .............................................................................................. 845
Coupled circuits............................................................................................................. 849
Dot rule for coupled circuits ........................................................................................... 857
Further problems on magnetically coupled circuits ....................................................... 864
44 Transmission lines................................................................................... 869
Introduction.................................................................................................................... 869
Transmission line primary constants ............................................................................. 869
Phase delay, wavelength and velocity of propagation .................................................. 871
Current and voltage relationships .................................................................................. 873
Characteristic impedance and propagation coefficient in terms of the primary
constants ....................................................................................................................... 875
Distortion on transmission lines..................................................................................... 882
Wave reflection and the reflection coefficient ................................................................ 885
Standing waves and the standing wave ratio ................................................................ 890
Further problems on transmission lines ........................................................................ 897
45 Transients and Laplace transforms ......................................................... 901
Introduction.................................................................................................................... 901
Response of R … C series circuit to a step input ............................................................ 901
Response of R … L series circuit to a step input ............................................................. 906
L … R … C series circuit response .................................................................................... 910
Introduction to Laplace transforms ................................................................................ 914
Inverse Laplace transforms and the solution of differential equations .......................... 921
Laplace transform analysis directly from the circuit diagram......................................... 930
L … R … C series circuit using Laplace transforms ........................................................... 944
Initial conditions............................................................................................................. 949
Further problems on transients and Laplace transforms ............................................... 952
Assignment 14.............................................................................................. 958
Main formulae for part 3 advanced circuit theory and technology................ 960
Complex numbers: ........................................................................................................ 960
General:......................................................................................................................... 960
R … L … C series circuit: ................................................................................................... 9600
LR … C network: .............................................................................................................. 961
LR … CR network: ........................................................................................................... 961
Determinants: ................................................................................................................ 961
Delta-star:...................................................................................................................... 961
Star-delta:...................................................................................................................... 961
Impedance matching: .................................................................................................... 961
Complex waveforms: ..................................................................................................... 961
Harmonic analysis: ........................................................................................................ 961
Hysteresis and Eddy current: ........................................................................................ 961
Dielectric loss: ............................................................................................................... 962
Field theory: ................................................................................................................... 962
Attenuators: ................................................................................................................... 962
Filter networks ............................................................................................................... 963
Magnetically coupled circuits......................................................................................... 963
Transmission lines:........................................................................................................ 964
Transients:..................................................................................................................... 964
Part 4 General Reference ...................................................................... 966
Standard electrical quantities „ their symbols and units ............................... 968
Greek alphabet............................................................................................. 971
Common prefixes ......................................................................................... 972
Resistor colour coding and ohmic values ..................................................... 973
Colour code for fixed resistors....................................................................................... 973
Letter and digit code for resistors .................................................................................. 973
Index............................................................................................................. 975