Teach yourself algebra for electric circuits

567 Pages·2001·11.52 MB·English

by  Kenneth Jenkins

TEACH YOURSELF ALGEBRA
FOR ELECTRICAL CIRCUITS
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TEACH YOURSELF ALGEBRA
FOR ELECTRIC CIRCUITS
K. W. JENKINS
McGRAW-HILL
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DOI: 10.1036/0071414711
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Manybookscanbehadonthesubjectofelectriccircuits.Someareelementary,requiring
little mathematical skills, while others require a considerable knowledge of calculus.
This book can be considered a compromise, in that it uses no calculus but does make
considerableuseofalgebra.Thisincludesordinaryalgebraandalsothespecialalgebrasof
logic and matrices. All are carefully explained in the text, along with interesting and
important applications.
Themannerinwhichthebookisusedwilldependofcourseupontheindividual.Some
will wish to start on page 1 and continue on consecutively from that point. Others might
want to pick and choose. For instance, on a first reading some might prefer to postpone
study of Chapter 11 and jump directly from Chapter 10 to Chapters 12 and 13.
Atanyrate,Ihopethatyou,asanindividual,willfindthebookinterestingand,inthe
long run, a valuable contribution to your professional advancement.
K. W. JENKINS
v
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CHAPTER 1 Electric Charge and Electric Field. Potential Difference 1
1.1 Electrification and Electric Charge 1
1.2 Coulomb’s Law and the Unit of Charge 8
1.3 Electric Field Strength 10
1.4 Potential difference; the Volt 12
CHAPTER 2 Electric Current. Ohm’s Law. Basic Circuit
Configurations 15
2.1 Electric Current 15
2.2 Electromotive Force 18
2.3 Electrical Resistance. Ohm’s Law. Power 21
2.4 Some Notes on Temperature Effects 25
2.5 The Series Circuit 27
2.6 The Parallel Circuit 32
2.7 Series-Parallel Circuits 35
CHAPTER 3 Determinants and Simultaneous Equations 38
3.1 Introduction to Determinants 38
3.2 The Second-Order Determinant 39
3.3 Minors and Cofactors. Value of any nth-Order Determinant 41
3.4 Some Important Properties of Determinants 46
3.5 Determinant Solution of Linear Simultaneous Equations 52
3.6 Systems of Homogeneous Linear Equations 55
CHAPTER 4 Basic Network Laws and Theorems 58
4.1 Introduction 58
4.2 Kirchhoff’s Current Law 58
4.3 Kirchhoff’s Voltage Law 60
4.4 The Method of Loop Currents 62
4.5 Conductance. Millman’s Theorem 66
4.6 Thevenin’s Theorem 68
4.7 Norton’s Theorem 70
4.8 The Method of Node Voltages 73
vii
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viii Contents
CHAPTER 5 Sinusoidal Waves. rms Value. As Vector Quantities 76
5.1 Introduction 76
5.2 The Sinusoidal Functions and the Tangent Function 77
5.3 Graphics. Extension beyond 90 Degrees, Positive and Negative 80
5.4 Choice of Waveform. Frequency. The Radian 88
5.5 Power; rms Value of a Sine Wave of Voltage or Current 93
5.6 Sinusoidal Voltages and Currents as Vectors 96
5.7 Power Calculations 105
5.8 Application of Loop Currents 108
CHAPTER 6 Algebra of Complex Numbers 114
6.1 Imaginary Numbers 114
6.2 Complex Numbers. Addition and Multiplication 119
6.3 Conjugates and Division of Complex Numbers 120
6.4 Graphical Representation of Complex Numbers 122
6.5 Exponential Form of a Complex Number 125
6.6 Operations in the Exponential and Polar Forms. De Moivre’s
Theorem 128
6.7 Powers and Roots of Complex Numbers 131
6.8 Complex Numbers as Vectors 134
CHAPTER 7 Inductance and Capacitance 136
7.1 Introduction 136
7.2 Introduction to Magnetism 137
7.3 Electromagnetism 138
7.4 Self-Inductance 140
7.5 The Unit of Inductance 142
7.6 Capacitors and Capacitance 144
7.7 Capacitors in Series and in Parallel 148
CHAPTER 8 Reactance and Impedance. Algebra of ac Networks 151
8.1 Inductive Reactance. Impedance 151
8.2 RL Networks 155
8.3 Capacitive Reactance. RC Networks 160
8.4 The General RLC Network. Admittance 165
8.5 Real and Apparent Power. Power Factor 169
8.6 Series Resonance 174
8.7 Parallel Resonance 180
CHAPTER 9 Impedance Transformation. Electric Filters 187
9.1 Impedance Transformation. The ‘‘L’’ Section 187
9.2 The ‘‘T’’ and ‘‘Pi’’ Equivalent Networks 190
9.3 Conversion of Pi to T and T to Pi 196