Electric Circuits and Networks : For GTU

561 Pages·2010·17.771 MB·English

by  K. S. Suresh Kumar

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Electric Circuits and Networks
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Electric Circuits
and Networks
For Gujarat Technological
University
K. S. Suresh Kumar
Associate Professor
Department of Electrical Engineering
National Institute of Technology Calicut
Calicut, Kerala
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Copyright © 2011 Dorling Kindersley (India) Pvt. Ltd
Licensees of Pearson Education in South Asia
No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent.
This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any
material present in this eBook at any time.
ISBN 9788131755112
eISBN 9789332506572
Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India
Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India
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This book is dedicated to the memory of
Karunakaran Sir
who was the class teacher for class X – C division during the academic year 1973–74 at
Government Boys’ High School, Attingal, Thiruvanathapuram District, Kerala, India.
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Contents
PREFACE XI
ROAD MAP TO THE SYLLABUS XV
1
CIRCUIT VARIABLES AND CIRCUIT ELEMENTS
Introduction 1
1.1 Electromotive Force, Potential and Voltage 2
1.2 A Voltage Source with a Resistance Connected at its Terminals 7
1.3 Two-terminal Capacitance 13
1.4 Two-terminal Inductance 15
1.5 Ideal Independent Two-terminal Electrical Sources 22
1.6 Power and Energy Relations for Two-terminal Elements 24
1.7 Classification of Two-terminal Elements 30
1.8 Multi-terminal Circuit Elements 34
1.9 Summary 37
1.10 Problems 38
2
BASIC CIRCUIT LAWS
Introduction 41
2.1 Kirchhoff's Voltage Law (KVL) 42
2.2 Kirchhoff's Current LaW (KCL) 48
2.3 Interconnections of Ideal Sources 52
2.4 Analysis of a Single-Loop Circuit 53
2.5 Analysis of a Single-Node-Pair Circuit 57
2.6 Analysis of Multi-Loop, Multi-Node Circuits 59
2.7 Summary 61
2.8 Problems 62
3
SINGLE ELEMENT CIRCUITS
Introduction 67
3.1 The Resistor 68
3.2 The Inductor 75
3.3 Series Connection of Inductors 90
3.4 Parallel Connection of Inductors 92
3.5 The Capacitor 97
3.6 Series Connection of Capacitors 103
3.7 Parallel Connection of Capacitors 106
3.8 Summary 108
3.9 Questions 109
3.10 Problems 110
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viii CONTENTS
4
NODAL ANALYSIS AND MESH ANALYSIS OF MEMORYLESS CIRCUITS
Introduction 115
4.1 The Circuit Analysis Problem 116
4.2 Nodal Analysis of Circuits Containing Resistors with Independent
Current Sources 118
4.3 Nodal Analysis of Circuits ContainingIndependent Voltage Sources 121
4.4 Source Transformation Theorem and its Use in Nodal Analysis 127
4.5 Nodal Analysis of Circuits ContainingDependent Current Sources 130
4.6 Nodal Analysis of Circuits ContainingDependent Voltage Sources 133
4.7 Mesh Analysis of Circuits with Resistors and Independent Voltage Sources 138
4.8 Mesh Analysis of Circuits with Independent Current Sources 143
4.9 Mesh Analysis of Circuits Containing Dependent Sources 148
4.10 Summary 151
4.11 Problems 152
5
CIRCUIT THEOREMS
Introduction 157
5.1 Linearity of a Circuit and Superposition Theorem 158
5.2 Star-Delta Transformation Theorem 165
5.3 Substitution Theorem 169
5.4 Compensation Theorem 172
5.5 Thevenin’s Theorem and Norton’s Theorem 174
5.6 Determination of Equivalents for Circuits with Dependent Sources 177
5.7 Reciprocity Theorem 181
5.8 Maximum Power Transfer Theorem 184
5.9 Millman’s Theorem 186
5.10 Summary 187
5.11 Problems 188
6
SIMPLE RLCIRCUITS IN TIME-DOMAIN
Introduction 193
6.1 The Series RLCircuit 194
6.2 Series RLCircuit with Unit Step Input – Qualitative Analysis 198
6.3 Series RLCircuit with Unit Step Input – Power Series Solution 200
6.4 Step Response of an RLCircuit by Solving Differential Equation 203
6.5 Features of RLCircuit Step Response 208
6.6 Steady-State Response and Forced Response 220
6.7 Linearity and Superposition Principle in Dynamic Circuits 224
6.8 Unit Impulse Response of Series RLCircuit 228
6.9 Series RLCircuit with Exponential Inputs 235
6.10 General Analysis Procedure for Single Time Constant RLCircuits 240
6.11 Summary 247
6.12 Questions 248
6.13 Problems 250
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CONTENTS ix
7
RCAND RLCCIRCUITS IN TIME-DOMAIN
Introduction 255
7.1 RCCircuit Equations 256
7.2 Zero-Input Response of RCCircuit 256
7.3 Zero-State Response of RCCircuits for Various Inputs 258
7.4 Periodic Steady-State in a Series RCCircuit 267
7.5 Sinusoidal Steady-State Frequency Response of First-Order RCCircuits 269
7.6 The Series RLCCircuit – Zero-Input Response 278
7.7 Impulse Response of Series RLCCircuit 293
7.8 Step Response of Series RLCCircuit 293
7.9 Standard Time-Domain Specifications for Second-Order Circuits 294
7.10 Examples on Impulse and Step Response of Series RLCCircuits 295
7.11 Frequency Response of Series RLCCircuit 301
7.12 The Parallel RLCCircuit 315
7.13 Summary 322
7.14 Questions 324
7.15 Problems 326
8
HIGHER ORDER CIRCUITS IN TIME-DOMAIN
Introduction 331
8.1 Analysis of Multi-Mesh and Multi-Node Dynamic Circuits 332
8.2 Generalisations for an nthOrder Linear Time-Invariant Circuit 346
8.3 Time-Domain Convolution Integral 349
8.4 Summary 360
8.5 Questions 361
8.6 Problems 362
9
ANALYSIS OF DYNAMIC CIRCUITS BY LAPLACE TRANSFORMS
Introduction 365
9.1 Circuit Response to Complex Exponential Input 367
9.2 Expansion of a Signal in terms of Complex Exponential Functions 368
9.3 Laplace Transforms of some Common Right-Sided Functions 371
9.4 The s-Domain System Function H(S) 373
9.5 Poles and Zeros of System Function and Excitation Function 375
9.6 Method of Partial Fractions for Inverting Laplace Transforms 376
9.7 Some Theorems on Laplace Transforms 381
9.8 Solution of Differential Equations by Laplace Transforms 386
9.9 The s-Domain Equivalent Circuit 388
9.10 Total Response of Circuits using s-Domain Equivalent Circuit 389
9.11 Network Functions and Pole-Zero Plots 400
9.12 Impulse Response of Network Functions from Pole-Zero Plots 406
9.13 Sinusoidal Steady-State Frequency Response from Pole-Zero Plots 408
9.14 Analysis of Coupled Coils using Laplace Transforms 413
9.15 Summary 420
9.16 Problems 422