K. MAHADEVAN. Professor Electrical and Electronics Engineering PSNA College of Engineering and Technology Dindigul, Tamil Nadu C.

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2 Electrical Circuit Analysis K. MAHADEVAN Professor Electrical and Electronics Engineering PSNA College of Engineering and Technology Dindigul, Tamil Nadu C. CHITRA Professor Electronics and Communication Engineering PSNA College of Engineering and Technology Dindigul, Tamil Nadu Delhi

3 ELECTRICAL CIRCUIT ANALYSIS K. Mahadevan and C. Chitra 2015 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Mohan Makhijani at Rekha Printers Private Limited, New Delhi

4 Dedicated to Our Parents

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6 Contents Preface xi Acknowledgements xiii 1. Introduction to DC Circuits International System of Units Network Terminology Lumped Circuit Versus Distributed Circuit Quantity of Electricity Charge Current Electric Potential Circuit Elements Resistance Inductance Capacitance Ohm s Law Specific Resistance (Resistivity) Conductance and Conductivity Open-Circuit and Short-Circuit Variation of Resistance with Temperature Electrical Power Electrical Energy Energy Sources Independent Sources Dependent Sources Resistances in Series Resistances in Parallel Star Delta Transformation Delta Star Transformation Star Delta Transformation 27 v

7 vi Contents 1.20 Conversion of Sources 34 Short Questions with Answers 38 Unsolved Problems Kirchhoff s Laws Introduction Kirchhoff s Current Law (KCL) Kirchhoff s Voltage Law (KVL) Current Division in Parallel Resistors Voltage Division in Series Resistors Mesh Analysis Nodal Analysis 76 Short Questions with Answers 87 Unsolved Problems Fundamentals of AC Circuits Introduction Generation of Alternating E.M.F Terminology Average and Root Mean Square Values Average Value Average Value of Sinusoidal Current Root Mean Square (RMS) Value or Effective Value RMS Value of Sinusoidal Current Form Factor and Peak Factor Form Factor Peak Factor In-Phase, Out-of-Phase and Phase Difference Phasor Representation Phasor Algebra and Operator j 108 Short Questions with Answers 112 Unsolved Problems Single-Phase AC Circuits Analysis of AC Circuits AC Circuit Containing Resistance Only AC Circuit Containing Inductance Only AC Circuit Containing Capacitance Only RL Series Circuit RC Series Circuit RLC Series Circuit Impedance Impedances in Series Impedances in Parallel Power and Power Factor in AC Circuits Parallel Circuits 131

8 Contents vii 4.5 Admittance Admittances in Series Admittances in Parallel 133 Short Questions with Answers 140 Unsolved Problems AC Network Analysis Introduction Mesh Analysis for AC Circuits Nodal Analysis for AC Circuits 149 Unsolved Problems Network Theorems Introduction Superposition Theorem Thevenin s Theorem Norton s Theorem Reciprocity Theorem Maximum Power Transfer Theorem Millman s Theorem Substitution Theorem Compensation Theorem Tellegen s Theorem 228 Short Questions with Answers 232 Unsolved Problems Three-Phase Circuits Introduction Generation of Three-phase E.M.F Advantages of Three-phase System Interconnection of Three Phases Balanced Y-Connection Balanced D Connection Unbalanced Loads Unbalanced D-Connected Load Unbalanced Y-Connected Load (Three-phase, Three-wire System) Solution of Three-phase, Three-wire, Y-Connected Load by Millman s Method Unbalanced Y-Connected Load (Three-phase, Four-wire System) Measurement of Power and Power Factor Three-wattmeter Method Two-wattmeter Method Power Factor Calculation Effect of Power Factor on Wattmeter Readings Reactive Power with Two-wattmeter Method One-wattmeter Method Reactive Power with One-wattmeter Method 269 Short Questions with Answers 272 Unsolved Problems 273

9 viii Contents 8. Magnetic Circuits Introduction Magnetic Circuit Terminology Composite Magnetic Circuit Determination of Ampere-Turns Parallel Magnetic Circuit Leakage Flux and Fringing Magnetisation (B H Curve) Electromagnetic Induction Faraday s Laws of Electromagnetic Induction Direction of Induced E.M.F. and Current Lenz s Law Fleming s Right-Hand Rule Induced E.M.F Dynamically Induced E.M.F Statically Induced E.M.F. 293 Short Questions with Answers 294 Unsolved Problems Coupled Circuits Introduction Self-inductance Mutual Inductance Coefficient of Coupling Dot Convention Analysis of Coupled Circuits Inductive Coupling in Series Series Aiding Series Opposing Inductive Coupling in Parallel Parallel Aiding Parallel Opposing Transformer Ideal Transformer Tuned Circuits Single-tuned Circuits Double-tuned Circuits 329 Short Questions with Answers 334 Unsolved Problems Resonance Series Resonance Effects of Series Resonance Reactance Curves 340

10 Contents ix Variation of Impedance with Frequency Resonance Curve Bandwidth of Series RLC Circuit Quality Factor of Series RLC Circuit Voltage Magnification in Series Resonance Parallel Resonance Susceptance Curves Variation of Impedance and Current with Frequency Bandwidth of Parallel RLC Circuit Quality Factor of Parallel RLC Circuit 356 Short Questions with Answers 363 Unsolved Problems DC Transients Introduction Free Response and Forced Response Initial Conditions Initial Conditions for Resistor Initial Conditions for Inductor Initial Conditions for Capacitor RL Transients Current Rise in RL Series Circuit (by Classical Method) Current Rise in RL Series Circuit (by Laplace Transformation Method) Current Decay in RL Series Circuit (by Classical Method) Current Decay in RL Series Circuit (by Laplace Transformation Method) RC Transients Charging in RC Series Circuit (by Classical Method) Charging in RC Series Circuit (by Laplace Transformation Method) Discharging in RC Series Circuit (by Classical Method) Discharging in RC Series Circuit (by Laplace Transformation Method) RLC Transients Response by Classical Method Response by Laplace Transformation Method 388 Short Questions with Answers 462 Unsolved Problems AC Transients RL Transients with Sinusoidal Excitation Response by Classical Method Response by Laplace Transformation Method RC Transients with Sinusoidal Excitation Response by Classical Method Response by Laplace Transformation Method RLC Transients with Sinusoidal Excitation Response by Classical Method Response by Laplace Transformation Method 489 Short Questions with Answers 520 Unsolved Problems 520

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