Schaum's Outline Series

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  • Theory and Problems of

    ELECTRICCIRCUITS

    Fourth Edition

    MAHMOOD NAHVI, Ph.D.Professor of Electrical Engineering

    California Polytechnic State University

    JOSEPH A. EDMINISTERProfessor Emeritus of Electrical Engineering

    The University of Akron

    Schaums Outline SeriesMcGRAW-HILL

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  • Copyright 2003, 1997, 1986, 1965] by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the UnitedStates of America. Except as permitted under the United States Copyright Act of 1976, no part of this publication may be repro-duced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written permis-sion of the publisher.

    0-07-142582-9

    The material in this eBook also appears in the print version of this title: 0-07-139307-2.

    All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of atrademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intentionof infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps.

    McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in cor-porate training programs. For more information, please contact George Hoare, Special Sales, at george_hoare@mcgraw-hill.com or (212) 904-4069.

    TERMS OF USEThis is a copyrighted work and The McGraw-Hill Companies, Inc. (McGraw-Hill) and its licensors reserve all rights inand to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and theright to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify,create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of itwithout McGraw-Hills prior consent. You may use the work for your own noncommercial and personal use; any other useof the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms.

    THE WORK IS PROVIDED AS IS. McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WAR-RANTIES AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROMUSING THE WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIAHYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED,INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PAR-TICULAR PURPOSE. McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the workwill meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill nor its licensorsshall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any dam-ages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work.Under no circumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, con-sequential or similar damages that result from the use of or inability to use the work, even if any of them has been advisedof the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether suchclaim or cause arises in contract, tort or otherwise.

    DOI: 10.1036/0071425829

    ebook_copyright 8 x 10.qxd 4/1/03 12:15 PM Page 1

  • This book is designed for use as a textbook for a first course in circuit analysis or as a supplement to

    standard texts and can be used by electrical engineering students as well as other engineereing and

    technology students. Emphasis is placed on the basic laws, theorems, and problem-solving techniques

    which are common to most courses.

    The subject matter is divided into 17 chapters covering duly-recognized areas of theory and study.

    The chapters begin with statements of pertinent definitions, principles, and theorems together with

    illustrative examples. This is followed by sets of solved and supplementary problems. The problems

    cover a range of levels of difficulty. Some problems focus on fine points, which helps the student to better

    apply the basic principles correctly and confidently. The supplementary problems are generally more

    numerous and give the reader an opportunity to practice problem-solving skills. Answers are provided

    with each supplementary problem.

    The book begins with fundamental definitions, circuit elements including dependent sources, circuit

    laws and theorems, and analysis techniques such as node voltage and mesh current methods. These

    theorems and methods are initially applied to DC-resistive circuits and then extended to RLC circuits by

    the use of impedance and complex frequency. Chapter 5 on amplifiers and op amp circuits is new. The op

    amp examples and problems are selected carefully to illustrate simple but practical cases which are of

    interest and importance in the students future courses. The subject of waveforms and signals is also

    treated in a new chapter to increase the students awareness of commonly used signal models.

    Circuit behavior such as the steady state and transient response to steps, pulses, impulses, and

    exponential inputs is discussed for first-order circuits in Chapter 7 and then extended to circuits of

    higher order in Chapter 8, where the concept of complex frequency is introduced. Phasor analysis,

    sinuosidal steady state, power, power factor, and polyphase circuits are thoroughly covered. Network

    functions, frequency response, filters, series and parallel resonance, two-port networks, mutual induc-

    tance, and transformers are covered in detail. Application of Spice and PSpice in circuit analysis is

    introduced in Chapter 15. Circuit equations are solved using classical differential equations and the

    Laplace transform, which permits a convenient comparison. Fourier series and Fourier transforms and

    their use in circuit analysis are covered in Chapter 17. Finally, two appendixes provide a useful summary

    of the complex number system, and matrices and determinants.

    This book is dedicated to our students from whom we have learned to teach well. To a large degree it

    is they who have made possible our satisfying and rewarding teaching careers. And finally, we wish to

    thank our wives, Zahra Nahvi and Nina Edminister for their continuing support, and for whom all these

    efforts were happily made.

    MAHMOOD NAHVI

    JOSEPH A. EDMINISTER

  • This page intentionally left blank.

  • CHAPTER 1 Introduction 11.1 Electrical Quantities and SI Units 11.2 Force, Work, and Power 11.3 Electric Charge and Current 21.4 Electric Potential 31.5 Energy and Electrical Power 41.6 Constant and Variable Functions 4

    CHAPTER 2 Circuit Concepts 72.1 Passive and Active Elements 72.2 Sign Conventions 82.3 Voltage-Current Relations 92.4 Resistance 102.5 Inductance 112.6 Capacitance 122.7 Circuit Diagrams 122.8 Nonlinear Resistors 13

    CHAPTER 3 Circuit Laws 243.1 Introduction 243.2 Kirchhoffs Voltage Law 243.3 Kirchhoffs Current Law 253.4 Circuit Elements in Series 253.5 Circuit Elements in Parallel 263.6 Voltage Division 283.7 Current Division 28

    CHAPTER 4 Analysis Methods 374.1 The Branch Current Method 374.2 The Mesh Current Method 384.3 Matrices and Determinants 384.4 The Node Voltage Method 404.5 Input and Output Resistance 414.6 Transfer Resistance 424.7 Network Reduction 424.8 Superposition 444.9 Thevenins and Nortons Theorems 45

    For more information about this title, click here.

    Copyright 2003, 1997, 1986, 1965 by The McGraw-Hill Companies, Inc. Click Here for Terms of Use.

  • 4.10 Maximum Power Transfer Theorem 47

    CHAPTER 5 Amplifiers and Operational Amplifier Circuits 645.1 Amplifier Model 645.2 Feedback in Amplifier Circuits 655.3 Operational Amplifiers 665.4 Analysis of Circuits Containing Ideal Op Amps 705.5 Inverting Circuit 715.6 Summing Circuit 715.7 Noninverting Circuit 725.8 Voltage Follower 745.9 Differental and Difference Amplifiers 755.10 Circuits Containing Several Op Amps 765.11 Integrator and Differentiator Circuits 775.12 Analog Computers 805.13 Low-Pass Filter 815.14 Comparator 82

    CHAPTER 6 Waveforms and Signals 1016.1 Introduction 1016.2 Periodic Functions 1016.3 Sinusoidal Functions 1036.4 Time Shift and Phase Shift 1036.5 Combinations of Periodic Functions 1066.6 The Average and Effective (RMS) Values 1076.7 Nonperiodic Functions 1086.8 The Unit Step Function 1096.9 The Unit Impulse Function 1106.10 The Exponential Function 1126.11 Damped Sinusoids 1146.12 Random Signals 115

    CHAPTER 7 First-Order Circuits 1277.1 Introduction 1277.2 Capacitor Discharge in a Resistor 1277.3 Establishing a DC Voltage Across a Capacitor 1297.4 The Source-Free RL Circuit 1307.5 Establishing a DC Current in an Inductor 1327.6 The Exponential Function Revisited 1327.7 Complex First-Order RL and RC Circuits 1347.8 DC Steady State in Inductors and Capacitors 1367.9 Transitions at Switching Time 1367.10 Response of First-Order Circuits to a Pulse 1397.11 Impulse Response of RC and RL Circuits 1407.12 Summary of Step and Impulse Responses in RC and RL Circuits 1417.13 Response of RC and RL Circuits to Sudden Exponential Excitations 1417.14 Response of RC and RL Circuits to Sudden Sinusoidal Excitations 1437.15 Summary of Forced Response in First-Order Circuits 1437.16 First-Order Active Circuits 143