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Theory and Problems of
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.
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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.
JOSEPH A. EDMINISTER
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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
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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