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**A List of Tables
**

**Table No. Title Page No.
**

1.1 The International System of Units (SI) 9
1.2 Derived Units in SI 9
1.3 Standardized Prefixes to Signify Powers of 10 9
1.4 Interpretation of Reference Directions in Fig. 1.5 13
4.1 Terms for Describing Circuits 91
4.2 PSpice Sensitivity Analysis Results 128
6.1 Terminal Equations for Ideal Inductors and Capacitors 203
6.2 Equations for Series- and Parallel-Connected Inductors and Capacitors 203
7.1 Value of for *t *Equal to Integral Multiples of 217
8.1 Natural Response Parameters of the Parallel *RLC *Circuit 269
8.2 The Response of a Second-Order Circuit is Overdamped, Underdamped, or Critically Damped 295
8.3 In Determining the Natural Response of a Second-Order Circuit, We First Determine Whether

it is Over-, Under-, or Critically Damped, and Then We Solve the Appropriate Equations 295 8.4 In Determining the Step Response of a Second-Order Circuit, We Apply the Appropriate

Equations Depending on the Damping 296 9.1 Impedance and Reactance Values 318 9.2 Admittance and Susceptance Values 322 9.3 Impedance and Related Values 345

10.1 Annual Energy Requirements of Electric Household Appliances 365
10.2 Three Power Quantities and Their Units 368
12.1 An Abbreviated List of Laplace Transform Pairs 435
12.2 An Abbreviated List of Operational Transforms 440
12.3 Four Useful Transform Pairs 451
13.1 Summary of the *s*-Domain Equivalent Circuits 468
13.2 Numerical Values of 492
14.1 Input and Output Voltage Magnitudes for Several Frequencies 527
15.1 Normalized (so that ) Butterworth Polynomials up to the Eighth Order 577
17.1 Fourier Transforms of Elementary Functions 653
17.2 Operational Transforms 658
18.1 Parameter Conversion Table 682
18.2 Terminated Two-Port Equations 688

**Greek Alphabet
**

A Alpha I Iota P Rho

B Beta K Kappa Sigma

Gamma Lambda T Tau

Delta M Mu Upsilon

E Epsilon N Nu Phi

Z Zeta Xi X Chi

H Eta O *o *Omicron Psi

Theta Pi OmegavÆpßu™ c°h xjz

f£nP ymd¢ tl¶g≠ s©kb ria

vc = 1 rad>s vo(t)

te- t>t

ELECTRIC CIRCUITS TENTH EDITION

*This page intentionally left blank *

ELECTRIC CIRCUITS TENTH EDITION

James W. Nilsson
*Professor Emeritus
*

*Iowa State University
*

Susan A. Riedel
*Marquette University
*

Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montréal Toronto

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ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0

*Vice President and Editorial Director:
*Marcia J. Horton

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*Cover Design: *Black Horse Designs
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*

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Credits and acknowledgments borrowed from other sources and reproduced, with permission, in this textbook appear on appropriate page within text.

**Copyright © 2015, 2008, 2005 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street,
Upper Saddle River, New Jersey, 07458. **All rights reserved. Manufactured in the United States of America.
This publication is protected by Copyright, and permission should be obtained from the publisher prior to any
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**Library of Congress Cataloging-in-Publication Data
**Nilsson, James William.

Electric circuits / James W. Nilsson, Professor Emeritus, Iowa State University, Susan A. Riedel, Marquette University.—Tenth edition.

pages cm ISBN-13: 978-0-13-376003-3 ISBN-10: 0-13-376003-0

1. Electric circuits. I. Riedel, Susan A. II. Title. TK545.N54 2015 621.319'2—dc23

2013037725

10 9 8 7 6 5 4 3 2

To Anna

*This page intentionally left blank *

**vii
**

Brief Contents
**List of Examples xiii
Preface xvii
**

**Chapter 1 Circuit Variables 2
Chapter 2 Circuit Elements 24
Chapter 3 Simple Resistive Circuits 56
Chapter 4 Techniques of Circuit Analysis 88
Chapter 5 The Operational Amplifier 144
Chapter 6 Inductance, Capacitance, and Mutual Inductance 174
Chapter 7 Response of First-Order RL and RC Circuits 212
Chapter 8 Natural and Step Responses of RLC Circuits 264
Chapter 9 Sinusoidal Steady-State Analysis 304
Chapter 10 Sinusoidal Steady-State Power Calculations 358
Chapter 11 Balanced Three-Phase Circuits 396
Chapter 12 Introduction to the Laplace Transform 426
Chapter 13 The Laplace Transform in Circuit Analysis 464
Chapter 14 Introduction to Frequency Selective Circuits 520
Chapter 15 Active Filter Circuits 556
Chapter 16 Fourier Series 602
Chapter 17 The Fourier Transform 642
Chapter 18 Two-Port Circuits 676
Appendix A The Solution of Linear Simultaneous Equations 703
Appendix B Complex Numbers 723
Appendix C More on Magnetically Coupled Coils and Ideal Transformers 729
Appendix D The Decibel 737
Appendix E Bode Diagrams 739
Appendix F An Abbreviated Table of Trigonometric Identities 757
Appendix G An Abbreviated Table of Integrals 759
Appendix H Common Standard Component Values 761
**

**Answers to Selected Problems 763
Index 775**

*This page intentionally left blank *

**ix
**

Contents
**List of Examples xiii
**

**Preface xvii
**

**Chapter 1 Circuit Variables 2
Practical Perspective: Balancing Power **

*3*

**1.1 Electrical Engineering: An Overview ***4
***1.2 The International System of Units ***8
***1.3 Circuit Analysis: An Overview ***10
***1.4 Voltage and Current ***11
***1.5 The Ideal Basic Circuit Element ***12
***1.6 Power and Energy ***14
*

*Practical Perspective: Balancing Power **17
Summary 18
Problems 19
*

**Chapter 2 Circuit Elements 24
Practical Perspective: Heating with Electric
Radiators **

*25*

**2.1 Voltage and Current Sources ***26
***2.2 Electrical Resistance (Ohm’s Law) ***30
***2.3 Construction of a Circuit Model ***34
***2.4 Kirchhoff’s Laws ***37
***2.5 Analysis of a Circuit Containing Dependent
**

**Sources ***42
Practical Perspective: Heating with Electric
Radiators 46
Summary 48
Problems 48
*

**Chapter 3 Simple Resistive Circuits 56
Practical Perspective: Resistive Touch
Screens **

*57*

**3.1 Resistors in Series ***58
***3.2 Resistors in Parallel ***59
***3.3 The Voltage-Divider and Current-Divider
**

**Circuits ***61
***3.4 Voltage Division and Current Division ***64
***3.5 Measuring Voltage and Current ***66
***3.6 Measuring Resistance—The Wheatstone
**

**Bridge ***69
***3.7 Delta-to-Wye (Pi-to-Tee) Equivalent
**

**Circuits ***71
Practical Perspective: Resistive Touch
Screens 73
Summary 75
Problems 76
*

**Chapter 4 Techniques of Circuit
Analysis 88
**

*Practical Perspective: Circuits with Realistic
Resistors **89
*

**4.1 Terminology ***90
***4.2 Introduction to the Node-Voltage
**

**Method ***93
***4.3 The Node-Voltage Method and Dependent
**

**Sources ***95
***4.4 The Node-Voltage Method: Some Special
**

**Cases ***96
***4.5 Introduction to the Mesh-Current
**

**Method ***99
***4.6 The Mesh-Current Method and Dependent
**

**Sources ***102
***4.7 The Mesh-Current Method: Some Special
**

**Cases ***103
***4.8 The Node-Voltage Method Versus the
**

**Mesh-Current Method ***106
***4.9 Source Transformations ***109
***4.10 Thévenin and Norton Equivalents ***113
***4.11 More on Deriving a Thévenin
**

**Equivalent ***117
***4.12 Maximum Power Transfer ***120
***4.13 Superposition ***122
*

*Practical Perspective: Circuits with Realistic
Resistors **125
Summary 129
Problems 130
*

**Chapter 5 The Operational
Amplifier 144
**

*Practical Perspective: Strain Gages **145
***5.1 Operational Amplifier Terminals ***146
***5.2 Terminal Voltages and Currents ***146
***5.3 The Inverting-Amplifier Circuit ***150
***5.4 The Summing-Amplifier Circuit ***152
***5.5 The Noninverting-Amplifier
**

**Circuit ***153
***5.6 The Difference-Amplifier Circuit ***155
***5.7 A More Realistic Model for the Operational
**

**Amplifier ***159
Practical Perspective: Strain
Gages 162
Summary 164
Problems 165*

**x **Contents

**Chapter 6 Inductance, Capacitance, and
Mutual Inductance 174
**

*Practical Perspective: Capacitive Touch
Screens **175
*

**6.1 The Inductor ***176
***6.2 The Capacitor ***182
***6.3 Series-Parallel Combinations of Inductance
**

**and Capacitance ***187
***6.4 Mutual Inductance ***189
***6.5 A Closer Look at Mutual Inductance ***193
*

*Practical Perspective: Capacitive Touch
Screens **200
Summary 202
Problems 204
*

**Chapter 7 Response of First-Order RL and
RC Circuits 212
**

*Practical Perspective: Artificial Pacemaker **213
***7.1 The Natural Response of an RL Circuit **

*214*

**7.2 The Natural Response of an**

*RC*Circuit*220*

**7.3 The Step Response of**

*RL*and*RC*Circuits*224*

**7.4 A General Solution for Step and Natural**

**Responses ***231
***7.5 Sequential Switching ***236
***7.6 Unbounded Response ***240
***7.7 The Integrating Amplifier ***241
*

*Practical Perspective: Artificial Pacemaker **245
Summary 246
Problems 247
*

**Chapter 8 Natural and Step Responses
of RLC Circuits 264
**

*Practical Perspective: Clock for Computer
Timing **265
*

**8.1 Introduction to the Natural Response of a
Parallel RLC Circuit **

*266*

**8.2 The Forms of the Natural Response of a
Parallel RLC Circuit **

*270*

**8.3 The Step Response of a Parallel RLC Circuit **

*280*

**8.4 The Natural and Step Response of a Series**

*RLC***Circuit ***285
***8.5 A Circuit with Two Integrating Amplifiers ***289
*

*Practical Perspective: Clock for Computer
Timing **293
Summary 295
Problems 296
*

**Chapter 9 Sinusoidal Steady-State
Analysis 304
**

*Practical Perspective: A Household Distribution
Circuit **305
*

**9.1 The Sinusoidal Source ***306
***9.2 The Sinusoidal Response ***309
***9.3 The Phasor ***310
***9.4 The Passive Circuit Elements in the Frequency
**

**Domain ***315
***9.5 Kirchhoff’s Laws in the Frequency
**

**Domain ***319
***9.6 Series, Parallel, and Delta-to-Wye
**

**Simplifications ***320
***9.7 Source Transformations and Thévenin-Norton
**

**Equivalent Circuits ***327
***9.8 The Node-Voltage Method ***330
***9.9 The Mesh-Current Method ***331
***9.10 The Transformer ***332
***9.11 The Ideal Transformer ***336
***9.12 Phasor Diagrams ***342
*

*Practical Perspective: A Household Distribution
Circuit **344
Summary 345
Problems 346
*

**Chapter 10 Sinusoidal Steady-State
Power Calculations 358
**

*Practical Perspective: Vampire
Power **359
*

**10.1 Instantaneous Power ***360
***10.2 Average and Reactive Power ***361
***10.3 The rms Value and Power Calculations ***366
***10.4 Complex Power ***368
***10.5 Power Calculations ***369
***10.6 Maximum Power Transfer ***376
*

*Practical Perspective: Vampire
Power **382
Summary 384
Problems 385
*

**Chapter 11 Balanced Three-Phase
Circuits 396
**

*Practical Perspective: Transmission and
Distribution of Electric Power **397
*

**11.1 Balanced Three-Phase Voltages ***398
***11.2 Three-Phase Voltage Sources ***399
***11.3 Analysis of the Wye-Wye Circuit ***400
***11.4 Analysis of the Wye-Delta Circuit ***405
***11.5 Power Calculations in Balanced Three-Phase
**

**Circuits ***408
***11.6 Measuring Average Power in Three-Phase
**

**Circuits ***413
Practical Perspective: Transmission and
Distribution of Electric Power 416
Summary 417
Problems 418*

Contents **xi
**

**Chapter 12 Introduction to the Laplace
Transform 426
**

*Practical Perspective: Transient Effects **427
***12.1 Definition of the Laplace Transform ***428
***12.2 The Step Function ***429
***12.3 The Impulse Function ***431
***12.4 Functional Transforms ***434
***12.5 Operational Transforms ***435
***12.6 Applying the Laplace Transform ***440
***12.7 Inverse Transforms ***442
***12.8 Poles and Zeros of F(s) **

*452*

**12.9 Initial- and Final-Value Theorems**

*453*

*Practical Perspective: Transient
Effects **456
Summary 457
Problems 458
*

**Chapter 13 The Laplace Transform in
Circuit Analysis 464
**

*Practical Perspective: Surge Suppressors **465
***13.1 Circuit Elements in the s Domain **

*466*

**13.2 Circuit Analysis in the**

*s*Domain*468*

**13.3 Applications**

*470*

**13.4 The Transfer Function**

*482*

**13.5 The Transfer Function in Partial Fraction**

**Expansions ***484
***13.6 The Transfer Function and the Convolution
**

**Integral ***487
***13.7 The Transfer Function and the Steady-State
**

**Sinusoidal Response ***493
***13.8 The Impulse Function in Circuit
**

**Analysis ***496
Practical Perspective: Surge Suppressors 503
Summary 504
Problems 505
*

**Chapter 14 Introduction to Frequency
Selective Circuits 520
**

*Practical Perspective: Pushbutton Telephone
Circuits **521
*

**14.1 Some Preliminaries ***522
***14.2 Low-Pass Filters ***524
***14.3 High-Pass Filters ***530
***14.4 Bandpass Filters ***534
***14.5 Bandreject Filters ***543
*

*Practical Perspective: Pushbutton Telephone
Circuits **548
Summary 548
Problems 549
*

**Chapter 15 Active Filter Circuits 556
Practical Perspective: Bass Volume
Control **

*557*

**15.1 First-Order Low-Pass and High-Pass
Filters ***558
*

**15.2 Scaling ***562
***15.3 Op Amp Bandpass and Bandreject Filters ***564
***15.4 Higher Order Op Amp Filters ***571
***15.5 Narrowband Bandpass and Bandreject
**

**Filters ***584
Practical Perspective: Bass Volume
Control 589
Summary 592
Problems 593
*

**Chapter 16 Fourier Series 602
Practical Perspective: Active High-Q Filters **

*603*

**16.1 Fourier Series Analysis: An Overview ***605
***16.2 The Fourier Coefficients ***606
***16.3 The Effect of Symmetry on the Fourier
**

**Coefficients ***609
***16.4 An Alternative Trigonometric Form of the
**

**Fourier Series ***615
***16.5 An Application ***617
***16.6 Average-Power Calculations with Periodic
**

**Functions ***621
***16.7 The rms Value of a Periodic Function ***624
***16.8 The Exponential Form of the Fourier
**

**Series ***625
***16.9 Amplitude and Phase Spectra ***628
*

*Practical Perspective: Active High-Q Filters **630
Summary 632
Problems 633
*

**Chapter 17 The Fourier Transform 642
Practical Perspective: Filtering Digital
Signals **

*643*

**17.1 The Derivation of the Fourier Transform ***644
***17.2 The Convergence of the Fourier Integral ***646
***17.3 Using Laplace Transforms to Find Fourier
**

**Transforms ***648
***17.4 Fourier Transforms in the Limit ***651
***17.5 Some Mathematical Properties ***653
***17.6 Operational Transforms ***655
***17.7 Circuit Applications ***659
***17.8 Parseval’s Theorem ***662
*

*Practical Perspective: Filtering Digital
Signals **669
Summary 670
Problems 670*

**xii **Contents

**Chapter 18 Two-Port Circuits 676
Practical Perspective: Characterizing an
Unknown Circuit **

*677*

**18.1 The Terminal Equations ***678
***18.2 The Two-Port Parameters ***679
***18.3 Analysis of the Terminated Two-Port
**

**Circuit ***687
***18.4 Interconnected Two-Port Circuits ***692
*

*Practical Perspective: Characterizing an
Unknown Circuit **695
Summary 696
Problems 696
*

**Appendix A The Solution of Linear
Simultaneous Equations 703
**

**A.1 Preliminary Steps ***703
***A.2 Cramer’s Method ***704
***A.3 The Characteristic Determinant ***704
***A.4 The Numerator Determinant ***704
***A.5 The Evaluation of a Determinant ***705
***A.6 Matrices ***707
***A.7 Matrix Algebra ***708
***A.8 Identity, Adjoint, and Inverse Matrices ***712
***A.9 Partitioned Matrices ***715
***A.10 Applications ***718
*

**Appendix B Complex Numbers 723
B.1 Notation ***723
***B.2 The Graphical Representation of a Complex
**

**Number ***724
***B.3 Arithmetic Operations ***725
***B.4 Useful Identities ***726
***B.5 The Integer Power of a Complex
**

**Number ***727
***B.6 The Roots of a Complex Number ***727
*

**Appendix C More on Magnetically
Coupled Coils and Ideal
Transformers 729
**

**C.1 Equivalent Circuits for Magnetically Coupled
Coils ***729
*

**C.2 The Need for Ideal Transformers in the
Equivalent Circuits ***733
*

**Appendix D The Decibel 737
**

**Appendix E Bode Diagrams 739
E.1 Real, First-Order Poles and Zeros ***739
***E.2 Straight-Line Amplitude Plots ***740
***E.3 More Accurate Amplitude Plots ***744
***E.4 Straight-Line Phase Angle Plots ***745
***E.5 Bode Diagrams: Complex Poles and Zeros ***747
***E.6 Amplitude Plots ***749
***E.7 Correcting Straight-Line Amplitude Plots ***750
***E.8 Phase Angle Plots ***753
*

**Appendix F An Abbreviated Table of
Trigonometric Identities 757
**

**Appendix G An Abbreviated Table of
Integrals 759
**

**Appendix H Common Standard
Component Values 761
**

**Answers to Selected Problems 763
**

**Index 775**

**xiii
**

List of Examples
**Chapter 1
1.1 Using SI Units and Prefixes for Powers of 10 ***10
***1.2 Relating Current and Charge ***14
***1.3 Relating Voltage, Current, Power, and Energy ***16
*

**Chapter 2
2.1 Testing Interconnections of Ideal Sources ***28
***2.2 Testing Interconnections of Ideal Independent
**

**and Dependent Sources ***29
***2.3 Calculating Voltage, Current, and Power for a
**

**Simple Resistive Circuit ***33
***2.4 Constructing a Circuit Model of a Flashlight ***34
***2.5 Constructing a Circuit Model Based on Terminal
**

**Measurements ***36
***2.6 Using Kirchhoff’s Current Law ***39
***2.7 Using Kirchhoff’s Voltage Law ***40
***2.8 Applying Ohm’s Law and Kirchhoff’s Laws to
**

**Find an Unknown Current ***40
***2.9 Constructing a Circuit Model Based on Terminal
**

**Measurements ***41
***2.10 Applying Ohm’s Law and Kirchhoff’s Laws to
**

**Find an Unknown Voltage ***44
***2.11 Applying Ohm’s Law and Kirchhoff’s Law in an
**

**Amplifier Circuit ***45
*

**Chapter 3
3.1 Applying Series-Parallel Simplification ***60
***3.2 Analyzing the Voltage-Divider Circuit ***62
***3.3 Analyzing a Current-Divider Circuit ***63
***3.4 Using Voltage Division and Current Division to
**

**Solve a Circuit ***66
***3.5 Using a d’Arsonval Ammeter ***68
***3.6 Using a d’Arsonval Voltmeter ***68
***3.7 Applying a Delta-to-Wye Transform ***72
*

**Chapter 4
4.1 Identifying Node, Branch, Mesh and Loop in a
**

**Circuit ***90
***4.2 Using the Node-Voltage Method ***94
***4.3 Using the Node-Voltage Method with
**

**Dependent Sources ***95
***4.4 Using the Mesh-Current Method ***101
***4.5 Using the Mesh-Current Method with
**

**Dependent Sources ***102
*

**4.6 Understanding the Node-Voltage Method
Versus Mesh-Current Method ***107
*

**4.7 Comparing the Node-Voltage and Mesh-Current
Methods ***108
*

**4.8 Using Source Transformations to Solve
a Circuit ***110
*

**4.9 Using Special Source Transformation
Techniques ***112
*

**4.10 Finding the Thévenin Equivalent of a Circuit
with a Dependent Source ***116
*

**4.11 Finding the Thévenin Equivalent Using a Test
Source ***118
*

**4.12 Calculating the Condition for Maximum Power
Transfer ***121
*

**4.13 Using Superposition to Solve a Circuit ***124
*

**Chapter 5
5.1 Analyzing an Op Amp Circuit ***149
***5.2 Designing an Inverting Amplifier ***151
***5.3 Designing a Noninverting Amplifier ***154
***5.4 Designing a Difference Amplifier ***155
*

**Chapter 6
6.1 Determining the Voltage, Given the Current,
**

**at the Terminals of an Inductor ***177
***6.2 Determining the Current, Given the Voltage,
**

**at the Terminals of an Inductor ***178
***6.3 Determining the Current, Voltage, Power,
**

**and Energy for an Inductor ***180
***6.4 Determining Current, Voltage, Power, and
**

**Energy for a Capacitor ***184
***6.5 Finding , , and Induced by a Triangular
**

**Current Pulse for a Capacitor ***185
***6.6 Finding Mesh-Current Equations for a Circuit
**

**with Magnetically Coupled Coils ***192
*

**Chapter 7
7.1 Determining the Natural Response of an
**

*RL *Circuit *218
***7.2 Determining the Natural Response of an
**

*RL *Circuit with Parallel Inductors *219
***7.3 Determining the Natural Response of an
**

*RC *Circuit *222
***7.4 Determining the Natural Response of an
**

*RC *Circuit with Series Capacitors *223
*

wpv

**xiv **List of Examples

**7.5 Determining the Step Response of an
RL Circuit **

*227*

**7.6 Determining the Step Response of an
RC Circuit **

*230*

**7.7 Using the General Solution Method to Find an
RC Circuit’s Step Response **

*233*

**7.8 Using the General Solution Method with Zero
Initial Conditions ***234
*

**7.9 Using the General Solution Method to Find an
RL Circuit’s Step Response **

*234*

**7.10 Determining the Step Response of a Circuit
with Magnetically Coupled Coils ***235
*

**7.11 Analyzing an RL Circuit that has Sequential
Switching **

*237*

**7.12 Analyzing an RC Circuit that has Sequential
Switching **

*239*

**7.13 Finding the Unbounded Response in an
RC Circuit **

*241*

**7.14 Analyzing an Integrating Amplifier ***243
***7.15 Analyzing an Integrating Amplifier that has
**

**Sequential Switching ***243
*

**Chapter 8
8.1 Finding the Roots of the Characteristic
**

**Equation of a Parallel RLC Circuit **

*269*

**8.2 Finding the Overdamped Natural Response of a**

**Parallel RLC Circuit **

*272*

**8.3 Calculating Branch Currents in the Natural**

**Response of a Parallel RLC Circuit **

*273*

**8.4 Finding the Underdamped Natural Response of**

**a Parallel RLC Circuit **

*275*

**8.5 Finding the Critically Damped Natural**

**Response of a Parallel RLC Circuit **

*278*

**8.6 Finding the Overdamped Step Response of a**

**Parallel RLC Circuit **

*282*

**8.7 Finding the Underdamped Step Response of a**

**Parallel RLC Circuit **

*283*

**8.8 Finding the Critically Damped Step Response**

**of a Parallel RLC Circuit **

*283*

**8.9 Comparing the Three-Step Response Forms**

*284*

**8.10 Finding Step Response of a Parallel**

*RLC*Circuit**with Initial Stored Energy ***284
***8.11 Finding the Underdamped Natural Response of
**

**a Series RLC Circuit **

*287*

**8.12 Finding the Underdamped Step Response of a**

**Series RLC Circuit **

*288*

**8.13 Analyzing Two Cascaded Integrating**

**Amplifiers ***290
***8.14 Analyzing Two Cascaded Integrating Amplifiers
**

**with Feedback Resistors ***293
*

**Chapter 9
9.1 Finding the Characteristics of a Sinusoidal
**

**Current ***307
***9.2 Finding the Characteristics of a Sinusoidal
**

**Voltage ***308
***9.3 Translating a Sine Expression to a Cosine
**

**Expression ***308
***9.4 Calculating the rms Value of a Triangular
**

**Waveform ***308
***9.5 Adding Cosines Using Phasors ***314
***9.6 Combining Impedances in Series ***321
***9.7 Combining Impedances in Series and in
**

**Parallel ***323
***9.8 Using a Delta-to-Wye Transform in the
**

**Frequency Domain ***325
***9.9 Performing Source Transformations in the
**

**Frequency Domain ***327
***9.10 Finding a Thévenin Equivalent in the
**

**Frequency Domain ***328
***9.11 Using the Node-Voltage Method in the
**

**Frequency Domain ***330
***9.12 Using the Mesh-Current Method in the
**

**Frequency Domain ***331
***9.13 Analyzing a Linear Transformer in the
**

**Frequency Domain ***335
***9.14 Analyzing an Ideal Transformer Circuit in the
**

**Frequency Domain ***340
***9.15 Using Phasor Diagrams to Analyze a
**

**Circuit ***342
***9.16 Using Phasor Diagrams to Analyze Capacitive
**

**Loading Effects ***343
*

**Chapter 10
10.1 Calculating Average and Reactive Power ***364
***10.2 Making Power Calculations Involving
**

**Household Appliances ***365
***10.3 Determining Average Power Delivered to a
**

**Resistor by Sinusoidal Voltage ***367
***10.4 Calculating Complex Power ***369
***10.5 Calculating Average and Reactive Power ***372
***10.6 Calculating Power in Parallel Loads ***373
***10.7 Balancing Power Delivered with Power
**

**Absorbed in an ac Circuit ***374
***10.8 Determining Maximum Power Transfer without
**

**Load Restrictions ***378
***10.9 Determining Maximum Power Transfer with
**

**Load Impedance Restriction ***379
***10.10 Finding Maximum Power Transfer with
**

**Impedance Angle Restrictions ***380
***10.11 Finding Maximum Power Transfer in a Circuit
**

**with an Ideal Transformer ***381*

List of Examples **xv
**

**Chapter 11
11.1 Analyzing a Wye-Wye Circuit ***403
***11.2 Analyzing a Wye-Delta Circuit ***406
***11.3 Calculating Power in a Three-Phase Wye-Wye
**

**Circuit ***411
***11.4 Calculating Power in a Three-Phase Wye-Delta
**

**Circuit ***411
***11.5 Calculating Three-Phase Power with
**

**an Unspecified Load ***412
***11.6 Computing Wattmeter Readings in Three-Phase
**

**Circuits ***415
*

**Chapter 12
12.1 Using Step Functions to Represent a Function
**

**of Finite Duration ***430
*

**Chapter 13
13.1 Deriving the Transfer Function of a Circuit ***483
***13.2 Analyzing the Transfer Function
**

**of a Circuit ***485
***13.3 Using the Convolution Integral to Find
**

**an Output Signal ***491
***13.4 Using the Transfer Function to Find
**

**the Steady-State Sinusoidal Response ***495
*

**Chapter 14
14.1 Designing a Low-Pass Filter ***527
***14.2 Designing a Series RC Low-Pass Filter **

*528*

**14.3 Designing a Series**

*RL*High-Pass Filter*532*

**14.4 Loading the Series**

*RL*High-Pass Filter*532*

**14.5 Designing a Bandpass Filter**

*538*

**14.6 Designing a Parallel**

*RLC*Bandpass Filter*539*

**14.7 Determining Effect of a Nonideal Voltage**

**Source on a RLC Bandpass Filter **

*540*

**14.8 Designing a Series**

*RLC*Bandreject Filter*546*

**Chapter 15
15.1 Designing a Low-Pass Op Amp Filter ***559
***15.2 Designing a High-Pass Op Amp Filter ***561
***15.3 Scaling a Series RLC Circuit **

*563*

**15.4 Scaling a Prototype Low-Pass Op Amp**

**Filter ***563
***15.5 Designing a Broadband Bandpass Op Amp
**

**Filter ***567
***15.6 Designing a Broadband Bandreject Op Amp
**

**Filter ***570
***15.7 Designing a Fourth-Order Low-Pass Op Amp
**

**Filter ***574
***15.8 Calculating Butterworth Transfer
**

**Functions ***577
*

**15.9 Designing a Fourth-Order Low-Pass
Butterworth Filter ***579
*

**15.10 Determining the Order of a Butterworth
Filter ***582
*

**15.11 An Alternate Approach to Determining
the Order of a Butterworth Filter ***582
*

**15.12 Designing a High- Q Bandpass Filter **

*586*

**15.13 Designing a High-**

*Q*Bandreject Filter*588*

**Chapter 16
16.1 Finding the Fourier Series of a Triangular
**

**Waveform with No Symmetry ***607
***16.2 Finding the Fourier Series of an Odd Function
**

**with Symmetry ***614
***16.3 Calculating Forms of the Trigonometric Fourier
**

**Series for Periodic Voltage ***616
***16.4 Calculating Average Power for a Circuit
**

**with a Periodic Voltage Source ***623
***16.5 Estimating the rms Value of a Periodic
**

**Function ***625
***16.6 Finding the Exponential Form of the Fourier
**

**Series ***627
*

**Chapter 17
17.1 Using the Fourier Transform to Find
**

**the Transient Response ***660
***17.2 Using the Fourier Transform to Find the
**

**Sinusoidal Steady-State Response ***661
***17.3 Applying Parseval’s Theorem ***664
***17.4 Applying Parseval’s Theorem to an Ideal
**

**Bandpass Filter ***665
***17.5 Applying Parseval’s Theorem to a Low-Pass
**

**Filter ***666
*

**Chapter 18
18.1 Finding the z Parameters of a Two-Port
**

**Circuit ***679
***18.2 Finding the a Parameters from
**

**Measurements ***681
***18.3 Finding h Parameters from Measurements
**

**and Table 18.1 ***684
***18.4 Analyzing a Terminated Two-Port Circuit ***690
***18.5 Analyzing Cascaded Two-Port Circuits ***694*

*This page intentionally left blank *

The first edition of Electric Circuits, an introductory circuits text, was pub- lished in 1983. It included 100 worked examples and about 600 problems. It did not include a student workbook, supplements for PSpice or MultiSim, or any web support. Support for instructors was limited to a solution man- ual for the problems and enlarged copies of many text figures, suitable for making transparencies.

Much has changed in the 31 years since Electric Circuits first appeared, and during that time this text has evolved to better meet the needs of both students and their instructors. As an example, the text now includes about 150 worked examples, about 1850 problems, and extensive supplements and web content. The tenth edition is designed to revise and improve the material presented in the text, in its supplements, and on the web. Yet the fundamental goals of the text are unchanged. These goals are:

• To build an understanding of concepts and ideas explicitly in terms of previous learning. Students are constantly challenged by the need to layer new concepts on top of previous concepts they may still be struggling to master.This text provides an important focus on helping students understand how new concepts are related to and rely upon concepts previously presented.

• To emphasize the relationship between conceptual understanding and problem-solving approaches. Developing problem-solving skills continues to be the central challenge in a first-year circuits course. In this text we include numerous Examples that present problem- solving techniques followed by Assessment Problems that enable students to test their mastery of the material and techniques intro- duced. The problem-solving process we illustrate is based on con- cepts rather than the use of rote procedures. This encourages students to think about a problem before attempting to solve it.

• To provide students with a strong foundation of engineering prac- tices. There are limited opportunities in a first-year circuit analysis course to introduce students to realistic engineering experiences. We continue to take advantage of the opportunities that do exist by including problems and examples that use realistic component values and represent realizable circuits. We include many problems related to the Practical Perspective problems that begin each chapter. We also include problems intended to stimulate the students’ interest in engineering, where the problems require the type of insight typical of a practicing engineer.

**WHY THIS EDITION?
**The tenth edition revision of *Electric Circuits *began with a thorough
review of the text. This review provided a clear picture of what matters
most to instructors and their students and led to the following changes:

• Problem solving is fundamental to the study of circuit analysis. Having a wealth of new problems to assign and work is a key to suc- cess in any circuits course. Therefore, existing end-of-chapter prob- lems were revised, and new end-of-chapter problems were added. As a result, more than 40% of the problems in the tenth edition have never appeared in any previous edition of the text.

**xvii
**

Preface

**xviii **Preface

• Both students and instructors want to know how the generalized techniques presented in a first-year circuit analysis course relate to problems faced by practicing engineers. The Practical Perspective problems provide this connection between circuit analysis and the real world. We have created new Practical Perspective problems for Chapters 2, 3, 6, 7, 8, and 10. Many of the new problems represent the world of the 21st century. Each Practical Perspective problem is solved, at least in part, at the end of the chapter, and additional end- of-chapter problems can be assigned to allow students to explore the Practical Perspective topic further.

• The PSpice and Multisim manuals have been revised to include screenshots from the most recent versions of these software simula- tion applications. Each manual presents the simulation material in the same order as the material is presented in the text. These manu- als continue to include examples of circuits to be simulated that are drawn directly from the text. The text continues to indicate end-of- chapter problems that are good candidates for simulation using either PSpice or Multisim.

• Students who could benefit from additional examples and practice problems can use the Student Workbook, which has been revised to reflect changes to the tenth edition of the text. This workbook has examples and problems covering the following material: balancing power, simple resistive circuits, node voltage method, mesh current method, Thévenin and Norton equivalents, op amp circuits, first- order circuits, second-order circuits, AC steady-state analysis, and Laplace transform circuit analysis.

• The Student Workbook now includes access to Video Solutions, complete, step-by-step solution walkthroughs to representative homework problems.

• Learning Catalytics, a “bring your own device” student engagement, assessment, and classroom intelligence system is now available with the tenth edition. With Learning Catalytics you can: • Use open-ended questions to get into the minds of students to

understand what they do or don’t know and adjust lectures accordingly.

• Use a wide variety of question types to sketch a graph, annotate a circuit diagram, compose numeric or algebraic answers, and more.

• Access rich analytics to understand student performance. • Use pre-built questions or add your own to make Learning

Catalytics fit your course exactly.

• MasteringEngineering is an online tutorial and assessment program that provides students with personalized feedback and hints and instructors with diagnostics to track students’ progress. With the tenth edition, MasteringEngineering will offer new tutorial homework prob- lems, Coaching Activities, and Adaptive Follow-Up assignments. Visit www.masteringengineering.com for more information.

**HALLMARK FEATURES
Chapter Problems
**Users of *Electric Circuits *have consistently rated the Chapter Problems
as one of the book’s most attractive features. In the tenth edition, there
are over 1650 end-of-chapter problems with approximately 40% that
have never appeared in a previous edition. Problems are organized at
the end of each chapter by section.

Preface **xix
**

**Practical Perspectives
**The tenth edition continues the use of Practical Perspectives introduced
with the chapter openers.They offer examples of real-world circuits, taken
from real-world devices. The Practical Perspectives for six of the chapters
are brand new to this edition. Every chapter begins with a brief descrip-
tion of a practical application of the material that follows. Once the chap-
ter material is presented, the chapter concludes with a quantitative
analysis of the Practical Perspective application. A group of end-of-chap-
ter problems directly relates to the Practical Perspective application.
Solving some of these problems enables you to understand how to apply
the chapter contents to the solution of a real-world problem.

**Assessment Problems
**Each chapter begins with a set of chapter objectives. At key points in the
chapter, you are asked to stop and assess your mastery of a particular
objective by solving one or more assessment problems. The answers to all
of the assessment problems are given at the conclusion of each problem, so
you can check your work. If you are able to solve the assessment problems
for a given objective, you have mastered that objective. If you need more
practice, several end-of-chapter problems that relate to the objective are
suggested at the conclusion of the assessment problems.

**Examples
**Every chapter includes many examples that illustrate the concepts
presented in the text in the form of a numeric example. There are
nearly 150 examples in this text. The examples are intended to illus-
trate the application of a particular concept, and also to encourage
good problem-solving skills.

**Fundamental Equations and Concepts
**Throughout the text, you will see fundamental equations and concepts
set apart from the main text.This is done to help you focus on some of the
key principles in electric circuits and to help you navigate through the
important topics.

**Integration of Computer Tools
**Computer tools can assist students in the learning process by providing a
visual representation of a circuit’s behavior, validating a calculated solu-
tion, reducing the computational burden of more complex circuits, and
iterating toward a desired solution using parameter variation.This compu-
tational support is often invaluable in the design process.The tenth edition
includes the support of PSpice® and Multisim®, both popular computer
tools for circuit simulation and analysis. Chapter problems suited for
exploration with PSpice and Multisim are marked accordingly.

**Design Emphasis
**The tenth edition continues to support the emphasis on the design of cir-
cuits in many ways. First, many of the Practical Perspective discussions
focus on the design aspects of the circuits. The accompanying Chapter
Problems continue the discussion of the design issues in these practical
examples. Second, design-oriented Chapter Problems have been labeled
explicitly, enabling students and instructors to identify those problems
with a design focus. Third, the identification of problems suited to explo-
ration with PSpice or Multisim suggests design opportunities using these

**xx **Preface

software tools. Fourth, some problems in nearly every chapter focus on the use of realistic component values in achieving a desired circuit design. Once such a problem has been analyzed, the student can proceed to a lab- oratory to build and test the circuit, comparing the analysis with the meas- ured performance of the actual circuit.

**Accuracy
**All text and problems in the tenth edition have undergone our strict
hallmark accuracy checking process, to ensure the most error-free book
possible.

**RESOURCES FOR STUDENTS
MasteringEngineering. **MasteringEngineering provides tutorial home-
work problems designed to emulate the instructor’s office hour environ-
ment, guiding students through engineering concepts with self-paced
individualized coaching. These in-depth tutorial homework problems pro-
vide students with feedback specific to their errors and optional hints that
break problems down into simpler steps. Visit www.masteringengineering
.com for more information.

**Student Workbook. **This resource teaches students techniques for solving
problems presented in the text. Organized by concepts, this is a valuable
problem-solving resource for all levels of students.

The Student Workbook now includes access to Video Solutions, com- plete, step-by-step solution walkthroughs to representative homework problems.

**Introduction to Multisim and Introduction to PSpice Manuals—**Updated
for the tenth edition, these manuals are excellent resources for those wish-
ing to integrate PSpice or Multisim into their classes.

**RESOURCES FOR INSTRUCTORS
**All instructor resources are available for download at www.pearson
highered.com. If you are in need of a login and password for this site,
please contact your local Pearson representative.

**Instructor Solutions Manual**—Fully worked-out solutions to Assessment
Problems and end-of-chapter problems.

**PowerPoint lecture images**—All figures from the text are available in
PowerPoint for your lecture needs. An additional set of full lecture slides
with embedded assessment questions are available upon request.

**MasteringEngineering. **This online tutorial and assessment program
allows you to integrate dynamic homework with automated grading and
personalized feedback. MasteringEngineering allows you to easily track
the performance of your entire class on an assignment-by-assignment
basis, or the detailed work of an individual student. For more information
visit www.masteringengineeing.com.

**Learning Catalytics**—This “bring your own device” student engagement,
assessment and classroom intelligence system enables you to measure
student learning during class, and adjust your lectures accordingly. A wide
variety of question and answer types allows you to author your own
questions, or you can use questions already authored into the system. For
more information visit www.learningcatalytics.com.

Preface **xxi
**

**PREREQUISITES
**In writing the first 12 chapters of the text, we have assumed that the
reader has taken a course in elementary differential and integral calculus.
We have also assumed that the reader has had an introductory physics
course, at either the high school or university level, that introduces the
concepts of energy, power, electric charge, electric current, electric poten-
tial, and electromagnetic fields. In writing the final six chapters, we have
assumed the student has had, or is enrolled in, an introductory course in
differential equations.

**COURSE OPTIONS
**The text has been designed for use in a one-semester, two-semester, or a
three-quarter sequence.

• *Single-semester course: *After covering Chapters 1–4 and Chapters 6–10
(omitting Sections 7.7 and 8.5) the instructor can choose from
Chapter 5 (operational amplifiers), Chapter 11 (three-phase circuits),
Chapters 13 and 14 (Laplace methods), and Chapter 18 (Two-Port
Circuits) to develop the desired emphasis.

• *Two-semester sequence: *Assuming three lectures per week, the first
nine chapters can be covered during the first semester, leaving
Chapters 10–18 for the second semester.

• *Academic quarter schedule: *The book can be subdivided into three
parts: Chapters 1–6, Chapters 7–12, and Chapters 13–18.

The introduction to operational amplifier circuits in Chapter 5 can be omitted without interfering with the reading of subsequent chapters. For example, if Chapter 5 is omitted, the instructor can simply skip Section 7.7, Section 8.5, Chapter 15, and those assessment problems and end-of- chapter problems in the chapters following Chapter 5 that pertain to oper- ational amplifiers.

There are several appendixes at the end of the book to help readers make effective use of their mathematical background. Appendix A reviews Cramer’s method of solving simultaneous linear equations and simple matrix algebra; complex numbers are reviewed in Appendix B;Appendix C contains additional material on magnetically coupled coils and ideal trans- formers;Appendix D contains a brief discussion of the decibel;Appendix E is dedicated to Bode diagrams; Appendix F is devoted to an abbreviated table of trigonometric identities that are useful in circuit analysis; and an abbreviated table of useful integrals is given in Appendix G. Appendix H provides tables of common standard component values for resistors, induc- tors, and capacitors, to be used in solving many end-of-chapter problems. Selected Answers provides answers to selected end-of-chapter problems.

**ACKNOWLEDGMENTS
**There were many hard-working people behind the scenes at our pub-
lisher who deserve our thanks and gratitude for their efforts on behalf of
the tenth edition. At Pearson, we would like to thank Andrew Gilfillan,
Rose Kernan, Gregory Dulles, Tim Galligan, and Scott Disanno for their
continued support and encouragement, their professional demeanor,
their willingness to lend an ear, and their months of long hours and no
weekends. The authors would also like to acknowledge the staff at
Integra Software Solutions for their dedication and hard work in typeset-
ting this text. The authors would also like to thank Kurt Norlin for his
help in accuracy checking the text and problems.

**xxii **Preface

We are very grateful for the many instructors and students who have done formal reviews of the text or offered positive feedback and suggestions for improvement more informally. We are pleased to receive email from instructors and students who use the book, even when they are pointing out an error we failed to catch in the review process. We have been contacted by people who use our text from all over the world, and we thank all of you for taking the time to do so. We use as many of your suggestions as possible to continue to improve the content, the pedagogy, and the presentation in this text. We are privi- leged to have the opportunity to impact the educational experience of the many thousands of future engineers who will use this text.

JAMES W. NILSSON SUSAN A. RIEDEL

ELECTRIC CIRCUITS TENTH EDITION