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5. A u s t r a l i a • B r a z i l • J a p a n • Ko r e a • M e x i c o • S i n g a p o r e • S p a i n • Un i t e d Ki n g d o m • Un i t e d S t a t e s
Allan H. Robbins
Wilhelm C. Miller
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6. Circuit Analysis: Theory and Practice,
Fifth Edition
Allan H. Robbins and Wilhelm C. Miller
Vice President, Editorial: Dave Garza
Director of Learning Solutions: Sandy Clark
Acquisitions Editor: Stacy Masucci
Managing Editor: Larry Main
Product Manager: Mary Clyne
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Endsheets © Cengage Learning 2013
Cover image:
Digital illustration of an electric circuit board
© Creations/www.Shutterstock.com
© 2013, 2007 Delmar, Cengage Learning
ALL RIGHTS RESERVED. No part of this work covered by the copyright herein
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Multisim is a trademark of National Instruments. This publication is independent
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and does not authorize, sponsor, endorse or otherwise approve this publication.
Library of Congress Control Number: 2011939565
ISBN-13: 978-1-1332-8100-9
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7. Preface x
To the Student xviii
I Foundation dc Concepts 01
1 Introduction 3
1.1 Introduction 4
1.2 The SI System of Units 6
1.3 Converting Units 8
1.4 Power of Ten Notation 10
1.5 Prefixes, Engineering Notation,
and Numerical Results 12
1.6 Circuit Diagrams 15
1.7 Circuit Analysis Using Computers
and Calculators 17
Problems 19
2 Voltage and Current 27
2.1 Atomic Theory Review 29
2.2 The Unit of Electrical Charge: The Coulomb 33
2.3 Voltage 34
2.4 Current 37
2.5 Practical dc Voltage Sources 39
2.6 Measuring Voltage and Current 44
2.7 Switches, Fuses, and Circuit Breakers 47
Problems 49
3 Resistance 55
3.1 Resistance of Conductors 56
3.2 Electrical Wire Tables 59
3.3 Resistance of Wires—Circular Mils 62
3.4 Temperature Effects 66
3.5 Types of Resistors 69
3.6 Color Coding of Resistors 73
3.7 Measuring Resistance—The Ohmmeter 75
3.8 Thermistors 77
3.9 Photoconductive Cells 78
3.10 Nonlinear Resistance 79
3.11 Conductance 82
3.12 Superconductors 83
Problems 85
4 Ohm’s Law, Power, and Energy 91
4.1 Ohm’s Law 92
4.2 Voltage Polarity and Current Direction 98
4.3 Power 100
4.4 Power Direction Convention 104
4.5 Energy 105
4.6 Efficiency 107
4.7 Nonlinear and Dynamic Resistances 110
4.8 Computer-Aided Circuit Analysis 111
Problems 118
II Basic dc Analysis 125
5 Series Circuits 127
5.1 Series Circuits 128
5.2 Kirchhoff’s Voltage Law 131
5.3 Resistors in Series 132
5.4 Voltage Sources in Series 136
v
Contents
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8. 5.5 Interchanging Series Components 137
5.6 The Voltage Divider Rule 138
5.7 Circuit Ground 141
5.8 Voltage Subscripts 142
5.9 Internal Resistance of Voltage Sources 147
5.10 Ammeter Loading Effects 148
5.11 Circuit Analysis Using Computers 150
Problems 153
6 Parallel Circuits 165
6.1 Parallel Circuits 166
6.2 Kirchhoff’s Current Law 167
6.3 Resistors in Parallel 171
6.4 Voltage Sources in Parallel 176
6.5 Current Divider Rule 177
6.6 Analysis of Parallel Circuits 182
6.7 Voltmeter Loading Effects 184
6.8 Circuit Analysis Using Computers 186
Problems 190
7 Series-Parallel Circuits 203
7.1 The Series-Parallel Network 204
7.2 Analysis of Series-Parallel Circuits 205
7.3 Applications of Series-Parallel Circuits 211
7.4 Potentiometers 217
7.5 Loading Effects of Instruments 219
7.6 Circuit Analysis Using Computers 223
Problems 229
8 Methods of Analysis 239
8.1 Constant-Current Sources 240
8.2 Source Conversions 242
8.3 Current Sources in Parallel and Series 245
8.4 Branch-Current Analysis 247
8.5 Mesh (Loop) Analysis 251
8.6 Nodal Analysis 258
8.7 Delta-Wye (Pi-Tee) Conversion 264
8.8 Bridge Networks 270
8.9 Circuit Analysis Using Computers 277
Problems 280
9 Network Theorems 289
9.1 Superposition Theorem 290
9.2 Thévenin’s Theorem 293
9.3 Norton’s Theorem 300
9.4 Maximum Power Transfer Theorem 308
9.5 Substitution Theorem 313
9.6 Millman’s Theorem 314
9.7 Reciprocity Theorem 316
9.8 Circuit Analysis Using Computers 318
Problems 324
III Capacitance and Inductance 333
10 Capacitors and Capacitance 335
10.1 Capacitance 336
10.2 Factors Affecting Capacitance 338
10.3 Electric Fields 341
10.4 Dielectrics 344
10.5 Nonideal Effects 345
10.6 Types of Capacitors 346
10.7 Capacitors in Parallel and Series 350
10.8 Capacitor Current and Voltage During
Charging 354
10.9 Energy Stored by a Capacitor 357
10.10 Capacitor Failures and Troubleshooting 357
Problems 359
11 Capacitor Charging, Discharging,
and Simple Waveshaping
Circuits 365
11.1 Introduction 366
11.2 Capacitor Charging Equations 370
11.3 Capacitor with an Initial Voltage 375
11.4 Capacitor Discharging Equations 376
11.5 More Complex Circuits 378
11.6 An RC Timing Application 385
11.7 Pulse Response of RC Circuits 386
11.8 Transient Analysis Using Computers 390
Problems 396
vi Contents
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9. 12 Magnetism and Magnetic
Circuits 405
12.1 The Nature of a Magnetic Field 406
12.2 Electromagnetism 408
12.3 Magnetic Flux and Flux Density 410
12.4 Magnetic Circuits and Their Applications 411
12.5 Air Gaps, Fringing, and Laminated Cores 413
12.6 Series Elements and Parallel Elements 414
12.7 Magnetic Circuits with dc Excitation 415
12.8 Magnetic Field Intensity and Magnetization
Curves 416
12.9 Ampere’s Circuital Law 418
12.10 Series Magnetic Circuits: Given ⌽, Find NI 420
12.11 Series-Parallel Magnetic Circuits 424
12.12 Series Magnetic Circuits: Given NI, Find ⌽ 425
12.13 Force Due to an Electromagnet 427
12.14 Properties of Magnetic Materials 428
12.15 Sensing and Measuring Magnetic Fields 430
Problems 430
13 Inductance and Inductors 435
13.1 Electromagnetic Induction 437
13.2 Induced Voltage and Inductance 438
13.3 Self-Inductance 440
13.4 Computing Induced Voltage 442
13.5 Inductances in Series and Parallel 444
13.6 Practical Considerations 445
13.7 Inductance and Steady State dc 447
13.8 Energy Stored by an Inductance 449
13.9 Inductor Troubleshooting Hints 450
Problems 450
14 Inductive Transients 457
14.1 Introduction 458
14.2 Current Buildup Transients 461
14.3 Interrupting Current in an Inductive
Circuit 465
14.4 De-Energizing Transients 467
14.5 More Complex Circuits 469
14.6 RL Transients Using Computers 474
Problems 478
IV Foundation ac Concepts 483
15 ac Fundamentals 485
15.1 Introduction 486
15.2 Generating ac Voltages 487
15.3 Voltage and Current Conventions for ac 490
15.4 Frequency, Period, Amplitude, and
Peak Value 492
15.5 Angular and Graphic Relationships for Sine
Waves 496
15.6 Voltages and Currents as Functions of Time 500
15.7 Introduction to Phasors 504
15.8 ac Waveforms and Average Value 512
15.9 Effective (RMS) Values 517
15.10 Rate of Change of a Sine Wave (Derivative) 522
15.11 ac Voltage and Current Measurement 522
15.12 Circuit Analysis Using Computers 524
Problems 526
16 R, L, and C Elements and the
Impedance Concept 535
16.1 Complex Number Review 536
16.2 Complex Numbers in ac Analysis 542
16.3 R, L, and C Circuits with Sinusoidal
Excitation 548
16.4 Resistance and Sinusoidal ac 548
16.5 Inductance and Sinusoidal ac 550
16.6 Capacitance and Sinusoidal ac 553
16.7 The Impedance Concept 557
16.8 Computer Analysis of ac Circuits 559
Problems 563
17 Power in ac Circuits 571
17.1 Introduction 572
17.2 Power to a Resistive Load 573
17.3 Power to an Inductive Load 574
17.4 Power to a Capacitive Load 576
17.5 Power in More Complex Circuits 577
17.6 Apparent Power 580
17.7 The Relationship between P, Q, and S 581
Contents vii
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10. 17.8 Power Factor 584
17.9 ac Power Measurement 588
17.10 Effective Resistance 590
17.11 Energy Relationships for ac 591
17.12 Circuit Analysis Using Computers 592
Problems 595
V Impedance Networks 601
18 ac Series-Parallel Circuits 603
18.1 Ohm’s Law for ac Circuits 604
18.2 ac Series Circuits 610
18.3 Kirchhoff’s Voltage Law and the Voltage
Divider Rule 616
18.4 ac Parallel Circuits 619
18.5 Kirchhoff’s Current Law and the Current
Divider Rule 624
18.6 Series-Parallel Circuits 626
18.7 Frequency Effects 630
18.8 Applications 635
18.9 Circuit Analysis Using Computers 639
Problems 644
19 Methods of ac Analysis 657
19.1 Dependent Sources 658
19.2 Source Conversion 660
19.3 Mesh (Loop) Analysis 663
19.4 Nodal Analysis 668
19.5 Delta-to-Wye and Wye-to-Delta
Conversions 674
19.6 Bridge Networks 677
19.7 Circuit Analysis Using Computers 682
Problems 686
20 ac Network Theorems 695
20.1 Superposition Theorem—Independent
Sources 696
20.2 Superposition Theorem—Dependent
Sources 700
20.3 Thévenin’s Theorem—Independent
Sources 702
20.4 Norton’s Theorem—Independent Sources 706
20.5 Thévenin’s and Norton’s Theorems for
Dependent Sources 711
20.6 Maximum Power Transfer Theorem 719
20.7 Circuit Analysis Using Computers 723
Problems 729
21 Resonance 737
21.1 Series Resonance 739
21.2 Quality Factor, Q 741
21.3 Impedance of a Series Resonant Circuit 744
21.4 Power, Bandwidth, and Selectivity of a Series
Resonant Circuit 745
21.5 Series-to-Parallel RL and RC Conversion 753
21.6 Parallel Resonance 758
21.7 Circuit Analysis Using Computers 767
Problems 770
22 Filters and the Bode Plot 781
22.1 The Decibel 782
22.2 Multistage Systems 789
22.3 Simple RC and RL Transfer Functions 791
22.4 The Low-Pass Filter 800
22.5 The High-Pass Filter 806
22.6 The Band-Pass Filter 811
22.7 The Band-Reject Filter 814
22.8 Circuit Analysis Using Computers 815
Problems 819
23 Transformers and Coupled
Circuits 829
23.1 Introduction 830
23.2 Iron-Core Transformers: The Ideal Model 834
23.3 Reflected Impedance 840
23.4 Power Transformer Ratings 842
23.5 Transformer Applications 842
23.6 Practical Iron-Core Transformers 848
23.7 Transformer Tests 852
23.8 Voltage and Frequency Effects 854
23.9 Loosely Coupled Circuits 855
23.10 Magnetically Coupled Circuits with Sinusoidal
Excitation 860
viii Contents
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11. 23.11 Coupled Impedance 862
23.12 Circuit Analysis Using Computers 864
Problems 867
24 Three-Phase Systems 875
24.1 Three-Phase Voltage Generation 876
24.2 Basic Three-Phase Circuit Connections 877
24.3 Basic Three-Phase Relationships 880
24.4 Examples 888
24.5 Power in a Balanced System 893
24.6 Measuring Power in Three-Phase Circuits 897
24.7 Unbalanced Loads 901
24.8 Power System Loads 904
24.9 Circuit Analysis Using Computers 904
Problems 908
25 Nonsinusoidal Waveforms 917
25.1 Composite Waveforms 919
25.2 Fourier Series 921
25.3 Fourier Series of Common Waveforms 926
25.4 Frequency Spectrum 931
25.5 Circuit Response to a Nonsinusoidal
Waveform 936
25.6 Circuit Analysis Using Computers 940
Problems 943
Appendix A
Multisim and PSpice 949
Appendix B
Mathematics in Circuit Analysis: A Brief Tutorial 956
Appendix C
Maximum Power Transfer Theorem 964
Appendix D
Answers to Odd-Numbered Problems 967
Glossary 979
Index 991
Contents ix
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12. x
Preface
The Book and Who It Is For
This textbook is written primarily for students in electronics technology and
electrical technology programs, engineering programs, and industrial training
programs at colleges, universities, and career schools and in industry. Its goal
continues to be to meet the training needs of today’s students, their professors,
and their instructors as it has throughout its four previous editions. An introduc-
tory circuit analysis textbook, it covers fundamentals of dc and ac circuits, meth-
ods of analysis, capacitance, inductance, magnetic circuits, basic transients,
Fourier analysis, and other topics. When students successfully complete a course
using this book, they will have a good working knowledge of basic circuit prin-
ciples and a demonstrated ability to solve a variety of circuit-related problems.
Text Organization
The book contains 25 chapters and is divided into 5 main parts: Foundation
dc Concepts, Basic dc Analysis, Capacitance and Inductance, Foundation ac
Concepts, and Impedance Networks. Chapters 1 through 4 are introductory.
They cover the foundation concepts of voltage, current, resistance, Ohm’s law,
and power. Chapters 5 through 9 focus on dc analysis methods. Included are
Kirchhoff’s laws, series and parallel circuits, mesh and nodal analysis,Y and ⌬
transformations, source transformations, Thévenin’s and Norton’s theorems,
the maximum power transfer theorem, and so on. Chapters 10 through 14 cover
capacitance, magnetism, and inductance, plus magnetic circuits and simple dc
transients. Chapters 15 through 17 cover foundation ac concepts; ac voltage
generation; and the basic ideas of frequency, period, phase, and so on. Phasors
and the impedance concept are introduced and used to solve simple problems.
Power in ac circuits is investigated and the concept of power factor and the
power triangle are introduced. Chapters 18 through 25 then apply these ideas.
Topics include ac versions of earlier dc techniques such as mesh and nodal
analysis, Thévenin’s theorem, and so on, as well as new ideas such as resonance,
filters, Bode techniques, three-phase systems, transformers, and nonsinusoidal
waveform analysis.
Several appendices round out the book. Appendix A provides operational
instructions, reference material, and tips for PSpice and Multisim users;
Appendix B is a math-and-calculator tutorial that describes typical mathemat-
ical and calculator usage in circuit analysis—including methods for solving
simultaneous equations; Appendix C shows how to apply calculus to derive the
maximum power transfer theorem for both dc circuits and ac circuits, while
Appendix D contains answers to odd-numbered end-of-chapter problems.
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13. Preface xi
Required Background
Students need a working knowledge of basic algebra and trigonometry and the
ability to solve second-order linear equations such as those found in mesh analysis.
They should be familiar with the SI metric system and the atomic nature of mat-
ter. Calculus is introduced gradually into later chapters for those who need it.
However, calculus is not an essential prerequisite or corequisite, as all topics can
be readily understood without it. Thus, students who know (or are studying) cal-
culus can use this knowledge to enrich their understanding of circuit theory,
whereas, because the calculus parts of the book can be omitted without any loss
of continuity, students unfamiliar with calculus can comfortably navigate around
it as they work through the chapters. (Calculus-based material is flagged by an
icon to identify it as optional material for advanced learners.)
Features of the Book
• A clearly written, easy-to-understand style emphasizes principles and
concepts.
• More than 1,200 diagrams and photos. Color and 3D visual effects are
used to illustrate and clarify ideas and to aid visual learners.
• Examples. Over 380 examples, worked out in step-by-step detail, help pro-
mote understanding and guide the student in problem solving.
• Practice Problems. These follow the presentation of key ideas, encouraging
the student to practice the skills just learned.
Each chapter opens with Key Terms, Outline, Objectives,
Chapter Preview, and Putting It in Perspective.
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14. xii Preface
• Key Terms at the beginning of each chapter identify new terms to be introduced.
• Competency-Based Objectives define the knowledge or skill that the stu-
dent is expected to gain from each chapter.
• Chapter Previews provide a context and a brief overview for the upcoming
chapter and answer the question “Why am I learning this?”
• Putting It in Perspective. These are short vignettes that provide interesting
background on people, events, and ideas that led to major advances or con-
tributions in electrical science.
• In-Process Learning Checks. These are short, self-test quizzes that provide
a quick check of the material just learned and help identify learning gaps.
• Putting It into Practice. These are end-of-chapter mini-projects—such as
assignments that require students to do some research or to reason their way
through realistic situations similar to what they might encounter in practice.
• Margin Notes. These include Practical Notes (which provide practical infor-
mation, e.g., tips on how to use meters) plus general notes that provide addi-
tional information or add a perspective to the material being studied.
• Audio Clips. These clips (found on our Web site) present a more in-depth
discussion of the most difficult topic for each chapter.
• Computer Simulations. Each chapter (beginning with Chapter 4) contains
a section on computer-aided circuit analysis using Multisim and PSpice.
New to this edition—now you are able to study the
circuits of the textbook “live” and fully functional
on your computer screen—see details elsewhere
in Appendix A. Over 180 simulations, each desig-
nated by an icon as indicated, are provided.
Practice Problems build problem-solving
skills and test student understanding.
In-Process Learning Checks provide a
quick review of material just studied.
Over 380 examples, worked out in step-by-step detail,
help promote understanding and guide the students in
problem solving. (This example is from Chapter 5.)
Pictorials help intro-
duce the idea of
schematic diagrams
in early chapters.
MultiSimPSPICE
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

15. Preface xiii
These sections provide step-by-step instructions on how to build circuits on
your screen, plus actual screen captures to show you what you should see
when you run the simulations.
• More than 1,600 end-of-chapter problems, Practice Problems, and
In-Process Learning Check problems are provided.
• Calculators. The use of calculators in circuit analysis has been integrated
throughout the text. (Calculator techniques are also discussed in Appendix B,
Mathematics in Circuit Analysis.)
• Answers to Odd-Numbered Problems. These are contained in Appendix D.
New and Improved Features of the Fifth Edition
Current users of a textbook generally expect that a new edition will retain the
features that attracted them to the book in the first place. For such users, we
have maintained the same basic structure that we used in the fourth edition,
with improvements made in presentation, examples, problems, photographs,
and the glossary. Additionally, the Multisim and PSpice material has been
updated to the latest revisions and some new examples have been added. For
users who would like to see us take advantage of new technologies such as the
Internet, electronic publishing, and circuit simulation software to provide an
Each chapter (as applicable) includes a section showing
how to use modern computer methods to solve circuits by
simulation. The first example below (from Chapter 14)
shows how to use Multisim to solve a transient problem,
while the second example (from Chapter 23) shows how to
use PSpice to solve a coupled circuit problem.
Putting It into Practice problems are provided at the end
of chapters and describe a work-related problem.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

16. xiv Preface
improved learning experience, we have done that, too. Prime examples of the
latter are the introduction of circuit simulation courseware (to permit interac-
tive, hands-on learning on a personal computer), the addition of CourseMate
(a multifaceted learning tool), and modernized and expanded Web sites for
students and instructors. These are all features that we hope will appeal to new
adopters as well. Let us look at each in turn.
Learning Circuit Theory Interactively on Your Computer (New)
While many students find it challenging to learn circuit theory simply by “read-
ing the book,” few have the resources necessary to establish their own personal
laboratories where they can work their way through the learning process using
real test and measurement equipment. However, the widespread use of comput-
ers and the availability of circuit simulation software now make it possible to
create a hands-on learning environment on a desktop (or laptop)—in essence, a
“virtual laboratory” (complete with multimeters, oscilloscopes, signal genera-
tors, and so on) where, along with our newly developed courseware, you can
study the circuits of the textbook “live” and interactively on your screen. You
can, for instance, open and close virtual switches to activate and deactivate sim-
ulated textbook circuits, measure voltage and current using virtual meters,
change and add circuit components to test new ideas, add new instrumentation,
initiate transients, view waveforms on virtual oscilloscopes, and in general,
interact with the textbook material in a manner that you simply cannot do by
reading from a printed page.
To implement this new feature, we have created approximately 180 pre-
built circuit simulation files in Multisim software. Available by printed access
code to purchasers of this book, these files address the most important circuit
analysis topics in the text. Simulations files are structured like mini-tutorials—
they begin with a short overview of the topic, walk you through its main ideas,
then guide you step-by-step through the simulation process. If you are a hands-
on learner or have difficulty visualizing theoretical concepts or would simply
like to gain a better understanding of circuit basics through practice, you
should find these simulations invaluable. (You need to have Multisim loaded on
your computer to run these simulations, but you need not be a Multisim expert
to use them.)
These files are intended for use by both students and instructional staff—
for example, students may use them as learning aids and instructional staff as
teaching aids. (Our Web site provides suggestions.) Note that the use of these
simulations is optional and that you can use or not use them as you wish.
Student Premium Website
Various icons appear throughout this text to indicate that additional learning
tools are available at our expanded and updated Student Premium Website for
Circuit Analysis. The printed access code at the back of this book will give stu-
dents online access to the following suite of learning tools:
• Learning Circuit Analysis Interactively on Your Computer: This is
the hands-on circuit simulation courseware described above.
• Multisim Beginner’s Tutorial: This tutorial guides you step by step
through the creation of Multisim circuit simulations. It supplements
the presentation of Section 4.8 of the textbook and serves as an aid to
creating your own simulations.
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

17. • PSpice Beginner’s Tutorial: This tutorial guides you step by step
through the creation of PSpice circuit simulations. It supplements the
presentation of Section 4.8 of the textbook.
• For Further Investigation (Mini-Tutorials): This is a collection of tuto-
rial articles that provide additional and/or advanced information to com-
plement that found in the textbook. Included are Advanced Studies in
Transients; Matrix Representation in Circuit Analysis; Significant Digits
and Numerical Accuracy; The Importance of Selectivity in Broadcast
Radio; Bode Plots—More Examples; Fourier Series; Using Analog
Multimeters; Appliance Grounding, Solving Simultaneous Equations with
Complex Coefficients and How to Use Excel to Sketch Graphs.
• Lab Pre-Study Simulations: The Oscilloscope: This is a group of five
hands-on, Multisim-based simulations that teach basic oscilloscope
usage and measurement techniques. It supplements our Lab Manual
(described later).
• Lab Pre-Study Simulation: Three-Phase Circuits: This is a hands-on,
Multisim-based simulation intended as preparation for three-phase labo-
ratory work. (If you have no three-phase lab facilities at your institution,
this simulation may serve as a useful substitute.)
• Multisim and PSpice Solutions: These are worked-out solutions to the
PSpice and Multisim examples studied in the computer-aided circuit
analysis sections of the various chapters.
• Technical Notes Concerning Simulations: Describes some of the prac-
tical issues involved with circuit simulations.
• Sample Quizzes: These sample questions give you a preview of the inter-
active quizzing feature available through CourseMate for Circuit Analysis.
To access the Student Premium Website, please visit www.cengagebrain.com.
At the cengagebrain.com home page, enter the printed access code found inside
the back cover of this book and click on the “Register” button. The Student
Premium Website will be added to your CengageBrain bookshelf.
CourseMate for Circuit Analysis (New)
CourseMate for Circuit Analysis is an integrated, Web-based learning solution
for building circuit analysis knowledge and skills. The CourseMate Web site
includes all of the Student Premium Website assets just listed, plus the follow-
ing suite of resources and study tools:
• An interactive eBook with highlighting, note taking, and search capabilities
• Interactive quizzes
• A set of student-focused PowerPoint slides
• Flashcards, crosswords, and other skill-building games
Instructors can use CourseMate for Circuit Analysis to access Instructor
Resources and other classroom management tools.
How to Access the CourseMate for Circuit Analysis Site
To access these supplemental materials or see a CourseMate demo, please visit
www.cengagebrain.com. At the cengagebrain.com home page, enter the ISBN
of your title (from the back cover of your book) using the search box at the top
of the page. This will take you to the product page where these resources can
be found.
Preface xv
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

18. The following table lists the full array of supplemental resources available with
this text and where they can be found:
• Learning Circuit Analysis
Interactively on Your Computer
• Multisim Beginner’s Tutorial
• Capture PSpice Beginner’s
Tutorial
• Audio Clips
• For Further Investigation
Mini-Tutorials
• Lab Pre-Study Simulations:
The Oscilloscope
• Lab Pre-Study Simulation:
Three-Phase Circuits
• Multisim and PSpice Solutions
• Technical Notes Concerning
Simulations
• Sample Quizzes
• Student-Focused
PowerPoint Slides
• Interactive Quizzing
• Electronic Glossary
• Flashcards
• Games
• eBook
CircuitSim
xvi Preface
© Cengage Learning 2013
Student Premium Reference
Website CourseMate Icon in Textbook
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

19. Teaching Resources
Laboratory Manual
The lab manual contains 28 hands-on labs (many with integrated computer
simulation exercises), plus a comprehensive guide to equipment and laboratory
measurements. Solutions to the lab manual may be found in the Instructor’s
Companion Website.
Instructor’s Companion Website
The Instructor’s Companion Website includes tools and instructional resources
to enrich your classroom and make your preparation time shorter. Instructors
may log in at www.cengagebrain.com and search on this textbook’s ISBN to
access the following resources:
• Instructor’s Guide. Contains step-by-step solutions to all end-of-chapter
(even and odd) problems and lab manual solutions, including waveforms,
circuit diagrams, and more.
• In-Process Quizzes. These are in-depth, ready-for-the-classroom tests.
Analytic in nature, patterned after—and similar in depth to—our end-of-
chapter problems, these tests can be likened to chapter-based mini-exams.
• PowerPoint®
Presentation. Slides for each chapter help you present
concepts and material featuring key graphics and illustrations from the
text. By importing graphics from the Image Library, you can create indi-
vidualized presentations.
• Image Library. Contains full-color images from the book that you can
use for slide shows, transparencies, and custom PowerPoint slides—or
that you can simply print to use as needed.
• Computerized Testbank. Questions of varying levels of difficulty are
provided in true/false and multiple-choice formats. These can be used to
supplement the more in-depth In-Process Quizzes described earlier.
PSpice and Multisim Versions Used in This Book
The versions of PSpice and Multisim used throughout this text are the ver-
sions current at the time of writing—see Appendix A. Also shown in
Appendix A are operational details for these products, as well as details about
downloads, Web sites, helpful tutorials, and so on. [Explanatory notes or
Multisim 9 versions of the Multisim material permit legacy software users to
fully participate in the computer-aided circuit analysis activities of this book,
as well as to use the CircuitSim circuit simulations (in sofar as the more lim-
ited features of Multisim 9 permit)—see our Web site for details.]
Preface xvii
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

20. To the Student
Learning circuit theory should be challenging, interesting, and (we hope) fun.
However, it is also hard work, because the knowledge and skills that you
seek can only be gained through practice. We offer a few guidelines.
1. As you go through the material, try to gain an appreciation of where the
theory comes from—that is, the basic experimental laws on which it is
based. This will help you better understand the foundation ideas on which
the theory is built.
2. Learn the terminology and definitions. Important new terms are introduced
frequently. Learn what they mean and where they are used.
3. Study each new section carefully and be sure that you understand the
basic ideas and how they are put together. Work your way through the
examples with your calculator. Try the practice problems, then the end-
of-chapter problems. Not every concept will be clear immediately, and
most likely many will require several readings before you gain an ade-
quate understanding.
4. When you are ready, test your understanding using the In-Process
Learning Checks (self-quizzes) located in each chapter.
5. When you have mastered the material, move on to the next block. For
those concepts that you are having difficulty with, consult your instructor
or some other authoritative source.
To aid in this process, you may want to take advantage of the new learning
support tools that we have provided, including the CircuitSim interactive, hands-
on computer simulations, and the CourseMate for Circuit Analysis tools.
Calculators for Circuit Analysis and Electronics
You will need a good scientific calculator. A good calculator will permit you to
more easily master the numerical aspects of problem solving, thereby leaving
you more time to concentrate on the theory itself. This is especially true for ac,
where complex number work dominates. There are some powerful calculators
on the market that handle complex-number arithmetic almost as easily as real-
number arithmetic—and there are some less expensive calculator models that
also do a credible job. You should acquire an appropriate calculator (after con-
sulting with your instructor), and learn to use it proficiently.
xviii
Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

21. xix
Acknowledgments
Many people have contributed to the development of this text. We begin by
expressing our thanks to our students for providing much-needed feedback.
Next, the reviewers and accuracy checkers: no textbook can be successful with-
out the dedication and commitment of such people. We thank the following:
Reviewers
Sami Antoun, DeVry University, Columbus, OH
G. Thomas Bellarmine, Florida A & M University
Harold Broberg, Purdue University
William Conrad, IUPUI—Indiana University–Purdue University Indianapolis
Franklin David Cooper, Tarrant County College, Fort Worth, TX
Lance Crimm, Southern Polytechnic State University, Marietta, GA
David Delker, Kansas State University
Fred Dreyfuss, Pace University, White Plains, NY
Timothy Haynes, Haywood Community College
Bruce Johnson, University of Nevada, Reno, NV
Jim Pannell, DeVry University, Irving, TX
Alan Price, DeVry University, Pomona, CA
Philip Regalbuto, Trident Technical College
William Routt, Wake Tech Community College, Raleigh, NC
Carlo Sapijaszko, DeVry University, Orlando, FL
Jeffrey Schwartz, DeVry University, Long Island City, NY
John Sebeson, DeVry University, Addison, IL
Hesham Shaalan, Texas A&M University, Corpus Christi, TX
Parker Sproul, DeVry University, Phoenix, AZ
Lloyd E. Stallkamp, Montana State University
Roman Stemprok, University of Texas
Richard Sturtevant, Springfield Tech Community College, Springfield, MA
Technical Accuracy Reviewers
Chia-chi Tsui, DeVry University, Long Island City, NY
Rudy Hofer, Conestoga College, Kitchener, Ontario
Marie Sichler, Red River College, Winnipeg, Manitoba
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

22. Reviewers of the 5th Edition
Karl Huehne, Purdue University, West Lafayette, IN
George Peters, St. Clair College, Windsor, Ontario
Ken Swayne, Pellissippi State Community College, Knoxville, TN
Technical Assistance for the 5th Edition
George Foster, Red River College, Winnipeg, Manitoba
Dan Moroz, Red River College, Winnipeg, Manitoba
The following firms and individuals supplied photographs, diagrams, and other
useful information:
xx Acknowledgments
Advance Devices Inc.
AT&T
AVX Corporation
B&K Precision Corporation
Bourns Inc.
Cadence Design Systems Inc.
Coilcraft Inc.
Fluke Corporation
Illinois Capacitor Inc.
IMRIS Inc.
JBL Professional
Kepco Inc.
National Instruments Corporation
Tektronix Inc.
United States Air Force, Nellis
Air Force Base
Vansco Electronics Ltd.
We express our deep appreciation to the staff at Delmar Cengage Learning
for their tireless efforts in putting this book together: To Stacy Masucci,
Acquisitions Editor, for helping to define the project and smooth the way;
Mary Clyne, Product Manager, for direction, encouragement, advice, and gen-
erally pulling the project together; David Arsenault, Senior Art Director, for
ensuring that the new text design was done right; Barbara LeFleur, Content
Project Manager, for helping to make the project work on the usual short dead-
line; Erica Glisson, Associate Marketing Manager, for helping get the book to
its intended clientele; and Andrea Timpano, former Editorial Assistant, for pro-
viding answers and timely assistance. We also wish to thank Tania Andrabi,
Associate Project Manager, CENVEO Publisher Services, and her colleagues
(in particular Kevin Campbell, copyeditor) along with Joan Conlon, Freelance
Developer, for guiding the book through the copyediting, page layout, and all
such related tasks required for the production of this edition of the text book.
To all these people and their staffs, a special thank you.
Lastly, we thank our wives and families for their support and perseverance
during the preparation of this edition.
Allan H. Robbins
Wilhelm C. Miller
January 2012
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

23. Allan H. Robbins graduated in Electrical Engineering, earning both a
Bachelor’s degree and a Master’s degree. After gaining industrial experi-
ence, he joined Red River College, where he served as an instructor and as head
of the Department of Electrical and Computer Technology. In addition to his
academic career, Allan has been a consultant and a small-business partner in
the electronics/microcomputer field. He began writing as a contributing author
for Osborne-McGraw-Hill in the early stages of the newly emerging micro-
computer field and, in addition to this title, is joint author of several other text-
books. He has served as Section Chairman for the Institute of Electrical and
Electronic Engineers and as a board member of several other organizations.
Wilhelm (Will) C. Miller obtained a diploma in Electronic Engineering
Technology from Red River Community College (now Red River College)
and later graduated from the University of Winnipeg with a degree in Physics
and Mathematics. He worked in the communications field for ten years,
including a one-year assignment with Saudi PTT in Jeddah, Saudi Arabia.
Will has served as both an instructor and chair in the Electrical/Electronic
Engineering Technology Department at Red River College. He currently
serves as the chair of the Canadian Technology Accreditation Board, which
ensures that accredited programs meet the Canadian National Technology
Benchmarks. Additionally, Will provides academic consulting services, most
recently in Korea and Mozambique.
About the Authors
xxi
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

24. Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

25. 1
1 Introduction
2 Voltage and Current
3 Resistance
4 Ohm’s Law, Power,
and Energy
IFOUNDATION dc CONCEPTS
I
C
ircuit theory provides the tools and concepts needed to understand and analyze
electrical and electronic circuits. The foundations of this theory were laid down
over the past several hundred years by a number of pioneer researchers, including
Count Alessandro Volta of Italy, Georg Simon Ohm of Germany, André Marie
Ampère of France, James Watt of Scotland, and others. In 1800, for example, Volta
developed an electric cell (battery) that provided the first source of what we now
call dc voltage. Around the same time, the concept of current was evolved (even
though nothing was known about the atomic structure of matter until much later).
In 1826, Ohm brought the two ideas together and experimentally determined the
relationship between voltage and current in a resistive circuit. This result, known
as Ohm’s law, set the stage for the development of modern-day circuit theory.
In Part I, we examine the foundation of this theory. We look at voltage, current,
power, energy, and the relationships between them. The ideas developed here are
profoundly important and constitute the fundamental ideas upon which all electri-
cal and electronic circuit theory is built. s
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.

26. s KEY TERMS
Application Software
Base
Block Diagram
Circuit Theory
Conversion Factor
Engineering Notation
Exponent
Horsepower (hp)
Joule
Multisim
Newton
Pictorial Diagram
Power of Ten Notation
Prefixes
PSpice
Resistance
Schematic Diagram
SI System
Watt
s OUTLINE
Introduction
The SI System of Units
Converting Units
Power of Ten Notation
Prefixes, Engineering
Notation, and
Numerical Results
Circuit Diagrams
Circuit Analysis Using
Computers and
Calculators
s OBJECTIVES
After studying this chapter, you will be able to
• describe the SI system of measurement,
• convert between various sets of units,
• use power of ten notation to simplify
handling of large and small numbers,
• express electrical units using standard prefix
notation such as ␮A, kV, mW, etc.,
• use a sensible number of significant digits
in calculations,
• describe what block diagrams are and why
they are used,
• convert a simple pictorial circuit to its
schematic representation,
• describe generally how computers and
calculators fit in the electrical and electronic
circuit analysis picture.
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Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.