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Basic Engineering

Circuit Analysis

11e

J. David Irwin

Auburn University

R. Mark Nelms

Auburn University

To my loving family:

Edie Geri, Bruno, Andrew, and Ryan

John, Julie, John David, and Abi

Laura

To my parents:

Robert and Elizabeth Nelms

vi

Chapterfourteen

• Chapter 1 Basic Concepts BRIEF CONTENTS
• Chapter 2 Resistive Circuits
• Chapter 3 Nodal and Loop Analysis Techniques
• Chapter 4 Operational Amplifiers
• Chapter 5 Additional Analysis Techniques
• Chapter 6 Capacitance and Inductance
• Chapter 7 First- and Second-Order Transient Circuits
• Chapter 8 AC Steady-State Analysis
• Chapter 9 Steady-State Power Analysis
• Chapter 10 Magnetically Coupled Networks
• Chapter 11 Polyphase Circuits
• Chapter 12 Variable-Frequency Network Performance
• Chapter 13 The Laplace Transform - Circuit Analysis Chapter 14 Application of the Laplace Transform to
• Chapter 15 Fourier Analysis Techniques
• Appendix Complex Numbers
• Basic Concepts Chapterone
• 1.1 System of Units
• 1.2 Basic Quantities
• 1.3 Circuit Elements
  • Summary
  • Problems
• Resistive Circuits Chaptertwo
• 2.1 Ohm’s Law
• 2.2 Kirchhoff’s Laws
• 2.3 Single-Loop Circuits
• 2.4 Single-Node-Pair Circuits
• 2.5 Series and Parallel Resistor Combinations
• 2.6 Wye Delta Transformations
• 2.7 Circuits with Dependent Sources
  • Summary
  • Problems
• Nodal and Loop Analysis Techniques Chapterthree
• 3.1 Nodal Analysis
• 3.2 Loop Analysis
  • Summary
  • Problems
• Operational Amplifiers Chapterfour
• 4.1 Introduction
• 4.2 Op-Amp Models
• 4.3 Fundamental Op-Amp Circuits
  • Summary
  • Problems
• Additional Analysis Techniques Chapterfi ve
• 5.1 Introduction
• 5.2 Superposition - 5.3 Thévenin’s and Norton’s Theorems - 5.4 Maximum Power Transfer - Summary - Problems - Capacitance and Inductance Chaptersix - 6.1 Capacitors - 6.2 Inductors - 6.3 Capacitor and Inductor Combinations - Summary - Problems - First- and Second-Order Transient Circuits Chapterseven - 7.1 Introduction - 7.2 First-Order Circuits - 7.3 Second-Order Circuits - Summary - Problems - AC Steady-State Analysis Chaptereight - 8.1 Sinusoids - 8.2 Sinusoidal and Complex Forcing Functions - 8.3 Phasors - 8.4 Phasor Relationships for Circuit Elements - 8.5 Impedance and Admittance - 8.6 Phasor Diagrams - 8.7 Basic Analysis Using Kirchhoff’s Laws - 8.8 Analysis Techniques - Summary - Problems - Steady-State Power Analysis Chapternine - 9.1 Instantaneous Power - 9.2 Average Power - 9.3 Maximum Average Power Transfer - 9.4 Effective or rms Values - 9.5 The Power Factor - 9.6 Complex Power
• 9.7 Power Factor Correction viii CONTENTS
• 9.8 Single-Phase Three-Wire Circuits
• 9.9 Safety Considerations
  • Summary
  • Problems
• Magnetically Coupled Networks Chapterten
• 10.1 Mutual Inductance
• 10.2 Energy Analysis
• 10.3 The Ideal Transformer
• 10.4 Safety Considerations
  • Summary
  • Problems
• Polyphase Circuits Chaptereleven
• 11.1 Three-Phase Circuits
• 11.2 Three-Phase Connections
• 11.3 Source/Load Connections
• 11.4 Power Relationships
• 11.5 Power Factor Correction
  • Summary
  • Problems
• Variable-Frequency Network Performance Chaptertwelve
• 12.1 Variable Frequency-Response Analysis
• 12.2 Sinusoidal Frequency Analysis
• 12.3 Resonant Circuits
• 12.4 Scaling
• 12.5 Filter Networks
  • Summary
  • Problems
• The Laplace Transform Chapterthirteen
• 13.1 Definition
• 13.2 Two Important Singularity Functions - 13.3 Transform Pairs - 13.4 Properties of the Transform - 13.5 Performing the Inverse Transform - 13.6 Convolution Integral - 13.7 Initial-Value and Final-Value Theorems - Transforms 13.8 Solving Differential Equations with Laplace - Summary - Problems - Circuit Analysis Application of the Laplace Transform to - 14.1 Laplace Circuit Solutions - 14.2 Circuit Element Models - 14.3 Analysis Techniques - 14.4 Transfer Function - 14.5 Steady-State Response - Summary - Problems - Fourier Analysis Techniques Chapterfi fteen - 15.1 Fourier Series - 15.2 Fourier Transform - Summary - Problems - Complex Numbers Appendix - Index

ix

PREFACE

Circuit analysis is not only fundamental to the entire breadth of electrical and computer engineering—the concepts studied here extend far beyond those boundaries. For this reason, it remains the starting point for many future engineers who wish to work in this field. The text and all the supplementary materials associated with it will aid you in reaching this goal. We strongly recommend while you are here to read the Preface closely and view all the resources available to you as a learner. One last piece of advice: Learning to analyze electric circuits is like learning to play a musical instrument. Most people take music lessons as a starting point. Then, they become proficient through practice, practice, and more practice. Lessons on circuit analysis are provided by your instructor and this textbook. Proficiency in circuit analysis can only be obtained through practice. Take advantage of the many opportunities throughout this textbook to practice, practice, and practice. In the end, you’ll be thankful you did.

The Eleventh Edition has been prepared based on a careful examination of feedback received from instructors and students. The revisions and changes made should appeal to a wide vari- ety of instructors. We are aware of significant changes taking place in the way this material is being taught and learned. Consequently, the authors and the publisher have created a formi- dable array of traditional and nontraditional learning resources to meet the needs of students and teachers of modern circuit analysis. By design, the book contains an enormous number of end-of-chapter problems that provide significant advantages for the instructor. As a time-saving measure, the instruc- tor can use this bank of problems to select both homework problems and exam questions, term after term, without repetition. Dedicated students will find this problem set, typically graduated in difficulty, an excellent resource for testing their understanding on a range of problems. Flipping the classroom has risen recently as an alternative mode of instruction, which attempts to help the student grasp the material quicker. Studies to date have shown that this mode also tends to minimize instructor office time. This book, with its combination of Learning Assessments, problem-solving videos, and WileyPLUS software, is an ideal vehicle for teaching in this format. These resources provide the instructor with the tools necessary to modify the format of the presentation in the hope of enhancing the student’s rapid understand- ing of the material. Engineering educators have long recognized that coupling traditional lecture courses with laboratory experiences enhances student interest and learning. The trend in hands-on learning has been spurred by the development of inexpensive USB-powered instruments and inexpensive portable laboratory kits that allow the student to explore electrical theory in environments that vary from a traditional laboratory classroom to an environment where the experiments can be performed anywhere at any time. Research has shown that students gain a deeper understanding of abstract theoretical concepts when the concepts are applied in practical circuits. The response of students, both male and female, to hands-on learning with such kits has been overwhelmingly positive. New to this edition, a list of such experiments is provided at the beginning of each chapter. The experiments, which demonstrate some of the concepts introduced in the chapters, can be conducted under the guidance of an instructor or independently. In accordance with the earlier editions, the book contains a plethora of examples that are designed to help the student grasp the salient features of the material quickly. A number of new examples have been introduced, and MATLAB ®^ has been employed, where appropriate, to provide a quick and easy software solution as a means of comparison, as well as to check on other solution techniques.

To the Student

To the Instructor

Examples are the mainstay of any circuit analysis text, and numerous examples have always been a trademark of this textbook. These examples provide a more graduated level of presen- tation with simple, medium, and challenging examples.

Hints can often be found in the page margins. They facilitate understanding and serve as reminders of key issues. See, for example, page 9.

Learning Assessments are a critical learning tool in this text. These exercises test the cumu- lative concepts to that point in a given section or sections. Not only is the answer provided, but a problem-solving video accompanies each of these exercises, demonstrating the solu- tion in step-by-step detail. The student who masters these is ready to move forward. See, for example, page 11.

Problem-Solving Strategies are step-by-step problem-solving techniques that many students find particularly useful. They answer the frequently asked question, “Where do I begin?” Nearly every chapter has one or more of these strategies, which are a kind of summation on problem solving for concepts presented. See, for example, page 44.

Problems have been greatly revised for the Eleventh Edition. This edition has over 400 new problems of varying depth and level. Any instructor will find numerous problems appropriate for any level class. There are approximately 1,400 problems in the Eleventh Edition! Included with the problems are FE Exam Problems for each chapter. If you plan on taking the FE Exam, these problems closely match problems you will typically find on the FE Exam.

Circuit Simulation and Analysis Software represents a fundamental part of engineering circuit design today. Software such as PSpice , MultiSim , and MATLAB allow engineers to design and simulate circuits quickly and efficiently. As an enhancement with enormous flexibility, all three of these software packages can be employed in the Eleventh Edition. In each case, online supplements are available that contain the solutions to numerous examples in each of these software programs. Instructors can opt to make this material available online or as part of a customized print edition, making this software an integral and effective part of the presentation of course material. The rich collection of material that is provided for this edition offers a distinctive and helpful way for exploring the book’s examples and exercises from a variety of simulation techniques.

WileyPLUS is an innovative, research-based, online environment for effective teaching and learning.

WHAT DO STUDENTS RECEIVE WITH WILEYPLUS? A Research-Based Design : WileyPLUS provides an online environment that integrates relevant resources, including the entire digital textbook, in an easy-to-navigate framework that helps students study more effectively.

WileyPLUS adds structure by organizing textbook content into smaller, more manage- able “chunks.” Related media, examples, and sample practice items reinforce the learning objectives. Innovative features such as calendars, visual progress tracking, and self-evaluation tools improve time management and strengthen areas of weakness.

One-on-One Engagement : With WileyPLUS, students receive 24/7 access to resources that promote positive learning outcomes. Students engage with related examples (in various media) and sample practice items, including:

FE Exam Questions Reading Quiz Questions

WileyPLUS

PREFACE xi

xii PREFACE

Circuit Solutions Learning Assessments Math Skills Assessments Measurable Outcomes : Throughout each study session, students can assess their progress and gain immediate feedback. WileyPLUS provides precise reporting of strengths and weaknesses, as well as individualized quizzes, so that students are confident that they are spending their time on the right things. With WileyPLUS, students always know the exact outcome of their efforts.

WHAT DO INSTRUCTORS RECEIVE WITH WILEYPLUS? WileyPLUS provides reli- able, customizable resources that reinforce course goals inside and outside of the classroom, as well as visibility into individual student progress. Precreated materials and activities help instruc- tors optimize their time.

Customizable Course Plan : WileyPLUS comes with a precreated course plan designed by a sub- ject matter expert uniquely for this course. Simple drag-and-drop tools make it easy to assign the course plan as-is or modify it to reflect your course syllabus. Precreated Activity Types include: Questions Readings and Resources Presentation Print Tests Concept Mastery Course Materials and Assessment Content: Lecture Notes PowerPoint Slides Image Gallery Instructor’s Manual Gradable Reading Assignment Questions (embedded with online text) Question Assignments: All end-of-chapter problems are coded algorithmically with hints, links to text, whiteboard/show work feature, and instructor-controlled problem-solving help. Gradebook : WileyPLUS provides instant access to reports on trends in class performance, stu- dent use of course materials, and progress toward learning objectives, helping inform decisions and drive classroom discussions.

Learn more about WileyPLUS at www.wileyplus.com.

Powered by proven technology and built on a foundation of cognitive research, WileyPLUS has enriched the education of millions of students in more than 20 countries.

The supplements list is extensive and provides instructors and students with a wealth of tradi- tional and modern resources to match different learning needs.

Problem-Solving Videos are offered again in the Eleventh Edition in an iPod-compatible format. The videos provide step-by-step solutions to Learning Assessments. Videos for Learning Assessments will follow directly after a chapter feature called Problem-Solving Strategy. Students who have used these videos with past editions have found them to be very helpful.

The Solutions Manual for the Eleventh Edition has been completely redone, checked, and double-checked for accuracy. Although it is hand-written to avoid typesetting errors, it is the most

Supplements

xiv PREFACE

The preparation of this book and the materials that support it have been handled with both enthusiasm and great care. The combined wisdom and leadership of our colleagues at Wiley has resulted in a tremendous team effort that has addressed every aspect of the presentation. This team included the following individuals:

VP and Executive Publisher, Don Fowley Executive Editor, Dan Sayre Product Designer, Jennifer Welter Executive Marketing Manager, Christopher Ruel Production Editor, James Metzger Senior Designer, Maureen Eide Senior Content Manager, Karoline Luciano Senior Photo Editor, Lisa Gee Associate Editor, Wendy Ashenberg Editorial Assistant, Francesca Baratta

Each member of this team played a vital role in preparing the package that is the Eleventh Edition of Basic Engineering Circuit Analysis. We are most appreciative of their many contributions. As in the past, we are most pleased to acknowledge the support that has been provided by numerous individuals to earlier editions of this book. Our Auburn colleagues who have helped are:

Thomas A. Baginski Travis Blalock Henry Cobb Elizabeth Devore Bill Dillard Zhi Ding Kevin Driscoll Brandon Eidson E. R. Graf L. L. Grigsby Charles A. Gross Stephen Haddock David C. Hill M. A. Honnell R. C. Jaeger Keith Jones Betty Kelley Ray Kirby

Matthew Langford Aleck Leedy George Lindsey Jo Ann Loden James L. Lowry David Mack Paulo R. Marino M. S. Morse Sung-Won Park John Parr Monty Rickles C. L. Rogers Tom Shumpert Les Simonton James Trivltayakhum Susan Williamson Jacinda Woodward

Many of our friends throughout the United States, some of whom are now retired, have also made numerous suggestions for improving the book:

David Anderson, University of Iowa Jorge Aravena, Louisiana State University Les Axelrod, Illinois Institute of Technology Richard Baker, UCLA Charles F. Bunting, Oklahoma State University John Choma, University of Southern California David Conner, University of Alabama at Birmingham James L. Dodd, Mississippi State University Kevin Donahue, University of Kentucky John Durkin, University of Akron Prasad Enjeti, Texas A&M University Earl D. Eyman, University of Iowa Arvin Grabel, Northeastern University Paul Gray, University of Wisconsin–Platteville Ashok Goel, Michigan Technological University

PREFACE xv

Walter Green, University of Tennessee Paul Greiling, UCLA Mohammad Habli, University of New Orleans John Hadjilogiou, Florida Institute of Technology Yasser Hegazy, University of Waterloo Keith Holbert, Arizona State University Aileen Honka, The MOSIS Service–USC Information Sciences Institute Marty Kaliski, Cal Poly, San Luis Obispo Ralph Kinney, Louisiana State University Muhammad A. Khaliq, Minnesota State University Robert Krueger, University of Wisconsin K. S. P. Kumar, University of Minnesota Jung Young Lee, UC Berkeley (student) Aleck Leedy, Murray State University Hongbin Li, Stevens Institute of Technology James Luster, Snow College Erik Luther, National Instruments Ian McCausland, University of Toronto Arthur C. Moeller, Marquette University Darryl Morrell, Arizona State University M. Paul Murray, Mississippi State University Burks Oakley II, University of Illinois at Champaign–Urbana John O’Malley, University of Florida Arnost Neugroschel, University of Florida William R. Parkhurst, Wichita State University Peyton Peebles, University of Florida Jian Peng, Southeast Missouri State University Clifford Pollock, Cornell University George Prans, Manhattan College Mark Rabalais, Louisiana State University Tom Robbins, National Instruments Armando Rodriguez, Arizona State University James Rowland, University of Kansas Robert N. Sackett, Normandale Community College Richard Sanford, Clarkson University Peddapullaiah Sannuti, Rutgers University Ronald Schulz, Cleveland State University M. E. Shafeei, Penn State University at Harrisburg Martha Sloan, Michigan Technological University Scott F. Smith, Boise State University Karen M. St. Germaine, University of Nebraska Janusz Strazyk, Ohio University Gene Stuffle, Idaho State University Thomas M. Sullivan, Carnegie Mellon University Saad Tabet, Florida State University Val Tareski, North Dakota State University Thomas Thomas, University of South Alabama Leonard J. Tung, Florida A&M University/Florida State University Marian Tzolov, Lock Haven University Darrell Vines, Texas Tech University Carl Wells, Washington State University Seth Wolpert, University of Maine

Finally, Dave Irwin wishes to express his deep appreciation to his wife, Edie, who has been most supportive of our efforts in this book. Mark Nelms would like to thank his parents, Robert and Elizabeth, for their support and encouragement.

J. David Irwin and R. Mark Nelms

EXPERIMENTS THAT HELP STUDENTS DEVELOP AN UNDERSTANDING OF BASIC ELECTRIC CIRCUIT CONCEPTS ARE: ■ Breadboard Basics: Learn the operation of a digital multimeter while mapping the connections on a breadboard via resistance measurements. ■ Resistance Tolerances: Measure the resistance of real resistors and apply statistical analysis to the experimental values to explain nominal resistance and tolerance. ■ Voltage Polarity and Direction of Current: Discover how dc currents and voltages are measured using a digital multimeter so that the resulting power calculated follows the passive sign convention.

ChapterOne

T H E L E A R N I N G G O A L S F O R T H I S

C H A P T E R A R E T H AT S T U D E N T S

S H O U L D B E A B L E T O :

■ Use appropriate SI units and standard prefixes when calculating voltages, currents, resistances, and powers. ■ Explain the relationships between basic electrical quantities: voltage, current, and power. ■ Use the appropriate symbols for independent and dependent voltage and current sources. ■ Calculate the value of the dependent sources when analyzing a circuit that contain independent and dependent sources. ■ Calculate the power absorbed by a circuit element using the passive sign convention.

BASIC

CONCEPTS

2 CHAPTER 1 B A S I C C O N C E P T S

The system of units we employ is the international system of units, the Système International des Unités, which is normally referred to as the SI standard system. This system, which is composed of the basic units meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), and candela (cd), is defined in all modern physics texts and therefore will not be defined here. However, we will discuss the units in some detail as we encounter them in our subsequent analyses. The standard prefixes that are employed in SI are shown in Fig. 1.1. Note the decimal relationship between these prefixes. These standard prefixes are employed throughout our study of electric circuits. Circuit technology has changed drastically over the years. For example, in the early 1960s the space on a circuit board occupied by the base of a single vacuum tube was about the size of a quarter (25-cent coin). Today that same space could be occupied by an Intel Pentium integrated circuit chip containing 50 million transistors. These chips are the engine for a host of electronic equipment.

1.

System of Units

1.

Basic Quantities

Before we begin our analysis of electric circuits, we must define terms that we will employ. However, in this chapter and throughout the book, our definitions and explanations will be as simple as possible to foster an understanding of the use of the material. No attempt will be made to give complete definitions of many of the quantities because such definitions are not only unnecessary at this level but are often confusing. Although most of us have an intuitive concept of what is meant by a circuit, we will simply refer to an electric circuit as an interconnection of electrical components, each of which we will describe with a mathematical model. The most elementary quantity in an analysis of electric circuits is the electric charge. Our interest in electric charge is centered around its motion, since charge in motion results in an energy transfer. Of particular interest to us are those situations in which the motion is confined to a definite closed path. An electric circuit is essentially a pipeline that facilitates the transfer of charge from one point to another. The time rate of change of charge constitutes an electric current. Mathematically, the relationship is expressed as

i ( t ) = dq ( t ) — dt

or q ( t ) = ∫−∞

t i ( x ) dx 1.

where i and q represent current and charge, respectively (lowercase letters represent time dependency, and capital letters are reserved for constant quantities). The basic unit of current is the ampere (A), and 1 ampere is 1 coulomb per second. Although we know that current flow in metallic conductors results from electron motion, the conventional current flow, which is universally adopted, represents the movement of positive charges. It is important that the reader think of current flow as the movement of positive charge regardless of the physical phenomena that take place. The symbolism that will be used to represent current flow is shown in Fig. 1.2. I 1 = 2 A in Fig. 1.2a indicates that at any point in the wire shown, 2 C of charge pass from left to right each second. I 2 = −3 A in Fig. 1.2b indicates that at any point in the wire shown, 3 C of charge pass from right to left each second. Therefore, it is important to specify not only the magnitude of the variable representing the current but also its direction. The two types of current that we encounter often in our daily lives, alternating current (ac) and direct current (dc), are shown as a function of time in Fig. 1.3. Alternating current is the common current found in every household and is used to run the refrigerator, stove, washing

Figure 1. Standard SI prefixes.

10 −^12

pico (p) nano (n) micro (μ) milli (m) kilo (k) mega (M) giga (G) tera (T)

10 −^9 10 −^6 10 −^3 1 103 10 6 109