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AC Electrical Circuit Analysis AC Electrical Circuit Analysis A Practical ApproachA Practical Approach

James M. FioreJames M. Fiore

2 AC Electrical Circuit AnalysisAC Electrical Circuit Analysis

A Practical ApproachA Practical Approach

by

James M. Fiore

Version 1.1.2, 22 April 2021

3 This AC Electrical Circuit Analysis, by James M. Fiore is copyrighted under the terms of a Creative Commons license: This work is freely redistributable for non-commercial use, share-alike with attribution Device data sheets and other product information are copyright by their respective owners and have been obtained through publicly accessible manufacturer's web sites.

Published by James M. Fiore via dissidents

ISBN13: 979-8605022282

For more information or feedback, contact:

James Fiore, Professor

Electrical Engineering Technology

Mohawk Valley Community College

1101 Sherman Drive

Utica, NY 13501

jfiore@mvcc.edu For the latest revisions, related titles, and links to low cost print versions, go to: www.mvcc.edu/jfiore or my mirror sites www.dissidents.com and www.jimfiore.org

YouTube Channel: Electronics with Professor Fiore

Cover art, Chapman's Contribution Redux, by the author 4

IntroductionIntroduction

Welcome to the AC Electrical Circuit Analysis, an open educational resource (OER). The goal of this text is to

introduce the theory and practical application of analysis of AC electrical circuits. It assumes familiarity with DC

circuit analysis. If you have not studied DC circuit analysis, it is strongly recommended that you read the

companion OER text, DC Electrical Circuit Analysis before continuing. Both texts are offered free of charge

under a Creative Commons non-commercial, share-alike with attribution license. For your convenience, along

with the free pdf and odt files, print copies are available at a very modest charge. Check my web sites for links.

This text is based on the earlier Workbook for AC Electrical Circuits, which it replaces. The original expository

text has been greatly expanded and includes many examples along with computer simulations. For the

convenience of those who used the Workbook, many of the problem sets are the same, with some re-ordering

depending on the chapter.

If you are already familiar with DC Electrical Circuit Analysis, the format of this title is similar. This text picks

up where the DC text leaves off; beginning with AC concepts such as sinusoidal waveforms, basic Fourier

decomposition of complex waveforms, complex numbers and the like. Also, reactance and impedance are

introduced along with phasor diagrams. Chapters on series, parallel and series-parallel RLC circuits commence.

Following these, network theorems along with nodal and mesh analysis are discussed for the AC case. The text

completes with chapters on AC power, resonance, and introductions to polyphase systems and magnetic circuits.

Each chapter begins with a set of learning objectives and concludes with practice exercises that are generally

divided into four major types: analysis, design, challenge and simulation. Many SPICE-based circuit simulators

are available, both free and commercial, that can be used with this text. The answers to most odd-numbered

exercises can be found in the Appendix. A table of standard resistor sizes is also in the Appendix, which is useful

for real-world design problems. If you have any questions regarding this workbook, or are interested in

contributing to the project, do not hesitate to contact me.

This text is part of a series of OER titles in the areas of electricity, electronics, audio and computer

programming. It includes three other textbooks covering semiconductor devices, operational amplifiers, and

embedded programming using the C language with the Arduino platform. There is a text covering DC electrical

circuits similar to this one, and also seven laboratory manuals; one for each of the five texts plus individual titles

covering computer programming using the Python language, and the science of sound. The most recent versions

of all of my OER texts and manuals may be found at my MVCC web site as well as my mirror site: www.dissidents.com

This text was created using several free and open software applications including Open Office, Dia, SciDAVis,

and XnView.

Special thanks to the following individuals for their efforts in reviewing and proofreading the DC and AC

Electrical Circuit Analysis texts: Glenn Ballard, John Markham, João Nuno Carvalho, Mark Steffka and Jim

Noon. 5

For the Have-nots and the Has-beens "Well, the people, I would say. There is no patent. Could you patent the sun?"

- Jonas Salk, inventor of the polio vaccine, when asked who owns the patent to it. 6

Table of ContentsTable of Contents

Chapter 1: Fundamentals.......10

1.0 Chapter Objectives........ 10

1.1 Introduction......... 10

1.2 Sinusoidal Waveforms....... 11

1.3 Basic Fourier Analysis........ 25

1.4 Complex Numbers........ 29

1.5 Reactance and Impedance....... 31

1.6 Phasor Diagrams........ 37

Summary......... 38

Exercises......... 39

Chapter 2: Series RLC Circuits...... 44

2.0 Chapter Objectives........ 44

2.1 Introduction......... 44

2.2 The Series Connection....... 44

2.3 Series Impedance........ 45

2.4 Series Circuit Analysis........ 48

2.5 Concerning Practical Inductors...... 61

Summary......... 63

Exercises......... 64

Chapter 3: Parallel RLC Circuits..... 80

3.0 Chapter Objectives........ 80

3.1 Introduction......... 80

3.2 The Parallel Connection...... 81

3.3 Parallel Impedance........ 81

3.4 Parallel Circuit Analysis....... 85

Summary.........100

Exercises.........101

Chapter 4: Series-Parallel RLC Circuits....110

4.0 Chapter Objectives........ 110

4.1 Introduction......... 110

4.3 The Series-Parallel Connection...... 110

4.4 Series-Parallel Impedance....... 111

4.5 Series-Parallel Circuit Analysis....... 114

Summary......... 132

Exercises......... 133

7 Chapter 5: Analysis Theorems and Techniques....144

5.0 Chapter Objectives........ 144

5.1 Introduction......... 144

5.2 Source Conversions........ 145

5.3 Superposition Theorem ....... 153

5.4 Thévenin's and Norton's Theorems...... 160

5.5 Maximum Power Transfer Theorem...... 170

5.6 Delta-Y (Pi-T) Conversions....... 179

Summary......... 185

Exercises......... 187

Chapter 6: Nodal and Mesh Analysis.....204

6.0 Chapter Objectives........ 204

6.1 Introduction......... 204

6.2 Nodal Analysis........ 205

6.3 Mesh Analysis........ 222

6.4 Dependent Sources........ 234

Summary......... 240

Exercises......... 242

Chapter 7: AC Power.......260

7.0 Chapter Objectives........ 260

7.1 Introduction......... 260

7.2 Power Waveforms........ 261

7.3 Power Triangle........ 273

7.4 Power Systems........ 280

Summary......... 286

Exercises......... 287

Chapter 8: Resonance.......294

8.0 Chapter Objectives........ 294

8.1 Introduction......... 294

8.2 Series Resonance........ 295

8.3 Parallel Resonance........ 310

Summary......... 329

Exercises......... 331

8

Chapter 9: Polyphase Power......338

9.0 Chapter Objectives........ 338

9.1 Introduction......... 338

9.2 Polyphase Definition........ 339

9.3 Three-Phase Connections....... 341

9.4 Power Factor Correction....... 354

Summary......... 364

Exercises......... 365

Chapter 10: Decibels and Bode Plots.....372

10.0 Chapter Objectives........ 372

10.1 Introduction........ 372

10.2 The Decibel......... 372

10.3 Bode Plots......... 383

10.4 Combining the Elements - Multi-Stage Effects..... 393

Summary......... 395

Exercises......... 396

Appendices

A: Standard Component Sizes.......399

B: Methods of Solution of Linear Simultaneous Equations...400

C: Equation Proofs........405

D: Answers to Selected Odd-Numbered Problems....408

E: Questions for Selected Odd Answers.....422

9

1 1 FundamentalsFundamentals

1.0 Chapter Learning Objectives1.0 Chapter Learning Objectives

After completing this chapter, you should be able to: •Describe sinusoidal waveforms in mathematical terms. •Express complex waveforms using basic Fourier analysis. •Perform mathematical operations using complex numbers. •Draw phasor diagrams for complex numbers. •Compute and plot capacitive and inductive reactance as a function of frequency. •Compute and plot complex impedance as a function of frequency.

•Describe the relationships between resistance, reactance, impedance, conductance, susceptance and

admittance

1.1 Introduction1.1 Introduction

In this chapter we begin our study of alternating current, or AC, electrical circuit analysis. As such, this chapter

is filled with foundational material that will be used in the remainder of this text. It is critical that the concepts

presented here be fully understood in order to achieve success in later chapters. We start with the mathematical

description of the most simple AC waveform, the sine wave. This includes parameters such as amplitude,

quotesdbs_dbs4.pdfusesText_8

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