Introductory Electrical Engineering With Math Explained in Accessible Language

Offers an understanding of the theoretical principles in electronic engineering, in clear and understandable terms

Introductory Electrical Engineering With Math Explained in Accessible Language offers a text that explores the basic concepts and principles of electrical engineering. The author—a noted expert on the topic—explains the underlying mathematics involved in electrical engineering through the use of examples that help with an understanding of the theory. The text contains clear explanations of the mathematical theory that is needed to understand every topic presented, which will aid students in engineering courses who may lack the necessary basic math knowledge. 

Designed to breakdown complex math concepts into understandable terms, the book incorporates several math tricks and knowledge such as matrices determinant and multiplication. The author also explains how certain mathematical formulas are derived. In addition, the text includes tables of integrals and other tables to help, for example, find resistors’ and capacitors’ values. The author provides the accessible language, examples, and images that make the topic accessible and understandable. This important book: 

•    Contains discussion of concepts that go from the basic to the complex, always using simplified language

•    Provides examples, diagrams, and illustrations that work to enhance explanations

•    Explains the mathematical knowledge that is crucial to understanding electrical concepts

•    Contains both solved exercises in-line with the explanations

Written for students, electronic hobbyists and technicians, Introductory Electrical Engineering With Math Explained in Accessible Language is a much-needed text that is filled with the basics concepts of electrical engineering with the approachable math that aids in an understanding of the topic.

MAGNO URBANO has worked in various fields including computer graphics, visual effects and programming for two of the largest broadcast companies in two continents: Globo TV Network in Brazil and RTP (Radio and Television of Portugal). Magno has developed and published about 120 applications for iPhone, iPad, macOS, and Apple TV, some of them hitting #1 or placing in the top 10 in multiple countries for several weeks. He has published 14 books in Europe, 2 in the United States, and over 50 courses on several themes.

About the Author xix

Preface xxi

Acknowledgement xxiii

Introduction xxv

Conventions: Used by this Book xxvii

1 Scientific Method: General Concepts 1

1.1 Introduction 1

1.2 Powers of 10 1

1.3 Roots 2

1.4 Scientific Notation as a Tool 2

2 Infinitesimal Calculus: A Brief Introduction 9

2.1 Introduction 9

2.2 The Concept Behind Calculus 9

3 Atom: Quarks, Protons, and Electrons 19

3.1 Introduction 19

3.2 Atoms and Quarks 19

3.3 Electrons 20

3.4 Strong Force and Weak Force 21

3.5 Conductors and Electricity 22

3.6 The Shells 23

3.7 Electric Potential 24

3.8 Current 25

3.9 Electric Resistance 25

4 Voltage and Current: Direct and Alternating Current and Voltage 27

4.1 Introduction 27

4.2 Terminology 27

4.3 Batteries 27

4.4 Danger Will Robison, Danger! 30

4.5 Direct Current 31

4.6 Relative Voltages 31

4.6.1 Mountains 32

4.7 Ground 33

4.8 Alternating Current 34

Exercises 38

Solutions 39

5 Resistors: The Most Fundamental Component 41

5.1 Introduction 41

5.2 Resistor 41

5.3 Electric Resistance 41

5.4 Symbols 41

5.5 Types of Resistor 42

5.6 Power 42

5.7 Color Code 42

5.8 Potentiometer 44

5.9 Trimpots 44

5.10 Practical Usage 45

5.11 Electric Characteristics 45

5.12 Resistors in Series 45

5.13 Resistors in Parallel 46

5.14 DC and AC Analysis 46

5.15 Input and Output Synchronism 47

Exercises 48

Solutions 48

6 Ohm’s Laws: Circuit Analysis 51

6.1 Introduction 51

6.2 Basic Rules of Electricity 51

6.3 First Ohm’s Law 52

6.4 Second Ohm’s Law 53

6.5 Examples 53

Exercises 58

Solutions 59

7 Delta–Wye Conversions: Circuit Analysis 63

7.1 Introduction 63

7.2 Delta Circuit 63

7.3 Delta–Wye Conversion 63

7.4 Wye–Delta Conversion 65

7.5 Examples 65

Exercises 69

Solutions 69

8 Capacitors: And Electric Charges 73

8.1 Introduction 73

8.2 History 73

8.3 How It Works 73

8.4 Electric Characteristics 77

8.5 Electric Field 78

8.6 Capacitance 78

8.7 Stored Energy 79

8.8 Voltage and Current 81

8.9 Examples 84

8.10 AC Analysis 87

8.11 Capacitive Reactance 88

8.12 Phase 88

8.13 Electrolytic Capacitor 91

8.14 Variable Capacitors 93

8.15 Capacitors in Series 93

8.16 Capacitors in Parallel 94

8.17 Capacitor Color Code 95

8.18 Capacitor Markings 96

Exercises 98

Solutions 98

9 Electromagnetism: And the World Revolution 103

9.1 Introduction 103

9.2 The Theory 103

9.3 Hans Christian Ørsted 103

9.4 The Right-Hand Rule 105

9.5 Faraday First Experiment 105

9.6 Faraday Second Experiment 106

9.7 Conclusion 107

10 Inductors: Temperamental Devices 109

10.1 Introduction 109

10.2 The Inductor 109

10.3 Coils and Magnets 110

10.4 Inductance 111

10.5 Variable Inductor 111

10.6 Series Inductance 112

10.7 Parallel Inductance 112

10.8 DC Analysis 113

10.9 Electromotive Force 116

10.10 Current Across an Inductor 116

10.11 AC Analysis 116

10.12 Out of Sync 119

Exercises 120

Solutions 120

11 Transformers: Not the Movie 123

11.1 Introduction 123

11.2 Connected by the Magnetic Field 124

11.3 Faraday’s Law 124

11.4 Primary and Secondary 124

11.5 Real-Life Transformer 125

11.6 Multiple Secondaries 125

11.7 Center Tap 126

11.8 Law of Conservation of Energy 127

11.9 Leakage Flux 127

11.10 Internal Resistance 128

11.11 Direct Current 128

12 Generators: And Motors 129

12.1 Introduction 129

12.2 Electric Generators 129

12.3 Electric Motor 131

13 Semiconductors: And Their Junctions 133

13.1 Introduction 133

13.2 It All Started with a Light Bulb 133

13.3 Semiconductors 135

14 Diodes and Transistors: Active Components 143

14.1 Introduction 143

14.2 Diodes 143

14.3 NPN Junction 143

14.4 Biasing 144

14.5 The Transistor, Finally! 144

15 Voltage and Current Sources: Circuit Analysis 147

15.1 Introduction 147

15.2 Independent DC Voltage Sources 147

15.3 Independent AC Voltage Sources 147

15.4 Dependent Voltage Sources 148

15.5 Independent Current Sources 149

15.6 Dependent Current Sources 149

16 Source Transformations: Circuit Analysis 151

16.1 Introduction 151

16.2 The Technique 151

16.3 Example 153

Exercises 160

Solutions 161

17 Impedance and Phase: Circuit Analysis 165

17.1 Introduction 165

17.2 This is Just a Phase 165

17.3 Impedance 166

17.4 Capacitive Impedance 167

17.5 Inductive Impedance 169

17.6 Examples 169

17.7 The Importance of Impedances in Real Life 173

Exercises 177

Solutions 177

18 Power: And Work 181

18.1 Introduction 181

18.2 Electric Power and Work 181

18.3 Powers in Parallel 182

18.4 Powers in Series 183

18.5 “Alternating” Power 184

18.6 Real, Apparent, and Reactive Power 188

Exercises 191

Solutions 192

19 Kirchhoff’s Laws: Circuit Analysis 197

19.1 Introduction 197

19.2 Kirchhoff’s Laws 197

19.3 Examples 199

Exercises 210

Solutions 211

20 Nodal Analysis: Circuit Analysis 215

20.1 Introduction 215

20.2 Examples 215

Exercises 226

Solutions 227

21 Thévenin’s Theorem: Circuit Analysis 235

21.1 Introduction 235

21.2 The Theorem 235

Exercises 250

Solutions 251

22 Norton’ Theorem: Circuit Analysis 257

22.1 Introduction 257

22.2 Norton’s Theorem 257

Exercises 263

Solutions 264

23 Superposition Theorem: Circuit Analysis 269

23.1 Introduction 269

23.2 The Theorem 269

23.3 Methodology 269

23.4 Example 270

Exercises 281

Solutions 282

24 Millman’s Theorem: Circuit Analysis 287

24.1 Introduction 287

24.2 Millman’s Theorem 287

24.3 Examples 291

Exercises 295

Solutions 295

25 RC Circuits: Voltage and Current Analysis in Circuits Containing Resistors and Capacitors in Series 297

25.1 Introduction 297

25.2 Charging a Capacitor 297

25.3 RC Time Constant 308

25.4 Examples 315

Exercises 328

Solutions 330

26 RL Circuits: Voltage and Current Analysis in Circuits Containing Resistors and Inductors in Series 341

26.1 Introduction 341

26.2 Energizing 341

26.3 De-energizing 349

26.4 Examples 354

Exercises 362

Solutions 365

27 RLC Circuits: Part 1: Voltage Analysis in Circuits Containing Resistors, Capacitors, and Inductors in Series 377

27.1 Introduction 377

27.2 A Basic RLC Series Circuit 377

27.3 Examples 408

Exercises 418

Solutions 419

28 RLC Circuits: Part 2: Current Analysis in Circuits Containing Resistors, Capacitors, and Inductors in Series 427

28.1 Introduction 427

28.2 The Circuit 427

28.3 Current Equations 430

28.4 Examples 432

Exercises 442

Solutions 443

29 Transistor Amplifiers: The Magic Component 451

29.1 Introduction 451

29.2 Transistor as Amplifiers 451

29.3 The Water Storage Tank 451

29.4 Current Gain 452

29.5 Power Supply Rails 452

29.6 Amplifying 452

29.7 Quiescent Operating Point 453

29.8 Amplifier Classes 454

Exercises 477

Solutions 479

30 Operational Amplifiers: A Brief Introduction 485

30.1 Introduction 485

30.2 Operational Amplifiers 485

30.3 How Op-Amp Works 486

30.4 Op-Amp Characteristics 488

30.5 Typical Configurations 488

31 Instrumentation and Bench: A Brief Introduction 509

31.1 Introduction 509

31.2 Multimeter 509

31.3 Voltmeter 510

31.4 Ammeter 511

31.5 Ohmmeter 512

31.6 Oscilloscope 513

31.7 Breadboards 513

31.8 Wire Diameter 515

31.9 Power Supply 516

31.10 Soldering Station 517

31.11 Soldering Fume Extractors 517

31.12 Lead-Free Solder 517

31.13 A Few Images of Real Products 518

Appendix A: International System of Units (SI) 521

Appendix B: Color Code: Resistors 523

Appendix C: Root Mean Square (RMS) Value 525

Appendix D: Complex Numbers 529

Appendix E: Table of Integrals 537

Appendix F: AWG Versus Metric System: Wire Cross Sections 539

Appendix G: Resistors: Commercial Values 541

Appendix H: Capacitors: Commercial Values 543

Appendix I: Inductors: Commercial Values 549

Appendix J: Simulation Tools 557

Appendix K: Glossary 559

Index 563

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