Title:

Basic mathematics for electricity and electronics

Author:

Singer, Bertrand B.

Personal Author:

Edition:

Fourth edition.

Publication Information:

New York : Gregg Division, McGraw-Hill, [1978]

©1978

Physical Description:

x, 678 pages ; 21 cm

General Note:

Includes index.

Language:

English

ISBN:

9780070574724

Format :

Book

### On Order

### Summary

### Summary

The math theory is developed in slow, simple stages and is directly applied to the solution of real problems. This method is backed up with "CHECKUPS" which act as a motivator, and "BRUSHUPS" which review the mathematical concepts immediately necessary for the continuance of the electrical development and applications. Copyright © Libri GmbH. All rights reserved.

### Table of Contents

Preface | p. xiii |

Chapter 1 Introduction to Electricity | p. 1 |

1-1 Basic Theory of Electricity | p. 1 |

1-2 Electrical Measurements and Circuits | p. 6 |

Assessment | p. 12 |

Solutions to Self-Tests and Reviews | p. 13 |

Chapter 2 Simple Electric Circuits | p. 14 |

2-1 Checkup on Fractions (Diagnostic Tests) | p. 14 |

2-2 Brushup on Fractions | p. 15 |

2-3 Ohm's Law | p. 24 |

2-4 Checkup on Decimals (Diagnostic Test) | p. 29 |

2-5 Introduction to Decimals | p. 30 |

2-6 Introduction to the Metric System | p. 37 |

2-7 Brushup on Decimals | p. 43 |

2-8 Review of Working with Decimals | p. 49 |

Assessment | p. 52 |

Solutions to Self-Tests and Reviews | p. 53 |

Chapter 3 Formulas | p. 54 |

3-1 Checkup on Formulas in Electrical Work (Diagnostic Test) | p. 54 |

3-2 Brushup on Formulas | p. 55 |

3-3 Positive and Negative Numbers | p. 62 |

3-4 Checkup on Using Formulas with Exponents (Diagnostic Test) | p. 66 |

3-5 Brushup on Formulas Containing Exponents | p. 67 |

3-6 Powers of 10 | p. 69 |

3-7 Units of Measurement in Electronics | p. 78 |

3-8 Using Electronic Units of Measurement in Simple Circuits | p. 82 |

3-9 Solving the Ohm's Law Formula for Current or Resistance | p. 84 |

3-10 Estimating Answers | p. 91 |

3-11 Review of Ohm's Law | p. 92 |

Assessment | p. 96 |

Solutions to Self-Tests and Reviews | p. 97 |

Chapter 4 Series Circuits | p. 98 |

4-1 Voltage, Current, and Resistance in Series Circuits | p. 98 |

4-2 Using Ohm's Law in Series Circuits | p. 102 |

4-3 Using Ohm's Law for Total Values in Series Circuits | p. 106 |

4-4 Power Distribution Line Currents | p. 112 |

4-5 Ground-Fault Protection | p. 115 |

4-6 Intermediate Review of Series Circuits | p. 116 |

4-7 Checkup on Formulas Involving Addition and Subtraction (Diagnostic Test) | p. 119 |

4-8 Brushup on Formulas Involving Addition and Subtraction | p. 119 |

4-9 Control of Current in a Series Circuit | p. 127 |

4-10 Review of Series Circuits | p. 131 |

Assessment | p. 134 |

Solutions to Self-Tests and Reviews | p. 135 |

Chapter 5 Parallel Circuits | p. 136 |

5-1 Total Voltage, Total Current, and Total Resistance in Parallel Circuits | p. 136 |

5-2 Using Ohm's Law in Parallel Circuits | p. 141 |

5-3 Check on Addition and Subtraction of Fractions (Diagnostic Test) | p. 144 |

5-4 Brushup on Addition of Fractions | p. 144 |

5-5 Brushup on Subtraction of Fractions | p. 149 |

5-6 Checkup on Solution of Formulas Involving Fractions (Diagnostic Test) | p. 153 |

5-7 Brushup on Solution of Fractional Equations | p. 153 |

5-8 Total Resistance in a Parallel Circuit | p. 160 |

5-9 Total Voltage in a Parallel Circuit | p. 165 |

5-10 Division of Current in a Parallel Circuit | p. 167 |

5-11 Review of Parallel Circuits | p. 172 |

Assessment | p. 175 |

Solutions to Self-Tests and Reviews | p. 176 |

Chapter 6 Combination Circuits | p. 177 |

6-1 Introduction to Combination Circuits | p. 177 |

6-2 Solving Parallel-Series Circuits | p. 178 |

6-3 Solving Series-Parallel Circuits | p. 183 |

6-4 Line Drop | p. 196 |

6-5 Distribution Systems | p. 201 |

6-6 Analysis With Ideal Circuit Elements | p. 207 |

Assessment | p. 210 |

Solutions to Self-Tests and Reviews | p. 211 |

Chapter 7 Electric Power | p. 212 |

7-1 Electric Power in Simple Circuits | p. 212 |

7-2 Total Power in an Electric Circuit | p. 215 |

7-3 Solving the Power Formula for Current or Voltage | p. 218 |

7-4 Intermediate Review of Power | p. 219 |

7-5 Squaring Powers of 10 | p. 221 |

7-6 The Exponential Power Formulas | p. 223 |

7-7 Checkup on Square Root (Diagnostic Test) | p. 226 |

7-8 Brushup on Square Root | p. 226 |

7-9 The Square Root of a Power of 10 | p. 233 |

7-10 Applications of the Exponential Power Formula | p. 236 |

7-11 Review of Electric Power | p. 239 |

Assessment | p. 242 |

Solutions to Self-Tests and Reviews | p. 243 |

Chapter 8 Algebra for Complex Electric Circuits | p. 244 |

8-1 Combining Like Terms | p. 244 |

8-2 Combining Unlike Terms | p. 246 |

8-3 Solving Simple Algebraic Equations | p. 248 |

8-4 Solving Equations by Transpositions and Cross Multiplication | p. 254 |

8-5 Combining Unlike Terms Involving Signed Numbers | p. 257 |

8-6 Solving Equations Which Have Unknowns and Numbers on Both Sides of the Equality Sign | p. 258 |

8-7 Solving Equations with Possible Negative Answers | p. 260 |

8-8 Removing Parentheses | p. 262 |

8-9 Solving Equations Containing Parentheses | p. 264 |

8-10 Solving Equations Containing Fractions | p. 267 |

8-11 Solving Simultaneous Equations by Addition | p. 270 |

8-12 Solving Simultaneous Equations by Substitution | p. 276 |

8-13 Review of Algebra | p. 279 |

Assessment | p. 282 |

Solutions to Self-Tests and Reviews | p. 283 |

Chapter 9 Kirchhoff's Laws | p. 284 |

9-1 Kirchhoff's Current Law | p. 284 |

9-2 Kirchhoff's Voltage Law | p. 286 |

9-3 Using Kirchhoff's Laws in Series Circuits | p. 289 |

9-4 Using Kirchhoff's Laws in Parallel Circuits | p. 296 |

9-5 Using Kirchhoff's Laws in Complex Circuits | p. 300 |

9-6 Review of Kirchhoff's Laws | p. 316 |

9-7 Equivalent Delta and Star Circuits | p. 319 |

9-8 Thevenin's Theorem | p. 325 |

9-9 Norton's Theorem | p. 338 |

9-10 Review | p. 342 |

Assessment | p. 343 |

Solutions to Self-Tests and Reviews | p. 344 |

Chapter 10 Applications of Series and Parallel Circuits | p. 345 |

10-1 Extending the Range of an Ammeter | p. 345 |

10-2 Reading Ammeters of Extended Range | p. 349 |

10-3 Extending the Range of a Voltmeter | p. 350 |

10-4 Review of Meters | p. 354 |

10-5 Voltage Dividers | p. 356 |

10-6 Resistance Measurement by the Voltage-Comparison Method. The Potentiometer Rule | p. 361 |

10-7 Resistance Measurement Using the Wheatstone Bridge | p. 366 |

10-8 Equivalent Circuits | p. 368 |

10-9 DC Equivalent Circuits for Self-Biased Transistor Circuits | p. 372 |

10-10 DC Equivalent Circuits for Fixed-Bias Transistor Circuits | p. 378 |

10-11 Transistor Equivalent Circuits | p. 381 |

10-12 Attenuators | p. 387 |

10-13 Power and Resistor Size | p. 394 |

Assessment | p. 396 |

Solutions to Self-Tests and Reviews | p. 397 |

Chapter 11 Efficiency | p. 398 |

11-1 Checkup on Percent (Diagnostic Test) | p. 398 |

11-2 Brushup on Percent | p. 399 |

11-3 Conversion Factors for Electric and Mechanical Power | p. 408 |

11-4 Efficiency of Electric Apparatus | p. 409 |

11-5 Finding the Output and Input of an Electric Device | p. 411 |

11-6 Load Matching for Power Transfer | p. 414 |

11-7 Review of Conversion Factors and Efficiency | p. 416 |

Assessment | p. 418 |

Solutions to Self-Tests and Reviews | p. 419 |

Chapter 12 Resistance of Wire | p. 420 |

12-1 Checkup on Ratio and Proportion (Diagnostic Test) | p. 420 |

12-2 Brushup on Ratio and Proportion | p. 421 |

12-3 Review of Ratio and Proportion | p. 431 |

12-4 The American Wire Gage Table | p. 432 |

12-5 Resistances of Wires of Different Materials | p. 437 |

12-6 Resistances of Wires of Different Lengths | p. 439 |

12-7 Resistances of Wires of Different Areas | p. 440 |

12-8 Resistance of Wires of Any Diameter, Any Length, or Any Material | p. 442 |

12-9 Finding the Length of Wire Needed to Make a Certain Resistance | p. 444 |

12-10 Finding the Diameter of Wire Needed to Make a Certain Resistance | p. 446 |

12-11 Temperature Coefficients of Resistance | p. 448 |

12-12 Review of Resistance of Wires | p. 457 |

Assessment | p. 459 |

Solutions to Self-Tests and Reviews | p. 460 |

Chapter 13 Size of Wiring | p. 461 |

13-1 Maximum Current-Carrying Capacities of Wires | p. 461 |

13-2 Finding the Minimum Size of Wire to Supply a Given Load | p. 464 |

13-3 Finding the Size of Wire Needed to Prevent Excessive Voltage Drops | p. 466 |

13-4 Temperature and Wire Size | p. 471 |

13-5 Review of Size of Wiring | p. 473 |

Assessment | p. 475 |

Solutions to Self-Tests and Reviews | p. 476 |

Chapter 14 Trigonometry for Alternating-Current Electricity | p. 477 |

14-1 Trigonometric Functions of a Right Triangle | p. 477 |

14-2 Using the Table of Trigonometric Functions | p. 484 |

14-3 Finding the Acute Angles of a Right Triangle | p. 485 |

14-4 Finding the Sides of a Right Triangle | p. 489 |

14-5 Review of Trigonometry | p. 493 |

Assessment | p. 496 |

Solutions to Self-Tests and Reviews | p. 497 |

Chapter 15 Introduction to AC Electricity | p. 498 |

15-1 Graphs | p. 498 |

15-2 The Generation of an AC Voltage | p. 506 |

15-3 Instantaneous Values, Maximum Values, and Phase Angles of an AC Wave | p. 514 |

15-4 Effective Value of an AC Wave | p. 516 |

15-5 Measuring Alternating Current with an Oscilloscope | p. 520 |

15-6 Vectors and Phasors | p. 523 |

15-7 The Pythagorean Theorem | p. 526 |

15-8 Power | p. 529 |

15-9 Harmonic Analysis | p. 532 |

Assessment | p. 539 |

Solutions to Self-Tests and Reviews | p. 540 |

Chapter 16 Inductance and Transformers | p. 541 |

16-1 Inductance | p. 541 |

16-2 Review of Inductance | p. 543 |

16-3 Reactance of a Coil | p. 544 |

16-4 Series Resistance and Inductance | p. 548 |

16-5 Real Inductor Losses and Quality | p. 556 |

16-6 Measuring the Inductance of a Coil | p. 559 |

16-7 Review of Coils and Inductance | p. 562 |

16-8 Transmission Lines | p. 563 |

16-9 Introduction to Ideal Transformers | p. 566 |

16-10 Current in a Transformer | p. 571 |

16-11 Impedance Changing Using Transformers | p. 575 |

16-12 Review of Ideal Transformers | p. 577 |

16-13 Real Transformers | p. 579 |

16-14 Efficiency of a Transformer | p. 587 |

16-15 Real Cables and Power Distribution | p. 591 |

Assessment | p. 603 |

Solutions to Self-Tests and Reviews | p. 604 |

Chapter 17 Capacitance | p. 605 |

17-1 Introduction to Capacitance | p. 605 |

17-2 Capacitors in Parallel | p. 607 |

17-3 Capacitors in Series | p. 609 |

17-4 Reactance of a Capacitor | p. 613 |

17-5 Current and Voltage in a Capacitor | p. 618 |

17-6 Measurement of Capacity | p. 620 |

17-7 A Real Capacitor | p. 621 |

17-8 Review of Capacitance | p. 629 |

Assessment | p. 630 |

Solutions to Self-Tests and Reviews | p. 631 |

Chapter 18 Series AC Circuits | p. 632 |

18-1 Simple Series AC Circuits | p. 632 |

18-2 Resistance and Capacitance in Series | p. 632 |

18-3 Resistance, Inductance, and Capacitance in Series | p. 637 |

18-4 Series Resonance | p. 645 |

18-5 Finding the Inductance or Capacitance Needed to Make a Series Resonant Circuit | p. 649 |

18-6 Review of Series AC Circuits | p. 652 |

Assessment | p. 656 |

Solutions to Self-Tests and Reviews | p. 657 |

Chapter 19 Parallel AC Circuits | p. 658 |

19-1 Simple Parallel AC Circuits | p. 658 |

19-2 Resistance and Inductance in Parallel | p. 664 |

19-3 Resistance, Inductance, and Capacitance in Parallel. The Equivalent Series Circuit | p. 669 |

19-4 Resolution of Phasors | p. 674 |

19-5 Power Filters and Ground Loops | p. 678 |

19-6 Parallel-Series AC Circuits | p. 689 |

19-7 Series-Parallel AC Circuits | p. 701 |

19-8 Parallel Resonance | p. 706 |

19-9 Review of Parallel AC Circuits | p. 709 |

Assessment | p. 714 |

Solutions to Self-Tests and Reviews | p. 715 |

Chapter 20 Alternating-Current Power | p. 716 |

20-1 Power and Power Factor | p. 716 |

20-2 Total Power Drawn by Combinations of Reactive Loads | p. 721 |

20-3 Power Drawn by Combinations of Resistive, Inductive, and Capacitive Loads | p. 729 |

20-4 Power-Factor Correction | p. 734 |

20-5 Review of AC Power | p. 745 |

20-6 Three-Wire Single-Phase 120/240 Circuits | p. 748 |

Assessment | p. 752 |

Solutions to Self-Tests and Reviews | p. 753 |

Chapter 21 Three-Phase Systems | p. 754 |

21-1 The Wye Connection | p. 754 |

21-2 The Delta Connection | p. 763 |

21-3 Review of Three-Phase Connections | p. 770 |

Assessment | p. 776 |

Chapter 22 Three-Phase Transformer Connections | p. 777 |

22-1 Overview of Three-Phase Transformer Connections | p. 777 |

22-2 Balanced Three-Phase Loads | p. 781 |

22-3 Three-Phase Power from Two Transformers | p. 795 |

Assessment | p. 801 |

Chapter 23 Mathematics for Logic Controls | p. 802 |

23-1 Introduction | p. 802 |

23-2 Simple Switches | p. 803 |

23-3 Truth Tables | p. 807 |

23-4 The OR Functions | p. 810 |

23-5 Summary of the Elementary Functions | p. 813 |

23-6 Systems of Elementary Functions | p. 815 |

23-7 Switching Circuit Inverter | p. 819 |

23-8 Relays in Logic Circuits | p. 821 |

23-9 Digital Logic Circuits | p. 829 |

Assessment | p. 835 |

Solutions to Self-Tests and Reviews | p. 836 |

Chapter 24 Signal Distribution | p. 837 |

24-1 Exponentials and Logarithms | p. 838 |

24-2 Review of Exponentials and Logs | p. 844 |

24-3 Bels and Decibels | p. 844 |

24-4 Voltage and Current Forms of the dB Equation | p. 845 |

24-5 Cables and Cable Losses | p. 848 |

Assessment | p. 852 |

Solutions to Self-Tests and Reviews | p. 853 |

Appendix A | p. 854 |

Color Codes | p. 854 |

Preferred Values of Components | p. 858 |

Trigonometric Functions of Decimal Degrees | p. 859 |

Appendix B | p. 854 |

Bibliography | p. 866 |

Answers to Selected Problems | p. 867 |

Answers to Internet Activities | p. 885 |

Index | p. 889 |