Cover image for Basic mathematics for electricity and electronics
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

Prefacep. xiii
Chapter 1 Introduction to Electricityp. 1
1-1 Basic Theory of Electricityp. 1
1-2 Electrical Measurements and Circuitsp. 6
Assessmentp. 12
Solutions to Self-Tests and Reviewsp. 13
Chapter 2 Simple Electric Circuitsp. 14
2-1 Checkup on Fractions (Diagnostic Tests)p. 14
2-2 Brushup on Fractionsp. 15
2-3 Ohm's Lawp. 24
2-4 Checkup on Decimals (Diagnostic Test)p. 29
2-5 Introduction to Decimalsp. 30
2-6 Introduction to the Metric Systemp. 37
2-7 Brushup on Decimalsp. 43
2-8 Review of Working with Decimalsp. 49
Assessmentp. 52
Solutions to Self-Tests and Reviewsp. 53
Chapter 3 Formulasp. 54
3-1 Checkup on Formulas in Electrical Work (Diagnostic Test)p. 54
3-2 Brushup on Formulasp. 55
3-3 Positive and Negative Numbersp. 62
3-4 Checkup on Using Formulas with Exponents (Diagnostic Test)p. 66
3-5 Brushup on Formulas Containing Exponentsp. 67
3-6 Powers of 10p. 69
3-7 Units of Measurement in Electronicsp. 78
3-8 Using Electronic Units of Measurement in Simple Circuitsp. 82
3-9 Solving the Ohm's Law Formula for Current or Resistancep. 84
3-10 Estimating Answersp. 91
3-11 Review of Ohm's Lawp. 92
Assessmentp. 96
Solutions to Self-Tests and Reviewsp. 97
Chapter 4 Series Circuitsp. 98
4-1 Voltage, Current, and Resistance in Series Circuitsp. 98
4-2 Using Ohm's Law in Series Circuitsp. 102
4-3 Using Ohm's Law for Total Values in Series Circuitsp. 106
4-4 Power Distribution Line Currentsp. 112
4-5 Ground-Fault Protectionp. 115
4-6 Intermediate Review of Series Circuitsp. 116
4-7 Checkup on Formulas Involving Addition and Subtraction (Diagnostic Test)p. 119
4-8 Brushup on Formulas Involving Addition and Subtractionp. 119
4-9 Control of Current in a Series Circuitp. 127
4-10 Review of Series Circuitsp. 131
Assessmentp. 134
Solutions to Self-Tests and Reviewsp. 135
Chapter 5 Parallel Circuitsp. 136
5-1 Total Voltage, Total Current, and Total Resistance in Parallel Circuitsp. 136
5-2 Using Ohm's Law in Parallel Circuitsp. 141
5-3 Check on Addition and Subtraction of Fractions (Diagnostic Test)p. 144
5-4 Brushup on Addition of Fractionsp. 144
5-5 Brushup on Subtraction of Fractionsp. 149
5-6 Checkup on Solution of Formulas Involving Fractions (Diagnostic Test)p. 153
5-7 Brushup on Solution of Fractional Equationsp. 153
5-8 Total Resistance in a Parallel Circuitp. 160
5-9 Total Voltage in a Parallel Circuitp. 165
5-10 Division of Current in a Parallel Circuitp. 167
5-11 Review of Parallel Circuitsp. 172
Assessmentp. 175
Solutions to Self-Tests and Reviewsp. 176
Chapter 6 Combination Circuitsp. 177
6-1 Introduction to Combination Circuitsp. 177
6-2 Solving Parallel-Series Circuitsp. 178
6-3 Solving Series-Parallel Circuitsp. 183
6-4 Line Dropp. 196
6-5 Distribution Systemsp. 201
6-6 Analysis With Ideal Circuit Elementsp. 207
Assessmentp. 210
Solutions to Self-Tests and Reviewsp. 211
Chapter 7 Electric Powerp. 212
7-1 Electric Power in Simple Circuitsp. 212
7-2 Total Power in an Electric Circuitp. 215
7-3 Solving the Power Formula for Current or Voltagep. 218
7-4 Intermediate Review of Powerp. 219
7-5 Squaring Powers of 10p. 221
7-6 The Exponential Power Formulasp. 223
7-7 Checkup on Square Root (Diagnostic Test)p. 226
7-8 Brushup on Square Rootp. 226
7-9 The Square Root of a Power of 10p. 233
7-10 Applications of the Exponential Power Formulap. 236
7-11 Review of Electric Powerp. 239
Assessmentp. 242
Solutions to Self-Tests and Reviewsp. 243
Chapter 8 Algebra for Complex Electric Circuitsp. 244
8-1 Combining Like Termsp. 244
8-2 Combining Unlike Termsp. 246
8-3 Solving Simple Algebraic Equationsp. 248
8-4 Solving Equations by Transpositions and Cross Multiplicationp. 254
8-5 Combining Unlike Terms Involving Signed Numbersp. 257
8-6 Solving Equations Which Have Unknowns and Numbers on Both Sides of the Equality Signp. 258
8-7 Solving Equations with Possible Negative Answersp. 260
8-8 Removing Parenthesesp. 262
8-9 Solving Equations Containing Parenthesesp. 264
8-10 Solving Equations Containing Fractionsp. 267
8-11 Solving Simultaneous Equations by Additionp. 270
8-12 Solving Simultaneous Equations by Substitutionp. 276
8-13 Review of Algebrap. 279
Assessmentp. 282
Solutions to Self-Tests and Reviewsp. 283
Chapter 9 Kirchhoff's Lawsp. 284
9-1 Kirchhoff's Current Lawp. 284
9-2 Kirchhoff's Voltage Lawp. 286
9-3 Using Kirchhoff's Laws in Series Circuitsp. 289
9-4 Using Kirchhoff's Laws in Parallel Circuitsp. 296
9-5 Using Kirchhoff's Laws in Complex Circuitsp. 300
9-6 Review of Kirchhoff's Lawsp. 316
9-7 Equivalent Delta and Star Circuitsp. 319
9-8 Thevenin's Theoremp. 325
9-9 Norton's Theoremp. 338
9-10 Reviewp. 342
Assessmentp. 343
Solutions to Self-Tests and Reviewsp. 344
Chapter 10 Applications of Series and Parallel Circuitsp. 345
10-1 Extending the Range of an Ammeterp. 345
10-2 Reading Ammeters of Extended Rangep. 349
10-3 Extending the Range of a Voltmeterp. 350
10-4 Review of Metersp. 354
10-5 Voltage Dividersp. 356
10-6 Resistance Measurement by the Voltage-Comparison Method. The Potentiometer Rulep. 361
10-7 Resistance Measurement Using the Wheatstone Bridgep. 366
10-8 Equivalent Circuitsp. 368
10-9 DC Equivalent Circuits for Self-Biased Transistor Circuitsp. 372
10-10 DC Equivalent Circuits for Fixed-Bias Transistor Circuitsp. 378
10-11 Transistor Equivalent Circuitsp. 381
10-12 Attenuatorsp. 387
10-13 Power and Resistor Sizep. 394
Assessmentp. 396
Solutions to Self-Tests and Reviewsp. 397
Chapter 11 Efficiencyp. 398
11-1 Checkup on Percent (Diagnostic Test)p. 398
11-2 Brushup on Percentp. 399
11-3 Conversion Factors for Electric and Mechanical Powerp. 408
11-4 Efficiency of Electric Apparatusp. 409
11-5 Finding the Output and Input of an Electric Devicep. 411
11-6 Load Matching for Power Transferp. 414
11-7 Review of Conversion Factors and Efficiencyp. 416
Assessmentp. 418
Solutions to Self-Tests and Reviewsp. 419
Chapter 12 Resistance of Wirep. 420
12-1 Checkup on Ratio and Proportion (Diagnostic Test)p. 420
12-2 Brushup on Ratio and Proportionp. 421
12-3 Review of Ratio and Proportionp. 431
12-4 The American Wire Gage Tablep. 432
12-5 Resistances of Wires of Different Materialsp. 437
12-6 Resistances of Wires of Different Lengthsp. 439
12-7 Resistances of Wires of Different Areasp. 440
12-8 Resistance of Wires of Any Diameter, Any Length, or Any Materialp. 442
12-9 Finding the Length of Wire Needed to Make a Certain Resistancep. 444
12-10 Finding the Diameter of Wire Needed to Make a Certain Resistancep. 446
12-11 Temperature Coefficients of Resistancep. 448
12-12 Review of Resistance of Wiresp. 457
Assessmentp. 459
Solutions to Self-Tests and Reviewsp. 460
Chapter 13 Size of Wiringp. 461
13-1 Maximum Current-Carrying Capacities of Wiresp. 461
13-2 Finding the Minimum Size of Wire to Supply a Given Loadp. 464
13-3 Finding the Size of Wire Needed to Prevent Excessive Voltage Dropsp. 466
13-4 Temperature and Wire Sizep. 471
13-5 Review of Size of Wiringp. 473
Assessmentp. 475
Solutions to Self-Tests and Reviewsp. 476
Chapter 14 Trigonometry for Alternating-Current Electricityp. 477
14-1 Trigonometric Functions of a Right Trianglep. 477
14-2 Using the Table of Trigonometric Functionsp. 484
14-3 Finding the Acute Angles of a Right Trianglep. 485
14-4 Finding the Sides of a Right Trianglep. 489
14-5 Review of Trigonometryp. 493
Assessmentp. 496
Solutions to Self-Tests and Reviewsp. 497
Chapter 15 Introduction to AC Electricityp. 498
15-1 Graphsp. 498
15-2 The Generation of an AC Voltagep. 506
15-3 Instantaneous Values, Maximum Values, and Phase Angles of an AC Wavep. 514
15-4 Effective Value of an AC Wavep. 516
15-5 Measuring Alternating Current with an Oscilloscopep. 520
15-6 Vectors and Phasorsp. 523
15-7 The Pythagorean Theoremp. 526
15-8 Powerp. 529
15-9 Harmonic Analysisp. 532
Assessmentp. 539
Solutions to Self-Tests and Reviewsp. 540
Chapter 16 Inductance and Transformersp. 541
16-1 Inductancep. 541
16-2 Review of Inductancep. 543
16-3 Reactance of a Coilp. 544
16-4 Series Resistance and Inductancep. 548
16-5 Real Inductor Losses and Qualityp. 556
16-6 Measuring the Inductance of a Coilp. 559
16-7 Review of Coils and Inductancep. 562
16-8 Transmission Linesp. 563
16-9 Introduction to Ideal Transformersp. 566
16-10 Current in a Transformerp. 571
16-11 Impedance Changing Using Transformersp. 575
16-12 Review of Ideal Transformersp. 577
16-13 Real Transformersp. 579
16-14 Efficiency of a Transformerp. 587
16-15 Real Cables and Power Distributionp. 591
Assessmentp. 603
Solutions to Self-Tests and Reviewsp. 604
Chapter 17 Capacitancep. 605
17-1 Introduction to Capacitancep. 605
17-2 Capacitors in Parallelp. 607
17-3 Capacitors in Seriesp. 609
17-4 Reactance of a Capacitorp. 613
17-5 Current and Voltage in a Capacitorp. 618
17-6 Measurement of Capacityp. 620
17-7 A Real Capacitorp. 621
17-8 Review of Capacitancep. 629
Assessmentp. 630
Solutions to Self-Tests and Reviewsp. 631
Chapter 18 Series AC Circuitsp. 632
18-1 Simple Series AC Circuitsp. 632
18-2 Resistance and Capacitance in Seriesp. 632
18-3 Resistance, Inductance, and Capacitance in Seriesp. 637
18-4 Series Resonancep. 645
18-5 Finding the Inductance or Capacitance Needed to Make a Series Resonant Circuitp. 649
18-6 Review of Series AC Circuitsp. 652
Assessmentp. 656
Solutions to Self-Tests and Reviewsp. 657
Chapter 19 Parallel AC Circuitsp. 658
19-1 Simple Parallel AC Circuitsp. 658
19-2 Resistance and Inductance in Parallelp. 664
19-3 Resistance, Inductance, and Capacitance in Parallel. The Equivalent Series Circuitp. 669
19-4 Resolution of Phasorsp. 674
19-5 Power Filters and Ground Loopsp. 678
19-6 Parallel-Series AC Circuitsp. 689
19-7 Series-Parallel AC Circuitsp. 701
19-8 Parallel Resonancep. 706
19-9 Review of Parallel AC Circuitsp. 709
Assessmentp. 714
Solutions to Self-Tests and Reviewsp. 715
Chapter 20 Alternating-Current Powerp. 716
20-1 Power and Power Factorp. 716
20-2 Total Power Drawn by Combinations of Reactive Loadsp. 721
20-3 Power Drawn by Combinations of Resistive, Inductive, and Capacitive Loadsp. 729
20-4 Power-Factor Correctionp. 734
20-5 Review of AC Powerp. 745
20-6 Three-Wire Single-Phase 120/240 Circuitsp. 748
Assessmentp. 752
Solutions to Self-Tests and Reviewsp. 753
Chapter 21 Three-Phase Systemsp. 754
21-1 The Wye Connectionp. 754
21-2 The Delta Connectionp. 763
21-3 Review of Three-Phase Connectionsp. 770
Assessmentp. 776
Chapter 22 Three-Phase Transformer Connectionsp. 777
22-1 Overview of Three-Phase Transformer Connectionsp. 777
22-2 Balanced Three-Phase Loadsp. 781
22-3 Three-Phase Power from Two Transformersp. 795
Assessmentp. 801
Chapter 23 Mathematics for Logic Controlsp. 802
23-1 Introductionp. 802
23-2 Simple Switchesp. 803
23-3 Truth Tablesp. 807
23-4 The OR Functionsp. 810
23-5 Summary of the Elementary Functionsp. 813
23-6 Systems of Elementary Functionsp. 815
23-7 Switching Circuit Inverterp. 819
23-8 Relays in Logic Circuitsp. 821
23-9 Digital Logic Circuitsp. 829
Assessmentp. 835
Solutions to Self-Tests and Reviewsp. 836
Chapter 24 Signal Distributionp. 837
24-1 Exponentials and Logarithmsp. 838
24-2 Review of Exponentials and Logsp. 844
24-3 Bels and Decibelsp. 844
24-4 Voltage and Current Forms of the dB Equationp. 845
24-5 Cables and Cable Lossesp. 848
Assessmentp. 852
Solutions to Self-Tests and Reviewsp. 853
Appendix Ap. 854
Color Codesp. 854
Preferred Values of Componentsp. 858
Trigonometric Functions of Decimal Degreesp. 859
Appendix Bp. 854
Bibliographyp. 866
Answers to Selected Problemsp. 867
Answers to Internet Activitiesp. 885
Indexp. 889