Basic Mathematics for Electricity and Electronics

by Singer, Bertrard; Forster, Harry; Schultz, Mitchel

• ISBN13: 9780028050225
• ISBN10: 0028050223
• Edition: 8th
• Format: Hardcover
• Copyright: 1999-10-22
• Publisher: McGraw-Hill Education

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.

Table of Contents

Preface	xiii
Introduction to Electricity	1	(13)
Basic Theory of Electricity	1	(5)
Electrical Measurements and Circuits	6	(8)
Assessment	12	(1)
Solutions to Self-Tests and Reviews	13	(1)
Simple Electric Circuits	14	(40)
Checkup on Fractions (Diagnostic Tests)	14	(1)
Brushup on Fractions	15	(9)
Ohm's Law	24	(5)
Checkup on Decimals (Diagnostic Test)	29	(1)
Introduction to Decimals	30	(7)
Introduction to the Metric System	37	(6)
Brushup on Decimals	43	(6)
Review of Working with Decimals	49	(5)
Assessment	52	(1)
Solutions to Self-Tests and Reviews	53	(1)
Formulas	54	(44)
Checkup on Formulas in Electrical Work (Diagnostic Test)	54	(1)
Brushup on Formulas	55	(7)
Positive and Negative Numbers	62	(4)
Checkup on Using Formulas with Exponents (Diagnostic Test)	66	(1)
Brushup on Formulas Containing Exponents	67	(2)
Powers of 10	69	(9)
Units of Measurement in Electronics	78	(4)
Using Electronic Units of Measurement in Simple Circuits	82	(2)
Solving the Ohm's Law Formula for Current or Resistance	84	(7)
Estimating Answers	91	(1)
Review of Ohm's Law	92	(6)
Assessment	96	(1)
Solutions to Self-Tests and Reviews	97	(1)
Series Circuits	98	(38)
Voltage, Current, and Resistance in Series Circuits	98	(4)
Using Ohm's Law in Series Circuits	102	(4)
Using Ohm's Law for Total Values in Series Circuits	106	(6)
Power Distribution Line Currents	112	(3)
Ground-Fault Protection	115	(1)
Intermediate Review of Series Circuits	116	(3)
Checkup on Formulas Involving Addition and Subtraction (Diagnostic Test)	119	(1)
Brushup on Formulas Involving Addition and Subtraction	119	(8)
Control of Current in a Series Circuit	127	(4)
Review of Series Circuits	131	(5)
Assessment	134	(1)
Solutions to Self-Tests and Reviews	135	(1)
Parallel Circuits	136	(41)
Total Voltage, Total Current, and Total Resistance in Parallel Circuits	136	(5)
Using Ohm's Law in Parallel Circuits	141	(3)
Check on Addition and Subtraction of Fractions (Diagnostic Test)	144	(1)
Brushup on Addition of Fractions	144	(5)
Brushup on Subtraction of Fractions	149	(4)
Checkup on Solution of Formulas Involving Fractions (Diagnostic Test)	153	(1)
Brushup on Solution of Fractional Equations	153	(7)
Total Resistance in a Parallel Circuit	160	(5)
Total Voltage in a Parallel Circuit	165	(2)
Division of Current in a Parallel Circuit	167	(5)
Review of Parallel Circuits	172	(5)
Assessment	175	(1)
Solutions to Self-Tests and Reviews	176	(1)
Combination Circuits	177	(35)
Introduction to Combination Circuits	177	(1)
Solving Parallel-Series Circuits	178	(5)
Solving Series-Parallel Circuits	183	(13)
Line Drop	196	(5)
Distribution Systems	201	(6)
Analysis With Ideal Circuit Elements	207	(5)
Assessment	210	(1)
Solutions to Self-Tests and Reviews	211	(1)
Electric Power	212	(32)
Electric Power in Simple Circuits	212	(3)
Total Power in an Electric Circuit	215	(3)
Solving the Power Formula for Current or Voltage	218	(1)
Intermediate Review of Power	219	(2)
Squaring Powers of 10	221	(2)
The Exponential Power Formulas	223	(3)
Checkup on Square Root (Diagnostic Test)	226	(1)
Brushup on Square Root	226	(7)
The Square Root of a Power of 10	233	(3)
Applications of the Exponential Power Formula	236	(3)
Review of Electric Power	239	(5)
Assessment	242	(1)
Solutions to Self-Tests and Reviews	243	(1)
Algebra for Complex Electric Circuits	244	(40)
Combining Like Terms	244	(2)
Combining Unlike Terms	246	(2)
Solving Simple Algebraic Equations	248	(6)
Solving Equations by Transpositions and Cross Multiplication	254	(3)
Combining Unlike Terms Involving Signed Numbers	257	(1)
Solving Equations Which Have Unknowns and Numbers on Both Sides of the Equality Sign	258	(2)
Solving Equations with Possible Negative Answers	260	(2)
Removing Parentheses	262	(2)
Solving Equations Containing Parentheses	264	(3)
Solving Equations Containing Fractions	267	(3)
Solving Simultaneous Equations by Addition	270	(6)
Solving Simultaneous Equations by Substitution	276	(3)
Review of Algebra	279	(5)
Assessment	282	(1)
Solutions to Self-Tests and Reviews	283	(1)
Kirchhoff's Laws	284	(61)
Kirchhoff's Current Law	284	(2)
Kirchhoff's Voltage Law	286	(3)
Using Kirchhoff's Laws in Series Circuits	289	(7)
Using Kirchhoff's Laws in Parallel Circuits	296	(4)
Using Kirchhoff's Laws in Complex Circuits	300	(16)
Review of Kirchhoff's Laws	316	(3)
Equivalent Delta and Star Circuits	319	(6)
Thevenin's Theorem	325	(13)
Norton's Theorem	338	(4)
Review	342	(3)
Assessment	343	(1)
Solutions to Self-Tests and Reviews	344	(1)
Applications of Series and Parallel Circuits	345	(53)
Extending the Range of an Ammeter	345	(4)
Reading Ammeters of Extended Range	349	(1)
Extending the Range of a Voltmeter	350	(4)
Review of Meters	354	(2)
Voltage Dividers	356	(5)
Resistance Measurement by the Voltage-Comparison Method. The Potentiometer Rule	361	(5)
Resistance Measurement Using the Wheatstone Bridge	366	(2)
Equivalent Circuits	368	(4)
DC Equivalent Circuits for Self-Biased Transistor Circuits	372	(6)
DC Equivalent Circuits for Fixed-Bias Transistor Circuits	378	(3)
Transistor Equivalent Circuits	381	(6)
Attenuators	387	(7)
Power and Resistor Size	394	(4)
Assessment	396	(1)
Solutions to Self-Tests and Reviews	397	(1)
Efficiency	398	(22)
Checkup on Percent (Diagnostic Test)	398	(1)
Brushup on Percent	399	(9)
Conversion Factors for Electric and Mechanical Power	408	(1)
Efficiency of Electric Apparatus	409	(2)
Finding the Output and Input of an Electric Device	411	(3)
Load Matching for Power Transfer	414	(2)
Review of Conversion Factors and Efficiency	416	(4)
Assessment	418	(1)
Solutions to Self-Tests and Reviews	419	(1)
Resistance of Wire	420	(41)
Checkup on Ratio and Proportion (Diagnostic Test)	420	(1)
Brushup on Ratio and Proportion	421	(10)
Review of Ratio and Proportion	431	(1)
The American Wire Gage Table	432	(5)
Resistance of Wires of Different Materials	437	(2)
Resistances of Wires of Different Lengths	439	(1)
Resistances of Wires of Different Areas	440	(2)
Resistance of Wires of Any Diameter, Any Length, or Any Material	442	(2)
Finding the Length of Wire Needed to Make a Certain Resistance	444	(2)
Finding the Diameter of Wire Needed to Make a Certain Resistance	446	(2)
Temperature Coefficients of Resistance	448	(9)
Review of Resistance of Wires	457	(4)
Assessment	459	(1)
Solutions to Self-Tests and Reviews	460	(1)
Size of Wiring	461	(16)
Maximum Current-Carrying Capacities of Wires	461	(3)
Finding the Minimum Size of Wire to Supply a Given Load	464	(2)
Finding the Size of Wire Needed to Prevent Excessive Voltage Drops	466	(5)
Temperature and Wire Size	471	(2)
Review of Size of Wiring	473	(4)
Assessment	475	(1)
Solutions to Self-Tests and Reviews	476	(1)
Trigonometry for Alternating-Current Electricity	477	(21)
Trigonometric Functions of a Right Triangle	477	(7)
Using the Table of Trigonometric Functions	484	(1)
Finding the Acute Angles of a Right Triangle	485	(4)
Finding the Sides of a Right Triangle	489	(4)
Review of Trigonometry	493	(5)
Assessment	496	(1)
Solutions to Self-Tests and Reviews	497	(1)
Introduction to AC Electricity	498	(43)
Graphs	498	(8)
The Generation of an AC Voltage	506	(8)
Instantaneous Values, Maximum Values, and Phase Angles of an AC Wave	514	(2)
Effective Value of an AC Wave	516	(4)
Measuring Alternating Current with an Oscilloscope	520	(3)
Vectors and Phasors	523	(3)
The Pythagorean Theorem	526	(3)
Power	529	(3)
Harmonic Analysis	532	(9)
Assessment	539	(1)
Solutions to Self-Tests and Reviews	540	(1)
Inductance and Transformers	541	(64)
Inductance	541	(2)
Review of Inductance	543	(1)
Reactance of a Coil	544	(4)
Series Resistance and Inductance	548	(8)
Real Inductor Losses and Quality	556	(3)
Measuring the Inductance of a Coil	559	(3)
Review of Coils and Inductance	562	(1)
Transmission Lines	563	(3)
Introduction to Ideal Transformers	566	(5)
Current in a Transformer	571	(4)
Impedance Changing Using Transformers	575	(2)
Review of Ideal Transformers	577	(2)
Real Transformers	579	(8)
Efficiency of a Transformer	587	(4)
Real Cables and Power Distribution	591	(14)
Assessment	603	(1)
Solutions to Self-Tests and Reviews	604	(1)
Capacitance	605	(27)
Introduction to Capacitance	605	(2)
Capacitors in Parallel	607	(2)
Capacitors in Series	609	(4)
Reactance of a Capacitor	613	(5)
Current and Voltage in a Capacitor	618	(2)
Measurement of Capacity	620	(1)
A Real Capacitor	621	(8)
Review of Capacitance	629	(3)
Assessment	630	(1)
Solutions to Self-Tests and Reviews	631	(1)
Series AC Circuits	632	(26)
Simple Series AC Circuits	632	(1)
Resistance and Capacitance in Series	632	(5)
Resistance, Inductance, and Capacitance in Series	637	(8)
Series Resonance	645	(4)
Finding the Inductance or Capacitance Needed to Make a Series Resonant Circuite	649	(3)
Review of Series AC Circuits	652	(6)
Assessment	656	(1)
Solutions to Self-Tests and Reviews	657	(1)
Parallel AC Circuits	658	(58)
Simple Parallel AC Circuits	658	(6)
Resistance and Inductance in Parallel	664	(5)
Resistance, Inductance, and Capacitance in Parallel. The Equivalent Series Circuit	669	(5)
Resolution of Phasors	674	(4)
Power Filters and Ground Loops	678	(11)
Parallel-Series AC Circuits	689	(12)
Series-Parallel AC Circuits	701	(5)
Parallel Resonance	706	(3)
Review of Parallel AC Circuits	709	(7)
Assessment	714	(1)
Solutions to Self-Tests and Reviews	715	(1)
Alternating-Current Power	716	(38)
Power and Power Factor	716	(5)
Total Power Drawn by Combinations of Reactive Loads	721	(8)
Power Drawn by Combinations of Resistive, Inductive, and Capacitive Loads	729	(5)
Power-Factor Correction	734	(11)
Review of AC Power	745	(3)
Three-Wire Single-Phase 120/240 Circuits	748	(6)
Assessment	752	(1)
Solutions to Self-Tests and Reviews	753	(1)
Three-Phase Systems	754	(23)
The Wye Connection	754	(9)
The Delta Connection	763	(7)
Review of Three-Phase Connections	770	(7)
Assessment	776	(1)
Three-Phase Transformer Connections	777	(25)
Overview of Three-Phase Transformer Connections	777	(4)
Balanced Three-Phase Loads	781	(14)
Three-Phase Power from Two Transformers	795	(7)
Assessment	801	(1)
Mathematics for Logic Controls	802	(35)
Introduction	802	(1)
Simple Switches	803	(4)
Truth Tables	807	(3)
The OR Functions	810	(3)
Summary of the Elementary Functions	813	(2)
Systems of Elementary Functions	815	(4)
Switching Circuit Inverter	819	(2)
Relays in Logic Circuits	821	(8)
Digital Logic Circuits	829	(8)
Assessment	835	(1)
Solutions to Self-Tests and Reviews	836	(1)
Signal Distribution	837	(17)
Exponentials and Logarithms	838	(6)
Review of Exponentials and Logs	844	(1)
Bels and Decibels	844	(1)
Voltage and Current Forms of the dB Equation	845	(3)
Cables and Cable Losses	848	(6)
Assessment	852	(1)
Solutions to Self-Tests and Reviews	853	(1)
Appendix A	854	(1)
Color Codes	854	(4)
Preferred Values of Components	858	(1)
Trigonometric Functions of Decimal Degrees	859
Appendix B	854	(12)
Bibliography	866	(1)
Answers to Selected Problems	867	(18)
Answers to Internet Activities	885	(4)
Index	889