AIWA 1-DC Service Manual
Fifth Edition, last update January 1, 2004
2
Lessons In Electric Circuits, Volume I – DC
By Tony R. Kuphaldt
Fifth Edition, last update January 1, 2004
c
° 1998-2003, Tony R. Kuphaldt
This book is published under the terms and conditions of the Design Science License. These
terms and conditions allow for free copying, distribution, and/or modification of this document by
the general public. The full Design Science License text is included in the last chapter.
As an open and collaboratively developed text, this book is distributed in the hope that it
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for more details.
Available in its entirety as part of the Open Book Project collection at http://www.ibiblio.org/obp
PRINTING HISTORY
• First Edition: Printed in June of 2000. Plain-ASCII illustrations for universal computer
readability.
• Second Edition: Printed in September of 2000. Illustrations reworked in standard graphic
(eps and jpeg) format. Source files translated to Texinfo format for easy online and printed
publication.
• Third Edition: Equations and tables reworked as graphic images rather than plain-ASCII text.
i
• Fourth Edition: Printed in August 2001. Source files translated to SubML format. SubML is
a simple markup language designed to easily convert to other markups like LATEX, HTML, or
DocBook using nothing but search-and-replace substitutions.
• Fifth Edition: Printed in August 2002. New sections added, and error corrections made, since
the fourth edition.
ii
Contents
1 BASIC CONCEPTS OF ELECTRICITY 1
1.1 Static electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Conductors, insulators, and electron flow . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Voltage and current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.6 Voltage and current in a practical circuit . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.7 Conventional versus electron flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2 OHM’s LAW 33
2.1 How voltage, current, and resistance relate . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2 An analogy for Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Power in electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4 Calculating electric power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.6 Nonlinear conduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.7 Circuit wiring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8 Polarity of voltage drops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
2.9 Computer simulation of electric circuits . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.10 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3 ELECTRICAL SAFETY 73
3.1 The importance of electrical safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Physiological effects of electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Shock current path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4 Ohm’s Law (again!) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.5 Safe practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.6 Emergency response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.7 Common sources of hazard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.8 Safe circuit design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.9 Safe meter usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.10 Electric shock data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.11 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
iii
iv CONTENTS
4 SCIENTIFIC NOTATION AND METRIC PREFIXES 113
4.1 Scientific notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.2 Arithmetic with scientific notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.3 Metric notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.4 Metric prefix conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.5 Hand calculator use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.6 Scientific notation in SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5 SERIES AND PARALLEL CIRCUITS 123
5.1 What are ”series” and ”parallel” circuits? . . . . . . . . . . . . . . . . . . . . . . . . 123
5.2 Simple series circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3 Simple parallel circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.4 Conductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.5 Power calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.6 Correct use of Ohm’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.7 Component failure analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.8 Building simple resistor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6 DIVIDER CIRCUITS AND KIRCHHOFF’S LAWS 165
6.1 Voltage divider circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
6.2 Kirchhoff’s Voltage Law (KVL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.3 Current divider circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.4 Kirchhoff’s Current Law (KCL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
6.5 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
7 SERIES-PARALLEL COMBINATION CIRCUITS 191
7.1 What is a series-parallel circuit? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7.2 Analysis technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
7.3 Re-drawing complex schematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
7.4 Component failure analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
7.5 Building series-parallel resistor circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 215
7.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
8 DC METERING CIRCUITS 229
8.1 What is a meter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
8.2 Voltmeter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
8.3 Voltmeter impact on measured circuit . . . . . . . . . . . . . . . . . . . . . . . . . . 240
8.4 Ammeter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
8.5 Ammeter impact on measured circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
8.6 Ohmmeter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
8.7 High voltage ohmmeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
8.8 Multimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
8.9 Kelvin (4-wire) resistance measurement . . . . . . . . . . . . . . . . . . . . . . . . . 277
8.10 Bridge circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
CONTENTS v
8.11 Wattmeter design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
8.12 Creating custom calibration resistances . . . . . . . . . . . . . . . . . . . . . . . . . . 293
8.13 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
9 ELECTRICAL INSTRUMENTATION SIGNALS 297
9.1 Analog and digital signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
9.2 Voltage signal systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
9.3 Current signal systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
9.4 Tachogenerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
9.5 Thermocouples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
9.6 pH measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
9.7 Strain gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
9.8 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
10 DC NETWORK ANALYSIS 325
10.1 What is network analysis? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
10.2 Branch current method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
10.3 Mesh current method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
10.4 Introduction to network theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
10.5 Millman’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
10.6 Superposition Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
10.7 Thevenin’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
10.8 Norton’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
10.9 Thevenin-Norton equivalencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
10.10Millman’s Theorem revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
10.11Maximum Power Transfer Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
10.12∆-Y and Y-∆ conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
10.13Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
11 BATTERIES AND POWER SYSTEMS 377
11.1 Electron activity in chemical reactions . . . . . . . . . . . . . . . . . . . . . . . . . . 377
11.2 Battery construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
11.3 Battery ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
11.4 Special-purpose batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
11.5 Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
11.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
12 PHYSICS OF CONDUCTORS AND INSULATORS 395
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
12.2 Conductor size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
12.3 Conductor ampacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
12.4 Fuses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
12.5 Specific resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
12.6 Temperature coefficient of resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
12.7 Superconductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
12.8 Insulator breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
vi CONTENTS
12.9 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
12.10Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
13 CAPACITORS 425
13.1 Electric fields and capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
13.2 Capacitors and calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
13.3 Factors affecting capacitance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
13.4 Series and parallel capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
13.5 Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
13.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
14 MAGNETISM AND ELECTROMAGNETISM 447
14.1 Permanent magnets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
14.2 Electromagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
14.3 Magnetic units of measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
14.4 Permeability and saturation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
14.5 Electromagnetic induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460
14.6 Mutual inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
14.7 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465
15 INDUCTORS 467
15.1 Magnetic fields and inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
15.2 Inductors and calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
15.3 Factors affecting inductance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
15.4 Series and parallel inductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
15.5 Practical considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
15.6 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483
16 RC AND L/R TIME CONSTANTS 485
16.1 Electrical transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
16.2 Capacitor transient response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
16.3 Inductor transient response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
16.4 Voltage and current calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491
16.5 Why L/R and not LR? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497
16.6 Complex voltage and current calculations . . . . . . . . . . . . . . . . . . . . . . . . 500
16.7 Complex circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
16.8 Solving for unknown time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
16.9 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
17 ABOUT THIS BOOK 509
17.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
17.2 The use of SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510
17.3 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
CONTENTS vii
18 CONTRIBUTOR LIST 513
18.1 How to contribute to this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
18.2 Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
18.2.1 Benjamin Crowell, Ph.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
18.2.2 Tony R. Kuphaldt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
18.2.3 Ron LaPlante . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
18.2.4 Jason Starck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
18.2.5 Warren Young . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
18.2.6 Your name here . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
18.2.7 Typo corrections and other “minor” contributions . . . . . . . . . . . . . . . 515
19 DESIGN SCIENCE LICENSE 517
19.1 0. Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
19.2 1. Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
19.3 2. Rights and copyright . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
19.4 3. Copying and distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
19.5 4. Modification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
19.6 5. No restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
19.7 6. Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
19.8 7. No warranty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
19.9 8. Disclaimer of liability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
Chapter 1
BASIC CONCEPTS OF
ELECTRICITY
1.1 Static electricity
It was discovered centuries ago that certain types of materials would mysteriously attract one another
after being rubbed together. For example: after rubbing a piece of silk against a piece of glass, the
silk and glass would tend to stick together. Indeed, there was an attractive force that could be
demonstrated even when the two materials were separated:
attraction
Glass rod Silk cloth
Glass and silk aren’t the only materials known to behave like this. Anyone who has ever brushed
up against a latex balloon only to find that it tries to stick to them has experienced this same phenomenon. Paraffin wax and wool cloth are another pair of materials early experimenters recognized
as manifesting attractive forces after being rubbed together:
1
2 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
attraction
Wax
Wool cloth
This phenomenon became even more interesting when it was discovered that identical materials,
after having been rubbed with their respective cloths, always repelled each other:
repulsion
Glass rod Glass rod
repulsion
Wax
It was also noted that when a piece of glass rubbed with silk was exposed to a piece of wax
rubbed with wool, the two materials would attract one another:
Wax
attraction
Wax
Glass rod
Furthermore, it was found that any material demonstrating properties of attraction or repulsion
1.1. STATIC ELECTRICITY 3
after being rubbed could be classed into one of two distinct categories: attracted to glass and repelled
by wax, or repelled by glass and attracted to wax. It was either one or the other: there were no
materials found that would be attracted to or repelled by both glass and wax, or that reacted to
one without reacting to the other.
More attention was directed toward the pieces of cloth used to do the rubbing. It was discovered
that after rubbing two pieces of glass with two pieces of silk cloth, not only did the glass pieces repel
each other, but so did the cloths. The same phenomenon held for the pieces of wool used to rub the
wax:
repulsion
Silk clothSilk cloth
repulsion
Wool cloth Wool cloth
Now, this was really strange to witness. After all, none of these objects were visibly altered by
the rubbing, yet they definitely behaved differently than before they were rubbed. Whatever change
took place to make these materials attract or repel one another was invisible.
Some experimenters speculated that invisible ”fluids” were being transferred from one object to
another during the process of rubbing, and that these ”fluids” were able to effect a physical force
over a distance. Charles Dufay was one the early experimenters who demonstrated that there were
definitely two different types of changes wrought by rubbing certain pairs of objects together. The
fact that there was more than one type of change manifested in these materials was evident by the
fact that there were two types of forces produced: attraction and repulsion. The hypothetical fluid
transfer became known as a charge.
One pioneering researcher, Benjamin Franklin, came to the conclusion that there was only one
fluid exchanged between rubbed objects, and that the two different ”charges” were nothing more
than either an excess or a deficiency of that one fluid. After experimenting with wax and wool,
Franklin suggested that the coarse wool removed some of this invisible fluid from the smooth wax,
causing an excess of fluid on the wool and a deficiency of fluid on the wax. The resulting disparity
4 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
in fluid content between the wool and wax would then cause an attractive force, as the fluid tried
to regain its former balance between the two materials.
Postulating the existence of a single ”fluid” that was either gained or lost through rubbing
accounted best for the observed behavior: that all these materials fell neatly into one of two categories
when rubbed, and most importantly, that the two active materials rubbed against each other always
fell into opposing categories as evidenced by their invariable attraction to one another. In other
words, there was never a time where two materials rubbed against each other both became either
positive or negative.
Following Franklin’s speculation of the wool rubbing something off of the wax, the type of charge
that was associated with rubbed wax became known as ”negative” (because it was supposed to have
a deficiency of fluid) while the type of charge associated with the rubbing wool became known as
”positive” (because it was supposed to have an excess of fluid). Little did he know that his innocent
conjecture would cause much confusion for students of electricity in the future!
Precise measurements of electrical charge were carried out by the French physicist Charles
Coulomb in the 1780’s using a device called a torsional balance measuring the force generated
between two electrically charged objects. The results of Coulomb’s work led to the development of
a unit of electrical charge named in his honor, the coulomb. If two ”point” objects (hypothetical
objects having no appreciable surface area) were equally charged to a measure of 1 coulomb, and
placed 1 meter (approximately 1 yard) apart, they would generate a force of about 9 billion newtons
(approximately 2 billion pounds), either attracting or repelling depending on the types of charges
involved.
It discovered much later that this ”fluid” was actually composed of extremely small bits of matter
called electrons, so named in honor of the ancient Greek word for amber: another material exhibiting
charged properties when rubbed with cloth. Experimentation has since revealed that all objects are
composed of extremely small ”building-blocks” known as atoms, and that these atoms are in turn
composed of smaller components known as particles. The three fundamental particles comprising
atoms are called protons, neutrons, and electrons. Atoms are far too small to be seen, but if we
could look at one, it might appear something like this:
1.1. STATIC ELECTRICITY 5
e
e
N
P
P
N
e e
N
N
P
P
P
P
N
N
e
e
e
= electron
P
= proton
N
= neutron
Even though each atom in a piece of material tends to hold together as a unit, there’s actually
a lot of empty space between the electrons and the cluster of protons and neutrons residing in the
middle.
This crude model is that of the element carbon, with six protons, six neutrons, and six electrons.
In any atom, the protons and neutrons are very tightly bound together, which is an important
quality. The tightly-bound clump of protons and neutrons in the center of the atom is called the
nucleus, and the number of protons in an atom’s nucleus determines its elemental identity: change
the number of protons in an atom’s nucleus, and you change the type of atom that it is. In fact,
if you could remove three protons from the nucleus of an atom of lead, you will have achieved the
old alchemists’ dream of producing an atom of gold! The tight binding of protons in the nucleus
is responsible for the stable identity of chemical elements, and the failure of alchemists to achieve
their dream.
Neutrons are much less influential on the chemical character and identity of an atom than protons,
although they are just as hard to add to or remove from the nucleus, being so tightly bound. If
neutrons are added or gained, the atom will still retain the same chemical identity, but its mass will
change slightly and it may acquire strange nuclear properties such as radioactivity.
However, electrons have significantly more freedom to move around in an atom than either
protons or neutrons. In fact, they can be knocked out of their respective positions (even leaving the
atom entirely!) by far less energy than what it takes to dislodge particles in the nucleus. If this
happens, the atom still retains its chemical identity, but an important imbalance occurs. Electrons
and protons are unique in the fact that they are attracted to one another over a distance. It is this
attraction over distance which causes the attraction between rubbed objects, where electrons are
moved away from their original atoms to reside around atoms of another object.
Electrons tend to repel other electrons over a distance, as do protons with other protons. The
only reason protons bind together in the nucleus of an atom is because of a much stronger force
6 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
called the strong nuclear force which has effect only under very short distances. Because of this
attraction/repulsion behavior between individual particles, electrons and protons are said to have
opposite electric charges. That is, each electron has a negative charge, and each proton a positive
charge. In equal numbers within an atom, they counteract each other’s presence so that the net
charge within the atom is zero. This is why the picture of a carbon atom had six electrons: to balance
out the electric charge of the six protons in the nucleus. If electrons leave or extra electrons arrive,
the atom’s net electric charge will be imbalanced, leaving the atom ”charged” as a whole, causing it
to interact with charged particles and other charged atoms nearby. Neutrons are neither attracted
to or repelled by electrons, protons, or even other neutrons, and are consequently categorized as
having no charge at all.
The process of electrons arriving or leaving is exactly what happens when certain combinations
of materials are rubbed together: electrons from the atoms of one material are forced by the rubbing
to leave their respective atoms and transfer over to the atoms of the other material. In other words,
electrons comprise the ”fluid” hypothesized by Benjamin Franklin. The operational definition of a
coulomb as the unit of electrical charge (in terms of force generated between point charges) was
found to be equal to an excess or deficiency of about 6,250,000,000,000,000,000 electrons. Or, stated
in reverse terms, one electron has a charge of about 0.00000000000000000016 coulombs. Being that
one electron is the smallest known carrier of electric charge, this last figure of charge for the electron
is defined as the elementary charge.
The result of an imbalance of this ”fluid” (electrons) between objects is called static electricity.
It is called ”static” because the displaced electrons tend to remain stationary after being moved
from one material to another. In the case of wax and wool, it was determined through further
experimentation that electrons in the wool actually transferred to the atoms in the wax, which is
exactly opposite of Franklin’s conjecture! In honor of Franklin’s designation of the wax’s charge
being ”negative” and the wool’s charge being ”positive,” electrons are said to have a ”negative”
charging influence. Thus, an object whose atoms have received a surplus of electrons is said to be
negatively charged, while an object whose atoms are lacking electrons is said to be positively charged,
as confusing as these designations may seem. By the time the true nature of electric ”fluid” was
discovered, Franklin’s nomenclature of electric charge was too well established to be easily changed,
and so it remains to this day.
• REVIEW:
• All materials are made up of tiny ”building blocks” known as atoms.
• All atoms contain particles called electrons, protons, and neutrons.
• Electrons have a negative (-) electric charge.
• Protons have a positive (+) electric charge.
• Neutrons have no electric charge.
• Electrons can be dislodged from atoms much easier than protons or neutrons.
• The number of protons in an atom’s nucleus determines its identity as a unique element.
1.2. CONDUCTORS, INSULATORS, AND ELECTRON FLOW 7
1.2 Conductors, insulators, and electron flow
The electrons of different types of atoms have different degrees of freedom to move around. With
some types of materials, such as metals, the outermost electrons in the atoms are so loosely bound
that they chaotically move in the space between the atoms of that material by nothing more than
the influence of room-temperature heat energy. Because these virtually unbound electrons are free
to leave their respective atoms and float around in the space between adjacent atoms, they are often
called free electrons.
In other types of materials such as glass, the atoms’ electrons have very little freedom to move
around. While external forces such as physical rubbing can force some of these electrons to leave
their respective atoms and transfer to the atoms of another material, they do not move between
atoms within that material very easily.
This relative mobility of electrons within a material is known as electric conductivity. Conductivity is determined by the types of atoms in a material (the number of protons in each atom’s
nucleus, determining its chemical identity) and how the atoms are linked together with one another.
Materials with high electron mobility (many free electrons) are called conductors, while materials
with low electron mobility (few or no free electrons) are called insulators.
Here are a few common examples of conductors and insulators:
• Conductors:
• silver
• copper
• gold
• aluminum
• iron
• steel
• brass
• bronze
• mercury
• graphite
• dirty water
• concrete
• Insulators:
• glass
8 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
• rubber
• oil
• asphalt
• fiberglass
• porcelain
• ceramic
• quartz
• (dry) cotton
• (dry) paper
• (dry) wood
• plastic
• air
• diamond
• pure water
It must be understood that not all conductive materials have the same level of conductivity,
and not all insulators are equally resistant to electron motion. Electrical conductivity is analogous
to the transparency of certain materials to light: materials that easily ”conduct” light are called
”transparent,” while those that don’t are called ”opaque.” However, not all transparent materials
are equally conductive to light. Window glass is better than most plastics, and certainly better than
”clear” fiberglass. So it is with electrical conductors, some being better than others.
For instance, silver is the best conductor in the ”conductors” list, offering easier passage for
electrons than any other material cited. Dirty water and concrete are also listed as conductors, but
these materials are substantially less conductive than any metal.
Physical dimension also impacts conductivity. For instance, if we take two strips of the same
conductive material – one thin and the other thick – the thick strip will prove to be a better conductor
than the thin for the same length. If we take another pair of strips – this time both with the same
thickness but one shorter than the other – the shorter one will offer easier passage to electrons than
the long one. This is analogous to water flow in a pipe: a fat pipe offers easier passage than a skinny
pipe, and a short pipe is easier for water to move through than a long pipe, all other dimensions
being equal.
It should also be understood that some materials experience changes in their electrical properties
under different conditions. Glass, for instance, is a very good insulator at room temperature, but
becomes a conductor when heated to a very high temperature. Gases such as air, normally insulating
materials, also become conductive if heated to very high temperatures. Most metals become poorer
conductors when heated, and better conductors when cooled. Many conductive materials become
perfectly conductive (this is called superconductivity) at extremely low temperatures.
1.2. CONDUCTORS, INSULATORS, AND ELECTRON FLOW 9
While the normal motion of ”free” electrons in a conductor is random, with no particular direction or speed, electrons can be influenced to move in a coordinated fashion through a conductive
material. This uniform motion of electrons is what we call electricity, or electric current. To be
more precise, it could be called dynamic electricity in contrast to static electricity, which is an unmoving accumulation of electric charge. Just like water flowing through the emptiness of a pipe,
electrons are able to move within the empty space within and between the atoms of a conductor.
The conductor may appear to be solid to our eyes, but any material composed of atoms is mostly
empty space! The liquid-flow analogy is so fitting that the motion of electrons through a conductor
is often referred to as a ”flow.”
A noteworthy observation may be made here. As each electron moves uniformly through a
conductor, it pushes on the one ahead of it, such that all the electrons move together as a group.
The starting and stopping of electron flow through the length of a conductive path is virtually
instantaneous from one end of a conductor to the other, even though the motion of each electron
may be very slow. An approximate analogy is that of a tube filled end-to-end with marbles:
Tube
Marble Marble
The tube is full of marbles, just as a conductor is full of free electrons ready to be moved by an
outside influence. If a single marble is suddenly inserted into this full tube on the left-hand side,
another marble will immediately try to exit the tube on the right. Even though each marble only
traveled a short distance, the transfer of motion through the tube is virtually instantaneous from
the left end to the right end, no matter how long the tube is. With electricity, the overall effect
from one end of a conductor to the other happens at the speed of light: a swift 186,000 miles per
second!!! Each individual electron, though, travels through the conductor at a much slower pace.
If we want electrons to flow in a certain direction to a certain place, we must provide the proper
path for them to move, just as a plumber must install piping to get water to flow where he or she
wants it to flow. To facilitate this, wires are made of highly conductive metals such as copper or
aluminum in a wide variety of sizes.
Remember that electrons can flow only when they have the opportunity to move in the space
between the atoms of a material. This means that there can be electric current only where there
exists a continuous path of conductive material providing a conduit for electrons to travel through. In
the marble analogy, marbles can flow into the left-hand side of the tube (and, consequently, through
the tube) if and only if the tube is open on the right-hand side for marbles to flow out. If the tube
is blocked on the right-hand side, the marbles will just ”pile up” inside the tube, and marble ”flow”
will not occur. The same holds true for electric current: the continuous flow of electrons requires
there be an unbroken path to permit that flow. Let’s look at a diagram to illustrate how this works:
A thin, solid line (as shown above) is the conventional symbol for a continuous piece of wire.
Since the wire is made of a conductive material, such as copper, its constituent atoms have many
free electrons which can easily move through the wire. However, there will never be a continuous or
uniform flow of electrons within this wire unless they have a place to come from and a place to go.
Let’s add an hypothetical electron ”Source” and ”Destination:”
Electron Electron
Source Destination
10 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
Now, with the Electron Source pushing new electrons into the wire on the left-hand side, electron
flow through the wire can occur (as indicated by the arrows pointing from left to right). However,
the flow will be interrupted if the conductive path formed by the wire is broken:
Electron Electron
Source Destination
no flow! no flow!
(break)
Since air is an insulating material, and an air gap separates the two pieces of wire, the oncecontinuous path has now been broken, and electrons cannot flow from Source to Destination. This
is like cutting a water pipe in two and capping off the broken ends of the pipe: water can’t flow if
there’s no exit out of the pipe. In electrical terms, we had a condition of electrical continuity when
the wire was in one piece, and now that continuity is broken with the wire cut and separated.
If we were to take another piece of wire leading to the Destination and simply make physical
contact with the wire leading to the Source, we would once again have a continuous path for electrons
to flow. The two dots in the diagram indicate physical (metal-to-metal) contact between the wire
pieces:
Electron Electron
Source Destination
(break)
no flow!
Now, we have continuity from the Source, to the newly-made connection, down, to the right, and
up to the Destination. This is analogous to putting a ”tee” fitting in one of the capped-off pipes and
directing water through a new segment of pipe to its destination. Please take note that the broken
segment of wire on the right hand side has no electrons flowing through it, because it is no longer
part of a complete path from Source to Destination.
It is interesting to note that no ”wear” occurs within wires due to this electric current, unlike
water-carrying pipes which are eventually corroded and worn by prolonged flows. Electrons do
encounter some degree of friction as they move, however, and this friction can generate heat in a
conductor. This is a topic we’ll explore in much greater detail later.
• REVIEW:
• In conductive materials, the outer electrons in each atom can easily come or go, and are called
free electrons.
• In insulating materials, the outer electrons are not so free to move.
• All metals are electrically conductive.
• Dynamic electricity, or electric current, is the uniform motion of electrons through a conductor.
Static electricity is an unmoving, accumulated charge formed by either an excess or deficiency
of electrons in an object.
• For electrons to flow continuously (indefinitely) through a conductor, there must be a complete,
unbroken path for them to move both into and out of that conductor.
1.3. ELECTRIC CIRCUITS 11
1.3 Electric circuits
You might have been wondering how electrons can continuously flow in a uniform direction through
wires without the benefit of these hypothetical electron Sources and Destinations. In order for the
Source-and-Destination scheme to work, both would have to have an infinite capacity for electrons
in order to sustain a continuous flow! Using the marble-and-tube analogy, the marble source and
marble destination buckets would have to be infinitely large to contain enough marble capacity for
a ”flow” of marbles to be sustained.
The answer to this paradox is found in the concept of a circuit: a never-ending looped pathway
for electrons. If we take a wire, or many wires joined end-to-end, and loop it around so that it forms
a continuous pathway, we have the means to support a uniform flow of electrons without having to
resort to infinite Sources and Destinations:
electrons can flow
in a path without
beginning or end,
continuing forever!
A marble-and-
hula-hoop "circuit"
Each electron advancing clockwise in this circuit pushes on the one in front of it, which pushes
on the one in front of it, and so on, and so on, just like a hula-hoop filled with marbles. Now, we
have the capability of supporting a continuous flow of electrons indefinitely without the need for
infinite electron supplies and dumps. All we need to maintain this flow is a continuous means of
motivation for those electrons, which we’ll address in the next section of this chapter.
It must be realized that continuity is just as important in a circuit as it is in a straight piece
of wire. Just as in the example with the straight piece of wire between the electron Source and
Destination, any break in this circuit will prevent electrons from flowing through it:
12 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
no flow!
continuous
electron flow cannot
occur anywhere
in a "broken" circuit!
(break)
no flow!
no flow!
An important principle to realize here is that it doesn’t matter where the break occurs. Any
discontinuity in the circuit will prevent electron flow throughout the entire circuit. Unless there is
a continuous, unbroken loop of conductive material for electrons to flow through, a sustained flow
simply cannot be maintained.
no flow!
continuous
electron flow cannot
occur anywhere
in a "broken" circuit!
no flow!
(break)
no flow!
• REVIEW:
• A circuit is an unbroken loop of conductive material that allows electrons to flow through
continuously without beginning or end.
• If a circuit is ”broken,” that means it’s conductive elements no longer form a complete path,
and continuous electron flow cannot occur in it.
• The location of a break in a circuit is irrelevant to its inability to sustain continuous electron
flow. Any break, anywhere in a circuit prevents electron flow throughout the circuit.
1.4. VOLTAGE AND CURRENT 13
1.4 Voltage and current
As was previously mentioned, we need more than just a continuous path (circuit) before a continuous
flow of electrons will occur: we also need some means to push these electrons around the circuit.
Just like marbles in a tube or water in a pipe, it takes some kind of influencing force to initiate flow.
With electrons, this force is the same force at work in static electricity: the force produced by an
imbalance of electric charge.
If we take the examples of wax and wool which have been rubbed together, we find that the
surplus of electrons in the wax (negative charge) and the deficit of electrons in the wool (positive
charge) creates an imbalance of charge between them. This imbalance manifests itself as an attractive
force between the two objects:
---
-
-
- -
- -
-
-
--Wax
+ +
- -
-
--
-
-
-
--
-
-
-
-
---
-
attraction
+
+
++
+++
+
+
+
+
+
+
+
+
+
+
+
+++
+
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
Wool cloth
If a conductive wire is placed between the charged wax and wool, electrons will flow through it,
as some of the excess electrons in the wax rush through the wire to get back to the wool, filling the
deficiency of electrons there:
+
+
+
+
+
+
+
+
+++
+
+
+
+ +
+
+
+
+
+
+
+
+
+
-
- -
-
-
-
---
-
-
-
-
-
-
-
-
-
Wax
+ + +
-
electron flow
- - wire
Wool cloth
The imbalance of electrons between the atoms in the wax and the atoms in the wool creates a
force between the two materials. With no path for electrons to flow from the wax to the wool, all
this force can do is attract the two objects together. Now that a conductor bridges the insulating
gap, however, the force will provoke electrons to flow in a uniform direction through the wire, if
only momentarily, until the charge in that area neutralizes and the force between the wax and wool
diminishes.
The electric charge formed between these two materials by rubbing them together serves to store
a certain amount of energy. This energy is not unlike the energy stored in a high reservoir of water
that has been pumped from a lower-level pond:
14 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
Reservoir
Energy stored
Water flow
Pump
Pond
The influence of gravity on the water in the reservoir creates a force that attempts to move the
water down to the lower level again. If a suitable pipe is run from the reservoir back to the pond,
water will flow under the influence of gravity down from the reservoir, through the pipe:
Reservoir
Energy released
Pond
It takes energy to pump that water from the low-level pond to the high-level reservoir, and the
movement of water through the piping back down to its original level constitutes a releasing of
energy stored from previous pumping.
1.4. VOLTAGE AND CURRENT 15
If the water is pumped to an even higher level, it will take even more energy to do so, thus more
energy will be stored, and more energy released if the water is allowed to flow through a pipe back
down again:
Reservoir
Energy stored
Energy released
Pump
Pond
Reservoir
More energy stored
Pump
Pond
More energy released
Electrons are not much different. If we rub wax and wool together, we ”pump” electrons away
16 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
from their normal ”levels,” creating a condition where a force exists between the wax and wool, as
the electrons seek to re-establish their former positions (and balance within their respective atoms).
The force attracting electrons back to their original positions around the positive nuclei of their
atoms is analogous to the force gravity exerts on water in the reservoir, trying to draw it down to
its former level.
Just as the pumping of water to a higher level results in energy being stored, ”pumping” electrons
to create an electric charge imbalance results in a certain amount of energy being stored in that
imbalance. And, just as providing a way for water to flow back down from the heights of the reservoir
results in a release of that stored energy, providing a way for electrons to flow back to their original
”levels” results in a release of stored energy.
When the electrons are poised in that static condition (just like water sitting still, high in a
reservoir), the energy stored there is called potential energy, because it has the possibility (potential)
of release that has not been fully realized yet. When you scuff your rubber-soled shoes against a
fabric carpet on a dry day, you create an imbalance of electric charge between yourself and the
carpet. The action of scuffing your feet stores energy in the form of an imbalance of electrons forced
from their original locations. If this charge (static electricity) is stationary, and you won’t realize
that energy is being stored at all. However, once you place your hand against a metal doorknob
(with lots of electron mobility to neutralize your electric charge), that stored energy will be released
in the form of a sudden flow of electrons through your hand, and you will perceive it as an electric
shock!
This potential energy, stored in the form of an electric charge imbalance and capable of provoking
electrons to flow through a conductor, can be expressed as a term called voltage, which technically is
a measure of potential energy per unit charge of electrons, or something a physicist would call specific
potential energy. Defined in the context of static electricity, voltage is the measure of work required
to move a unit charge from one location to another, against the force which tries to keep electric
charges balanced. In the context of electrical power sources, voltage is the amount of potential
energy available (work to be done) per unit charge, to move electrons through a conductor.
Because voltage is an expression of potential energy, representing the possibility or potential for
energy release as the electrons move from one ”level” to another, it is always referenced between
two points. Consider the water reservoir analogy:
1.4. VOLTAGE AND CURRENT 17
Reservoir
Drop
Location #1
Drop
Location #2
Because of the difference in the height of the drop, there’s potential for much more energy to be
released from the reservoir through the piping to location 2 than to location 1. The principle can be
intuitively understood in dropping a rock: which results in a more violent impact, a rock dropped
from a height of one foot, or the same rock dropped from a height of one mile? Obviously, the drop
of greater height results in greater energy released (a more violent impact). We cannot assess the
amount of stored energy in a water reservoir simply by measuring the volume of water any more
than we can predict the severity of a falling rock’s impact simply from knowing the weight of the
rock: in both cases we must also consider how far these masses will drop from their initial height.
The amount of energy released by allowing a mass to drop is relative to the distance between its
starting and ending points. Likewise, the potential energy available for moving electrons from one
point to another is relative to those two points. Therefore, voltage is always expressed as a quantity
between two points. Interestingly enough, the analogy of a mass potentially ”dropping” from one
height to another is such an apt model that voltage between two points is sometimes called a voltage
drop.
Voltage can be generated by means other than rubbing certain types of materials against each
other. Chemical reactions, radiant energy, and the influence of magnetism on conductors are a few
ways in which voltage may be produced. Respective examples of these three sources of voltage
are batteries, solar cells, and generators (such as the ”alternator” unit under the hood of your
automobile). For now, we won’t go into detail as to how each of these voltage sources works – more
important is that we understand how voltage sources can be applied to create electron flow in a
circuit.
Let’s take the symbol for a chemical battery and build a circuit step by step:
18 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
1
Battery
+
2
Any source of voltage, including batteries, have two points for electrical contact. In this case,
we have point 1 and point 2 in the above diagram. The horizontal lines of varying length indicate
that this is a battery, and they further indicate the direction which this battery’s voltage will try
to push electrons through a circuit. The fact that the horizontal lines in the battery symbol appear
separated (and thus unable to serve as a path for electrons to move) is no cause for concern: in real
life, those horizontal lines represent metallic plates immersed in a liquid or semi-solid material that
not only conducts electrons, but also generates the voltage to push them along by interacting with
the plates.
Notice the little ”+” and ”-” signs to the immediate left of the battery symbol. The negative
(-) end of the battery is always the end with the shortest dash, and the positive (+) end of the
battery is always the end with the longest dash. Since we have decided to call electrons ”negatively”
charged (thanks, Ben!), the negative end of a battery is that end which tries to push electrons out
of it. Likewise, the positive end is that end which tries to attract electrons.
With the ”+” and ”-” ends of the battery not connected to anything, there will be voltage
between those two points, but there will be no flow of electrons through the battery, because there
is no continuous path for the electrons to move.
Water analogy
Reservoir
Electric Battery
No flow
1
Battery
+
2
No flow (once the
reservoir has been
completely filled)
Pump
Pond
The same principle holds true for the water reservoir and pump analogy: without a return pipe
1.4. VOLTAGE AND CURRENT 19
back to the pond, stored energy in the reservoir cannot be released in the form of water flow. Once
the reservoir is completely filled up, no flow can occur, no matter how much pressure the pump
may generate. There needs to be a complete path (circuit) for water to flow from the pond, to the
reservoir, and back to the pond in order for continuous flow to occur.
We can provide such a path for the battery by connecting a piece of wire from one end of the
battery to the other. Forming a circuit with a loop of wire, we will initiate a continuous flow of
electrons in a clockwise direction:
Electric Circuit
1
Battery
+
2
electron flow!
Water analogy
Reservoir
water flow!
water flow!
Pump
Pond
So long as the battery continues to produce voltage and the continuity of the electrical path
20 CHAPTER 1. BASIC CONCEPTS OF ELECTRICITY
isn’t broken, electrons will continue to flow in the circuit. Following the metaphor of water moving
through a pipe, this continuous, uniform flow of electrons through the circuit is called a current. So
long as the voltage source keeps ”pushing” in the same direction, the electron flow will continue to
move in the same direction in the circuit. This single-direction flow of electrons is called a Direct
Current, or DC. In the second volume of this book series, electric circuits are explored where the
direction of current switches back and forth: Alternating Current, or AC. But for now, we’ll just
concern ourselves with DC circuits.
Because electric current is composed of individual electrons flowing in unison through a conductor
by moving along and pushing on the electrons ahead, just like marbles through a tube or water
through a pipe, the amount of flow throughout a single circuit will be the same at any point. If we
were to monitor a cross-section of the wire in a single circuit, counting the electrons flowing by, we
would notice the exact same quantity per unit of time as in any other part of the circuit, regardless
of conductor length or conductor diameter.
If we break the circuit’s continuity at any point, the electric current will cease in the entire loop,
and the full voltage produced by the battery will be manifested across the break, between the wire
ends that used to be connected:
no flow!
1
Battery
-
(break)
voltage
drop
+
+
2
no flow!
Notice the ”+” and ”-” signs drawn at the ends of the break in the circuit, and how they
correspond to the ”+” and ”-” signs next to the battery’s terminals. These markers indicate the
direction that the voltage attempts to push electron flow, that potential direction commonly referred
to as polarity. Remember that voltage is always relative between two points. Because of this fact,
the polarity of a voltage drop is also relative between two points: whether a point in a circuit gets
labeled with a ”+” or a ”-” depends on the other point to which it is referenced. Take a look at the
following circuit, where each corner of the loop is marked with a number for reference:
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