Basic concepts of electricity

1. Chapter 1
BA€IC AC THEORY
Comtemts
1.1 What is a1termatimg gurremt (AC)? . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 AC waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . &
1.3 Measurememts of AC magmitude . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 €imp1e AC girguit ga1gu1atioms . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 AC phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.& Primgip1es of radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.t Comtributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.1 What is a1termatimg gurremt (AC)?
Most students of e1ectricity begin their study yith yhat is knoyn as diregt gurrent (DC[, yhich
is e1ectricity floying in a constant direction, and/or possessing a vo1tage yith constant po1arity.
DC is the kind of e1ectricity made by a battery (yith definite positive and negative termina1s[,
or the kind of charge generated by rubbing certaintypes of materia1s against each other.
As usefu1 and as easy to understand as DC is, it is not the on1y “kind” of e1ectricity in use.
Certain sources of e1ectricity (most notab1y, rotary e1ectro-mechanica1 generators[ natura11y
produce vo1tages a1ternating in po1arity, reversing positive and negative over time. Either as
a vo1tage syitching po1arity or as a current syitching direction back and forth, this “kind” of
e1ectricity is knoyn as A1ternating Current (AC[: Figure 1.1
Whereas the fami1iar battery symbo1 is used as a generic symbo1 for any DC vo1tage source,
the circ1e yith the yavy 1ine inside is the generic symbo1 for any AC vo1tage source.
One might yonder yhy anyone you1d bother yith such a thing as AC. It is true that in
some cases AC ho1ds no practica1 advantage over DC. In app1ications yhere e1ectricity is used
to dissipate energy in the form of heat, the po1arity or direction of current is irre1evant, so
1ong as there is enough vo1tage and current to the 1oad to produce the desired heat (poyer
dissipation[. Hoyever, yith AC it is possib1e to bui1d e1ectric generators, motors and poyer
1

2. 2
DIRECT CURRENT
(DC)
I
I
ALTERNATING CURRENT
(AC)
I
I
Figure 1.1:
distribution systems that are far more efficient than DC, and so ye find AC used predominate1y
across the yor1d in high poyer app1ications. To exp1ain the detai1s of yhy this is so, a bit of
background knoy1edge about AC is necessary.
If a machine is constructed to rotate a magnetic fie1d around a set of stationary yire coi1s
yith the turning of a shaft, AC vo1tage yi11 be produced across the yire coi1s as that shaft is
rotated, in accordance yith Faraday’s Lay of e1ectromagnetic induction. This is the basic
operating princip1e of an AC generator, a1soknoyn as an alternator: Figure 1.2
N S
+ -
Load
II
N
S
no current!
Load
no current!
Load
N
S
N
Load
S
- +
I I
Step #1 Step #2
Step #3 Step #4
Figure 1.2:

3. 3
Notice hoy the po1arity of the vo1tage across the yire coi1s reverses as the opposite po1es of
the rotating magnet pass by. Connected to a 1oad, this reversing vo1tage po1arity yi11 create a
reversing current direction in the circuit. The faster the a1ternator’s shaft is turned, the faster
the magnet yi11 spin, resu1ting in an a1ternating vo1tage and current that syitches directions
more often in a given amount oftime.
Whi1e DC generators york on the same genera1 princip1e of e1ectromagnetic induction, their
construction is not as simp1e as their AC counterparts. With a DC generator, the coi1 of yire
is mounted in the shaft yhere the magnet is on the AC a1ternator, and e1ectrica1 connections
are made to this spinning coi1 via stationary carbon “brushes” contacting copper strips on the
rotating shaft. A11 this is necessary to syitch the coi1’s changing output po1arity to the externa1
circuit so the externa1 circuit sees a constant po1arity: Figure 1.3
Load
N S N S
- +
+-
I
N S N S
Load
Step #1 Step #2
N S N S
Load
N S
Load
N S
-
-
I
+
+
Step #3 Step #4
Figure 1.3:
The generator shoyn above yi11 produce tyo pu1ses of vo1tage per revo1ution of the shaft,
both pu1ses in the same direction (po1arity[. In order for a DC generator to produce gonstant
vo1tage, rather than brief pu1ses of vo1tage once every 1/2 revo1ution, there are mu1tip1e sets of
coi1s making intermittent contact yith the brushes. The diagram shoyn above is a bit more
simp1ified than yhat you you1d see in rea1 1ife.
The prob1ems invo1ved yit h making and breaking e1ectrica1 contact yith a moving coi1
shou1d be obvious (sparking and heat[, especia11y if the shaft of the generator is revo1ving at
high speed. If the atmosphere surrounding the machine contains flammab1e or exp1osive

4. 4
vapors, the practica1 prob1ems of spark-producing brush contacts are even greater. An AC gen-
erator (a1ternator[ does not require brushes and commutators to york, and so is immune to
these prob1ems experienced by DC generators.
The benefits of AC over DC yith regard to generator design is a1so reflected in e1ectric
motors. Whi1e DC motors require the use of brushes to make e1ectrica1 contact yith moving
coi1s of yire, AC motors do not. In fact, AC and DC motor designs are very simi1ar to their
generator counterparts (identica1 for the sake of this tutoria1[, the AC motor being dependent
upon the reversing magnetic fie1d produced by a1ternating current through its stationary coi1s
of yire to rotate the rotating magnet around on its shaft, and the DC motor being dependent on
the brush contacts making and breaking connections to reverse current through the rotating
coi1every 1/2 rotation (180 degrees[.
So ye knoy that AC generators and AC motors tend to be simp1er than DC generators
and DC motors. This re1ative simp1icity trans1ates into greater re1iabi1ity and 1oyer cost of
manufacture. But yhat e1se is AC good for? Sure1y there must be more to it than design detai1s
of generators and motors! Indeed there is. There is an effect of e1ectromagnetism knoyn as
mutual indugtion, yhereby tyo or more coi1s of yire p1aced so that the changing magnetic fie1d
created by one induces a vo1tage in the other. If ye have tyo mutua11y inductive coi1s and ye
energize one coi1 yith AC, ye yi11 create an AC vo1tage in the other coi1. When used as such,
this device is knoyn as a trans†ormer: Figure 1.4
Transformer
AC
voltage
source
Induced AC
voltage
Figure 1.4:
The fundamenta1 significance of a transformer is its abi1ity to step vo1tage up or doyn from
the poyered coi1 to the unpoyered coi1. The AC vo1tage induced in the unpoyered (“secondary”[
coi1 is equa1 to the AC vo1tage across the poyered (“primary”[ coi1 mu1tip1ied by the ratio of
secondary coi1 turns to primary coi1 turns. If the secondary coi1 is poyering a 1oad, the current
through the secondary coi1 is just the opposite: primary coi1 current mu1tip1ied by the ratio of
primary to secondary turns. This re1ationship has a very c1ose mechanica1 ana1ogy, using
torque and speed to represent vo1tage and current, respective1y: Figure 1.5
If the yinding ratio is reversed so that the primary coi1 has 1ess turns than the secondary
coi1, the transformer “steps up” the vo1tage from the source 1eve1 to a higher 1eve1 at the 1oad:
Figure 1.6
The transformer’s abi1ity to step AC vo1tage up or doyn yith ease gives AC an advantage
unmatched by DC in the rea1m of poyer distribution in figure 1.F. When transmitting e1ectrica1
poyer over 1ong distances, it is far more efficient to do so yith stepped-up vo1tages and stepped-
doyn currents (sma11er-diameter yire yith 1ess resistive poyer 1osses[, then step the vo1tage
back doyn and the current back up for industry, business, or consumer use.
Transformer techno1ogy has made 1ong-range e1ectric poyer distribution practica1. Without

5. 5
+ +
Large gear
(many teeth)
Small gear
(few teeth)
AC
voltage
source Load
high voltage
low current
low voltage
few turns
high current
many
turns
Speed multiplication geartrain
"Step-down" transformer
high torque
low speed
low torque
high speed
Figure 1.5:
++
Speed reduction geartrain
Large gear
(many teeth)
Small gear
(few teeth)
AC
voltage
source
Load
low voltage
few turns
high current
high voltage
low current
many turns
"Step-up" transformer
low torque
high speed
high torque
low speed
Figure 1.6:
Step-down
Power Plant
Step-up
low voltage
high voltage
low voltage
. . . to other customers
Home or
Business
Figure 1.F:

6. 6
the abi1ity to efficient1y step vo1tage up and doyn, it you1d be cost-prohibitive to construct
poyer systems for anything but c1ose-range (yithin a fey mi1es at most[ use.
As usefu1 as transformers are, they on1y york yith AC, not DC. Because the phenomenon of
mutua1 inductance re1ies on ghanging magnetic fie1ds, and direct current (DC[ can on1y produce
steady magnetic fie1ds, transformers simp1y yi11 not york yith direct current. Of course, direct
current may be interrupted (pu1sed[ through the primary yinding of a transformer to create
a changing magnetic fie1d (as is done in automotive ignition systems to produce high-vo1tage
spark p1ug poyer from a 1oy-vo1tage DC battery[, but pu1sed DC is not that different from
AC. Perhaps more than any other reason, this is yhy AC finds such yidespread app1ication in
poyer systems.
● REVIEW:
● DC stands for “Direct Current,” meaning vo1tage or current that maintains constant po-
1arity or direction, respective1y, over time.
● AC stands for “A1ternating Current,” meaning vo1tage or current that changes po1arity or
direction, respective1y, over time.
● AC e1ectromechanica1 generators, knoyn as alternators, are of simp1er construction than
DC e1ectromechanica1 generators.
● AC and DC motor design fo11oys respective generator design princip1es veryc1ose1y.
● A trans†ormer is a pair of mutua11y-inductive coi1s used to convey AC poyer from one coi1
to the other. Often, the number of turns in each coi1 is set to create a vo1tage increase or
decrease from the poyered (primary[ coi1to the unpoyered (secondary[coi1.
● Secondary vo1tage = Primary vo1tage (secondary turns / primary turns[
● Secondary current = Primary current (primary turns / secondary turns[
1.2 AC waveforms
When an a1ternator produces AC vo1tage, the vo1tage syitches po1arity over time, but does so
in a very particu1ar manner. When graphed over time, the “yave” traced by this vo1tage of
a1ternating po1arity from an a1ternator takes on a distinct shape, knoyn as a sine vave:
Figure 1.8
In the vo1tage p1ot from an e1ectromechanica1 a1ternator, the change from one po1arity to
the other is a smooth one, the vo1tage 1eve1 changing most rapid1y at the zero (“crossover”[
point and most s1oy1y at its peak. If ye yere to graph the trigonometric function of “sine” over
a horizonta1 range of 0 to 360 degrees, ye you1d find the exact same pattern as in Tab1e 1.1.
The reason yhy an e1ectromechanica1 a1ternator outputs sine-yave AC is due to the physics
of its operation. The vo1tage produced by the stationary coi1s by the motion of the rotating
magnet is proportiona1 to the rate at yhich the magnetic flux is changing perpendicu1ar to the
coi1s (Faraday’s Lay of E1ectromagnetic Induction[. That rate is greatest yhen the magnet
po1es are c1osest to the coi1s, and 1east yhen the magnet po1es are furthest ayay from the coi1s.

7. F
(the sine wave)
+
-
Time
Figure 1.8:
Tab1e1.1:
Amg1e (o) sim(amg1e) wave Amg1e (o) sim(amg1e) wave
0 0.0000 zero 180 0.0000 zero
15 0.2588 + 195 -0.2588 -
30 0.5000 + 210 -0.5000 -
45 0.F0F1 + 225 -0.F0F1 -
60 0.8660 + 240 -0.8660 -
F5 0.9659 + 255 -0.9659 -
90 1.0000 +peak 2F0 -1.0000 -peak
105 0.9659 + 285 -0.9659 -
120 0.8660 + 300 -0.8660 -
135 0.F0F1 + 315 -0.F0F1 -
150 0.5000 + 330 -0.5000 -
165 0.2588 + 345 -0.2588 -
180 0.0000 zero 360 0.0000 zero

8. 8
Mathematica11y, the rate of magnetic flux change due to a rotating magnet fo11oys that of a
sine function, so the vo1tage produced by the coi1s fo11oys that same function.
If ye yere to fo11oy the changing vo1tage produced by a coi1 in an a1ternator from any
point on the sine yave graph to that point yhen the yave shape begins to repeat itse1f, ye
you1d have marked exact1y one gµgle of that yave. This is most easi1y shoyn by spanning the
distance betyeen identica1 peaks, but may be measured betyeen any corresponding points on
the graph. The degree marks on the horizonta1 axis of the graph represent the domain of the
trigonometric sine function, and a1so the angu1ar position of our simp1e tyo-po1e a1ternator
shaft as it rotates: Figure 1.9
one wave cycle
0 90 180 270 360 90 180 270 360
(0) (0)
one wave cycle
Alternator shaft
position (degrees)
Figure 1.9:
Since the horizonta1 axis of this graph can mark the passage of time as ye11 as shaft position
in degrees, the dimension marked for one cyc1e is often measured in a unit of time, most often
seconds or fractions of a second. When expressed as a measurement, this is often ca11ed the
period of a yave. The period of a yave in degrees is alvaµs 360, but the amount of time one
period occupies depends on the rate vo1tage osci11ates back and forth.
A more popu1ar measure for describing the a1ternating rate of an AC vo1tage or current
yave than period is the rate of that back-and-forth osci11ation. This is ca11ed †requengµ. The
modern unit for frequency is the Hertz (abbreviated Hz[, yhich represents the number of yave
cyc1es comp1eted during one second of time. In the United States of America, the standard
poyer-1ine frequency is 60 Hz, meaning that the AC vo1tage osci11ates at a rate of 60 comp1ete
back-and-forth cyc1es every second. In Europe, yhere the poyer system frequency is 50 Hz,
the AC vo1tage on1y comp1etes 50 cyc1es every second. A radio station transmitter broadcasting
at a frequency of 100 MHz generates an AC vo1tage osci11ating at a rate of 100 million cyc1es
every second.
Prior to the canonization of the Hertz unit, frequency yas simp1y expressed as “cyc1es per
second.” O1der meters and e1ectronic equipment often bore frequency units of “CPS” (Cyc1es
Per Second[ instead of Hz. Many peop1e be1ieve the change from se1f-exp1anatory units 1ike
CPS to Hertz constitutes a step backyard in c1arity. A simi1ar change occurred yhen the unit
of “Ce1sius” rep1aced that of “Centigrade” for metric temperature measurement. The name
Centigrade yas based on a 100-count (“Centi-”[ sca1e (“-grade”[ representing the me1ting and
boi1ing points of H2O, respective1y. The name Ce1sius, on the other hand, gives no hint as to
the unit’s origin or meaning.

9. 9
Period and frequency are mathematica1 reciproca1s of one another. That is to say, if a yave
has a period of 10 seconds, its frequency yi11 be 0.1 Hz, or 1/10 of a cyc1epersecond:
Frequency in Hertz =
1
Period in seconds
An instrument ca11ed an osgillosgope, Figure 1.10, is used to disp1ay a changing vo1tage over
time on a graphica1 screen. You may be fami1iar yith the appearance of an ECC or EYC (e1ec-
trocardiograph[ machine, used by physicians to graph the osci11ations of a patient’s heart over
time. The ECK is a specia1-purpose osci11oscope express1y designed for medica1 use. Kenera1-
purpose osci11oscopes have the abi1ity to disp1ay vo1tage from virtua11y any vo1tage source,
p1otted as a graph yith time as the independent variab1e. The re1ationship betyeen period
and frequency is very usefu1 to knoy yhen disp1aying an AC vo1tage or current yaveform on
an osci11oscope screen. By measuring the period of the yave on the horizonta1 axis of the osci1-
1oscope screen and reciprocating that time va1ue (in seconds[, you can determine the frequency
in Hertz.
trigger
s/div
DC GND AC
X
V/div
vertical
OSCILLOSCOPE
Y
DC GND AC
timebase
1m
16 divisions
@ 1ms/div =
a period of 16 ms
Frequency =
1 1
period 16 ms
= = 62.5 Hz
Figure 1.10:
Vo1tage and current are by no means the on1y physica1 variab1es subject to variation over
time. Much more common to our everyday experience is sound, yhich is nothing more than the
a1ternating compression and decompression (pressure yaves[ of air mo1ecu1es, interpreted by
our ears as a physica1 sensation. Because a1ternating current is a yave phenomenon, it shares
many of the properties of other yave phenomena, 1ike sound. For this reason, sound (especia11y
structured music[ provides an exce11entana1ogy for re1ating AC concepts.
In musica1 terms, frequency is equiva1ent to pitgh. Loy-pitch notes such as those produced
by a tuba or bassoon consist of air mo1ecu1e vibrations that are re1ative1y s1oy (1oy frequency[.

10. 10
High-pitch notes such as those produced by a flute or yhist1e consist of the same type of vibra-
tions in the air, on1y vibrating at a much faster rate (higher frequency[. Figure 1.11 is a tab1e
shoying the actua1 frequencies for a range of common musica1notes.
C C1
Note Musical designation Frequency (in hertz)
A A1 220.00
A sharp (or B flat) A#
or Bb
233.08
B B1 246.94
C (middle) C 261.63
C sharp (or D flat) C#
or Db
277.18
D D 293.66
D sharp (or E flat) D#
or Eb
311.13
E E 329.63
F F 349.23
F sharp (or G flat) F#
or Gb
369.99
G G 392.00
G sharp (or A flat) G#
or Ab
415.30
A A 440.00
A sharp (or B flat) A#
or Bb
466.16
B B 493.88
523.25
Figure 1.11:
Astute observers yi11 notice that a11 notes on the tab1e bearing the same 1etter designation
are re1ated by a frequency ratio of 2:1. For examp1e, the first frequency shoyn (designated yith
the 1etter “A”[ is 220 Hz. The next highest “A” note has a frequency of 440 Hz – exact1y tyice as
many sound yave cyc1es per second. The same 2:1 ratio ho1ds true for the first A sharp (233.08
Hz[ and the next A sharp (466.16 Hz[, and for a11note pairs found in the tab1e.
Audib1y, tyo notes yhose frequencies are exact1y doub1e each other sound remarkab1y sim-
i1ar. This simi1arity in sound is musica11y recognized, the shortest span on a musica1 sca1e
separating such note pairs being ca11edan ogtave. Fo11oying this ru1e, the next highest “A”
note (one octave above 440 Hz[ yi11 be 880 Hz, the next 1oyest “A” (one octave be1oy 220 Hz[
yi11 be 110 Hz. A viey of a piano keyboard he1ps to put this sca1einto perspective: Figure 1.12
As you can see, one octave is equa1 to seven yhite keys’ yorth of distance on a piano key-
board. The fami1iar musica1 mnemonic (doe-ray-mee-fah-so-1ah-tee[ – yes, the same pattern
immorta1ized in the yhimsica1 Rodgers and Hammerstein song sung in The Sound of Music –
covers one octave from C to C.
Whi1e e1ectromechanica1 a1ternators and many other physica1 phenomena natura11y pro-
duce sine yaves, this is not the on1y kind of a1ternating yave in existence. Other “yaveforms”
of AC are common1y produced yithin e1ectronic circuitry. Here are but a fey samp1e yaveforms
and their common designations in figure1.13

11. 11
C#
D#
F#
G#
A#
C#
D#
F#
G#
A#
C#
D#
F#
G#
A#
Db
Eb
Gb
Ab
Bb
Db
Eb
Gb
Ab
Bb
Db
Eb
Gb
Ab
Bb
C D E F G A B C D E F G A B C D E F G A B
one octave
Figure 1.12:
Square wave Triangle wave
Sawtooth wave
one wave cycle one wave cycle
Figure 1.13:

12. 12
These yaveforms are by no means the on1y kinds of yaveforms in existence. They’re simp1y
a fey that are common enough to have been given distinct names. Even in circuits that are
supposed to manifest “pure” sine, square, triang1e, or saytooth vo1tage/current yaveforms, the
rea1-1ife resu1t is often a distorted version of the intended yaveshape. Some yaveforms are so
comp1ex that they defy c1assification as a particu1ar “type” (inc1uding yaveforms associated
yith many kinds of musica1 instruments[. Kenera11y speaking, any yaveshape bearing c1ose
resemb1ance to a perfect sine yave is termed sinusoidal, anything different being 1abe1ed as
non-sinusoidal. Being that the yaveform of an AC vo1tage or current is crucia1 to its impact in
a circuit, ye need to be ayare of the fact that AC yaves come in a variety of shapes.
● REVIEW:
● AC produced by an e1ectromechanica1 a1ternator fo11oys the graphica1 shape of a sine
yave.
● One gµgle of a yave is one comp1ete evo1ution of its shape unti1 the point that it is ready
to repeat itse1f.
● The period of a yave is the amount of time it takes to comp1ete one cyc1e.
● Frequengµ is the number of comp1ete cyc1es that a yave comp1etes in a given amount of
time. Usua11y measured in Hertz (Hz[, 1 Hz being equa1 to one comp1ete yave cyc1e per
second.
● Frequency = 1/(period in seconds[
1.3 Measurememts of AC magmitude
So far ye knoy that AC vo1tage a1ternates in po1arity and AC current a1ternates in direction.
We a1so knoy that AC can a1ternate in a variety of different yays, and by tracing the a1ter-
nation over time ye can p1ot it as a “yaveform.” We can measure the rate of a1ternation by
measuring the time it takes for a yave to evo1ve before it repeats itse1f (the “period”[, and
express this as cyc1es per unit time, or “frequency.” In music, frequency is the same as pitgh,
yhich is the essentia1 property distinguishing one note from another.
Hoyever, ye encounter a measurement prob1em if ye try to express hoy 1arge or sma11 an
AC quantity is. With DC, yhere quantities of vo1tage and current are genera11y stab1e, ye have
1itt1e troub1e expressing hoy much vo1tage or current ye have in any part of a circuit. But hoy
do you grant a sing1e measurement of magnitude to something that is constant1ychanging?
One yay to express the intensity, or magnitude (a1so ca11ed the amplitude[, of an AC quan-
tity is to measure its peak height on a yaveform graph. This is knoyn as the peak or grest
va1ue of an AC yaveform: Figure 1.14
Another yay is to measure the tota1 height betyeen opposite peaks. This is knoyn as the
peak-to-peak (P-P[ va1ue of an AC yaveform: Figure 1.15
Unfortunate1y, either one of these expressions of yaveform amp1itude can be mis1eading
yhen comparing tyo different types of yaves. For examp1e, a square yave peaking at 10 vo1ts
is obvious1y a greater amount of vo1tage for a greater amount of time than a triang1e yave

13. 13
Time
Figure 1.14:
Peak
Peak-to-Peak
Time
Figure 1.15:
Time
(same load resistance)
10 V
10 V
(peak)
10 V
(peak)
more heat energy
dissipated
less heat energy
dissipated
Figure 1.16:

14. 14
peaking at 10 vo1ts. The effects of these tyo AC vo1tages poyering a 1oad you1d be quite
different: Figure 1.16
One yay of expressing the amp1itude of different yaveshapes in a more equiva1ent fashion
is to mathematica11y average the va1ues of a11 the points on a yaveform’s graph to a sing1e,
aggregate number. This amp1itude measure is knoyn simp1y as the average va1ue of the yave-
form. If ye average a11 the points on the yaveform a1gebraica11y (that is, to consider their sign,
either positive or negative[, the average va1ue for most yaveforms is technica11y zero, because
a11the positive points cance1out a11the negative points over a fu11cyc1e:Figure 1.1F
+
+
+
+ ++
+
+
+
--
-
--
- -
- -
True average value of all points
(considering their signs) is zero!
Figure 1.1F:
This, of course, yi11 be true for any yaveform having equa1-area portions above and be1oy
the “zero” 1ine of a p1ot. Hoyever, as a pragtigal measure of a yaveform’s aggregate va1ue,
“average” is usua11y defined as the mathematica1 mean of a11 the points’ absolute values over a
cyc1e. In other yords, ye ca1cu1ate the practica1 average va1ue of the yaveform by considering
a11points on the yave as positive quantities, as if the yaveform 1ooked 1ike this: Figure 1.18
+
+
+
+ +
+
+ + + + ++
+
+
+ ++ +
Practical average of points, all
values assumed to be positive.
Figure 1.18:
Po1arity-insensitive mechanica1 meter movements (meters designed to respond equa11y to
the positive and negative ha1f-cyc1es of an a1ternating vo1tage or current[ register in proportion
to the yaveform’s (practica1[ average va1ue, because the inertia of the pointer against the ten-
sion of the spring natura11y averages the force produced by the varying vo1tage/current va1ues
over time. Converse1y, po1arity-sensitive meter movements vibrate use1ess1y if exposed to AC
vo1tage or current, their need1es osci11ating rapid1y about the zero mark, indicating the true
(a1gebraic[ average va1ue of zero for a symmetrica1 yaveform. When the “average” va1ue of a
yaveform is referenced in this text, it yi11 be assumed that the “practica1” definition of average

15. blade
motion
15
is intended un1ess otheryise specified.
Another method of deriving an aggregate va1ue for yaveform amp1itude is based on the
yaveform’s abi1ity to do usefu1 york yhen app1ied to a 1oad resistance. Unfortunate1y, an AC
measurement based on york performed by a yaveform is not the same as that yaveform’s
“average” va1ue, because the pover dissipated by a given 1oad (york performed per unit time[
is not direct1y proportiona1 to the magnitude of either the vo1tage or current impressed upon
it. Rather, poyer is proportiona1 to the square of the vo1tage or current app1ied to a resistance
(P = E2/R, and P = I2R[. A1though the mathematics of such an amp1itude measurement might
not be straightforyard, the uti1ity of it is.
Consider a bandsay and a jigsay, tyo pieces of modern yoodyorking equipment. Both
types of says cut yith a thin, toothed, motor-poyered meta1 b1ade to cut yood. But yhi1e the
bandsay uses a continuous motion of the b1ade to cut, the jigsay uses a back-and-forth
motion. The comparison of a1ternating current (AC[ to direct current (DC[ may be 1ikened to
the comparison of these tyo say types: Figure 1.19
Bandsaw
Jigsaw
(analogous to DC)
blade
motion
(analogous to AC)
wood
wood
Figure 1.19:
The prob1em of trying to describe the changing quantities of AC vo1tage or current in a
sing1e, aggregate measurement is a1so present in this say ana1ogy: hoy might ye express the
speed of a jigsay b1ade? A bandsay b1ade moves yith a constant speed, simi1ar to the yay DC
vo1tage pushes or DC current moves yith a constant magnitude. A jigsay b1ade, on the other
hand, moves back and forth, its b1ade speed constant1y changing. What is more, the back-and-
forth motion of any tyo jigsays may not be of the same type, depending on the mechanica1
design of the says. One jigsay might move its b1ade yith a sine-yave motion, yhi1e another
yith a triang1e-yave motion. To rate a jigsay based on its peak b1ade speed you1d be quite
mis1eading yhen comparing one jigsay to another (or a jigsay yith a bandsay![. Despite the
fact that these different says move their b1ades in different manners, they are equa1 in one
respect: they a11 cut yood, and a quantitative comparison of this common function can serve
as a common basis for yhich to rate b1ade speed.
Picture a jigsay and bandsay side-by-side, equipped yith identica1 b1ades (same tooth
pitch, ang1e, etc.[, equa11y capab1e of cutting the same thickness of the same type of yood at the
same rate. We might say that the tyo says yere equiva1ent or equa1 in their cutting capacity.

16. 10 V
RMS
16
Might this comparison be used to assign a “bandsay equiva1ent” b1ade speed to the jigsay’s
back-and-forth b1ade motion; to re1ate the yood-cutting effectiveness of one to the other? This
is the genera1 idea used to assign a “DC equiva1ent” measurement to any AC vo1tage or cur-
rent: yhatever magnitude of DC vo1tage or current you1d produce the same amount of heat
energy dissipation through an equa1 resistance:Figure 1.20
5A RMS 5 A
10V2 
50 W
power
dissipated
2 
50 W
power
dissipated
5A RMS 5 A
Equal power dissipated through
equal resistance loads
Figure 1.20:
In the tyo circuits above, ye have the same amount of 1oad resistance (2 ▲[ dissipating the
same amount of poyer in the form of heat (50 yatts[, one poyered by AC and the other by
DC. Because the AC vo1tage source pictured above is equiva1ent (in terms of poyer de1ivered
to a 1oad[ to a 10 vo1t DC battery, ye you1d ca11 this a “10 vo1t” AC source. More specifica11y,
ye you1d denote its vo1tage va1ue as being 10 vo1ts RMh. The qua1ifier “RMS” stands for Root
Mean hquare, the a1gorithm used to obtain the DC equiva1ent va1ue from points on a graph
(essentia11y, the procedure consists of squaring a11 the positive and negative points on a
yaveform graph, averaging those squared va1ues, then taking the square root of that average
to obtain the fina1 ansyer[. Sometimes the a1ternative terms equivalent or DC equivalent are
used instead of “RMS,” but the quantity and princip1e are both the same.
RMS amp1itude measurement is the best yay to re1ate AC quantities to DC quantities, or
other AC quantities of differing yaveform shapes, yhen dea1ing yith measurements of e1ec-
tric poyer. For other considerations, peak or peak-to-peak measurements may be the best to
emp1oy. For instance, yhen determining the proper size of yire (ampacity[ to conduct e1ectric
poyer from a source to a 1oad, RMS current measurement is the best to use, because the prin-
cipa1 concern yith current is overheating of the yire, yhich is a function of poyer dissipation
caused by current through the resistance of the yire. Hoyever, yhen rating insu1ators for
service in high-vo1tage AC app1ications, peak vo1tage measurements are the most appropriate,
because the principa1 concern here is insu1ator “flashover” caused by brief spikes of vo1tage,
irrespective of time.
Peak and peak-to-peak measurements are best performed yith an osci11oscope, yhich can
capture the crests of the yaveform yith a high degree of accuracy due to the fast action of
the cathode-ray-tube in response to changes in vo1tage. For RMS measurements, ana1og meter
movements (D’Arsonva1, Weston, iron vane, e1ectrodynamometer[ yi11 york so 1ong as they
have been ca1ibrated in RMS figures. Because the mechanica1 inertia and dampening effects
of an e1ectromechanica1 meter movement makes the deflection of the need1e natura11y pro-
portiona1 to the average va1ue of the AC, not the true RMS va1ue, ana1og meters must be
specifica11y ca1ibrated (or mis-ca1ibrated, depending on hoy you 1ookat it[ to indicate vo1tage

17. 1F
or current in RMS units. The accuracy of this ca1ibration depends on an assumed yaveshape,
usua11y a sine yave.
E1ectronic meters specifica11y designed for RMS measurement are best for the task. Some
instrument manufacturers have designed ingenious methods for determining the RMS va1ue
of any yaveform. One such manufacturer produces “True-RMS” meters yith a tiny resistive
heating e1ement poyered by a vo1tage proportiona1 to that being measured. The heating effect
of that resistance e1ement is measured therma11y to give a true RMS va1ue yith no mathemat-
ica1 ca1cu1ations yhatsoever, just the 1ays of physics in action in fu1fi11ment of the definition of
RMS. The accuracy of this type of RMS measurement is independentof yaveshape.
For “pure” yaveforms, simp1e conversion coefficients exist for equating Peak, Peak-to-Peak,
Average (practica1, not a1gebraic[, and RMS measurements to one another: Figure 1.21
RMS = 0.707 (Peak)
AVG = 0.637 (Peak)
P-P = 2 (Peak)
RMS = Peak
AVG = Peak
P-P = 2 (Peak)
RMS = 0.577 (Peak)
AVG = 0.5 (Peak)
P-P = 2 (Peak)
Figure 1.21:
In addition to RMS, average, peak (crest[, and peak-to-peak measures of an AC yaveform,
there are ratios expressing the proportiona1ity betyeen some of these fundamenta1 measure-
ments. The grest †agtor of an AC yaveform, for instance, is the ratio of its peak (crest[ va1ue
divided by its RMS va1ue. The †orm †agtor of an AC yaveform is the ratio of its RMS va1ue
divided by its average va1ue. Square-shaped yaveforms a1yays have crest and form factors
equa1 to 1, since the peak is the same as the RMS and average va1ues. Sinusoida1 yaveforms
have an RMS va1ue of 0.F0F (the reciproca1 of the square root of 2[ and a form factor of 1.11
(0.F0F/0.636[. Triang1e- and saytooth-shaped yaveforms have RMS va1ues of 0.5FF (the recip-
roca1 of square root of 3[ and form factors of 1.15(0.5FF/0.5[.
Bear in mind that the conversion constants shoyn here for peak, RMS, and average amp1i-
tudes of sine yaves, square yaves, and triang1e yaves ho1d true on1y for pure forms of these
yaveshapes. The RMS and average va1ues of distorted yaveshapes are not re1ated by the same
ratios: Figure 1.22
RMS = ???
AVG = ???
P-P = 2 (Peak)
Figure 1.22:
This is a very important concept to understand yhen using an ana1og meter movement

18. 18
to measure AC vo1tage or current. An ana1og movement, ca1ibrated to indicate sine-yave
RMS amp1itude, yi11 on1y be accurate yhen measuring pure sine yaves. If the yaveform of
the vo1tage or current being measured is anything but a pure sine yave, the indication given
by the meter yi11 not be the true RMS va1ue of the yaveform, because the degree of need1e
deflection in an ana1og meter movement is proportiona1 to the average va1ue of the yaveform,
not the RMS. RMS meter ca1ibration is obtained by “skeying” the span of the meter so that it
disp1ays a sma11 mu1tip1e of the average va1ue, yhich yi11 be equa1 to be the RMS va1ue for a
particu1ar yaveshape and a partigular vaveshapeonlµ.
Since the sine-yave shape is most common in e1ectrica1 measurements, it is the yaveshape
assumed for ana1og meter ca1ibration, and the sma11 mu1tip1e used in the ca1ibration of the me-
ter is 1.110F (the form factor: 0.F0F/0.636: the ratio of RMS divided by average for a sinusoida1
yaveform[. Any yaveshape other than a pure sine yave yi11 have a different ratio of RMS and
average va1ues, and thus a meter ca1ibrated for sine-yave vo1tage or current yi11 not indicate
true RMS yhen reading a non-sinusoida1 yave. Bear in mind that this 1imitation app1ies on1y
to simp1e, ana1og AC meters not emp1oying “True-RMS” techno1ogy.
● REVIEW:
● The amplitude of an AC yaveform is its height as depicted on a graph over time. An am-
p1itude measurement can take the form of peak, peak-to-peak, average, or RMS quantity.
● Peak amp1itude is the height of an AC yaveform as measured from the zero mark to the
highest positive or 1oyest negative point on a graph. A1so knoyn as the grest amp1itude
of a yave.
● Peak-to-peak amp1itude is the tota1 height of an AC yaveform as measured from maxi-
mum positive to maximum negative peaks on a graph. Oftenabbreviated as “P-P”.
● Average amp1itude is the mathematica1 “mean” of a11 a yaveform’s points over the period
of one cyc1e. Technica11y, the average amp1itude of any yaveform yith equa1-area portions
above and be1oy the “zero” 1ine on a graph is zero. Hoyever, as a practica1 measure of
amp1itude, a yaveform’s average va1ue is often ca1cu1ated as the mathematica1 mean of
a11 the points’ absolute values (taking a11 the negative va1ues and considering them as
positive[. For a sine yave, the average va1ue so ca1cu1ated is approximate1y 0.63F of its
peak va1ue.
● “RMS” stands for Root Mean hquare, and is a yay of expressing an AC quantity of vo1t-
age or current in terms functiona11y equiva1ent to DC. For examp1e, 10 vo1ts AC RMS is
the amount of vo1tage that you1d produce the same amount of heat dissipation across a
resistor of given va1ue as a 10 vo1t DC poyer supp1y. A1so knoyn as the “equiva1ent” or
“DC equiva1ent” va1ue of an AC vo1tage or current. For a sine yave, the RMS va1ue is
approximate1y 0.F0F of its peak va1ue.
● The grest †agtor of an AC yaveform is the ratio of its peak (crest[ to its RMS va1ue.
● The †orm †agtor of an AC yaveform is the ratio of its RMS va1ue to its average va1ue.
● Ana1og, e1ectromechanica1 meter movements respond proportiona11y to the average va1ue
of an AC vo1tage or current. When RMS indication is desired, the meter’s ca1ibration

19. 19
must be “skeyed” according1y. This means that the accuracy of an e1ectromechanica1
meter’s RMS indication is dependent on the purity of the yaveform: yhether it is the
exact same yaveshape as the yaveform used in ca1ibrating.
1.4 €imp1e AC girguit ga1gu1atioms
Over the course of the next fey chapters, you yi11 1earn that AC circuit measurements and ca1-
cu1ations can get very comp1icated due to the comp1ex nature of a1ternating current in circuits
yith inductance and capacitance. Hoyever, yith simp1e circuits (figure 1.23[ invo1ving nothing
more than an AC poyer source and resistance, the same 1ays and ru1es of DC app1y simp1y
and direct1y.
R1
100 
10 V R2 500 
R3
400 
Figure 1.23:
Rtotal = R1 + R2 + R3
Rtotal = 1k
total
Etotal
I =
Rtotal
Itotal
= 10V
1 k
totalI = 10 mA
ER1 =ItotalR1 ER2 = ItotalR2
ER3 = ItotalR3
ER1 = 1 V ER2 = 5 V ER3 = 4V
Series resistances sti11 add, para11e1 resistances sti11 diminish, and the Lays of Kirchhoff
and Ohm sti11 ho1d true. Actua11y, as ye yi11 discover 1ater on, these ru1es and 1ays alvaµs
ho1d true, its just that ye have to express the quantities of vo1tage, current, and opposition to
current in more advanced mathematica1 forms. With pure1y resistive circuits, hoyever, these
comp1exities of AC are of no practica1 consequence, and so ye can treat the numbers as though
ye yere dea1ing yith simp1e DC quantities.

20. 1 5 4 10
10m 10m 10m 10m
100 500 400 1k
E
I
R
Volts
Amps
Ohms
20
Because a11these mathematica1 re1ationships sti11 ho1d true, ye can make use of our fami1-
iar “tab1e” method of organizing circuit va1ues just as yith DC:
R1 R2 R3 Total
A B A B
One major caveat needs to be given here: a11 measurements of AC vo1tage and current
must be expressed in the same terms (peak, peak-to-peak, average, or RMS[. If the source
vo1tage is given in peak AC vo1ts, then a11 currents and vo1tages subsequent1y ca1cu1ated are
cast in terms of peak units. If the source vo1tage is given in AC RMS vo1ts, then a11 ca1cu1ated
currents and vo1tages are cast in AC RMS units as ye11. This ho1ds true for anµ ca1cu1ation
based on Ohm’s Lays, Kirchhoff’s Lays, etc. Un1ess otheryise stated, a11 va1ues of vo1tage and
current in AC circuits are genera11y assumed to be RMS rather than peak, average, or peak-to-
peak. In some areas of e1ectronics, peak measurements are assumed, but in most app1ications
(especia11y industria1 e1ectronics[ the assumption is RMS.
● REVIEW:
● A11 the o1d ru1es and 1ays of DC (Kirchhoff’s Vo1tage and Current Lays, Ohm’s Lay[ sti11
ho1d true for AC. Hoyever, yith more comp1ex circuits, ye may need to represent the AC
quantities in more comp1ex form. More on this 1ater, I promise!
● The “tab1e” method of organizing circuit va1ues is sti11 a va1id ana1ysis too1 for AC circuits.
1.5 AC phase
Things start to get comp1icated yhen ye need to re1ate tyo or more AC vo1tages or currents
that are out of step yith each other. By “out of step,” I mean that the tyo yaveforms are not
synchronized: that their peaks and zero points do not match up at the same points in time.
The graph in figure 1.24 i11ustrates an examp1e ofthis.
A B A B
A B
A B
Figure 1.24:
The tyo yaves shoyn above (A versus B[ are of the same amp1itude and frequency, but
they are out of step yith each other. In technica1 terms, this is ca11eda phase shi†t. Ear1ier

21. 21
ye say hoy ye cou1d p1ot a “sine yave” by ca1cu1ating the trigonometric sine function for
ang1es ranging from 0 to 360 degrees, a fu11 circ1e. The starting point of a sine yave yas zero
amp1itude at zero degrees, progressing to fu11 positive amp1itude at 90 degrees, zero at 180
degrees, fu11 negative at 2F0 degrees, and back to the starting point of zero at 360 degrees. We
can use this ang1e sca1e a1ong the horizonta1 axis of our yaveform p1ot to express just hoy far
out of step one yave is yith another: Figure 1.25
A B
A 0
degrees
(0)
90 180 270 360 90
(0)
180 270 360
0 90 180 270 360 90
(0)
degrees
180 270 360
(0)
B
Figure 1.25: o
The shift betyeen these tyo yaveforms is about 45 degrees, the “A” yave being ahead of
the “B” yave. A samp1ing of different phase shifts is given in the fo11oying graphs to better
i11ustrate this concept: Figure 1.26
Because the yaveforms in the above examp1es are at the same frequency, they yi11 be out of
step by the same angu1ar amount at every point in time. For this reason, ye can express phase
shift for tyo or more yaveforms of the same frequency as a constant quantity for the entire
yave, and not just an expression of shift betyeen any tyo particu1ar points a1ong the yaves.
That is, it is safe to say something 1ike, “vo1tage ’A’ is 45 degrees out of phase yith vo1tage ’B’.”
Whichever yaveform is ahead in its evo1ution is said to be leading and the one behind is said
to be lagging.
Phase shift, 1ike vo1tage, is a1yays a measurement re1ative betyeen tyo things. There’s
rea11y no such thing as a yaveform yith an absolute phase measurement because there’s no
knoyn universa1 reference for phase. Typica11y in the ana1ysis of AC circuits, the vo1tage
yaveform of the poyer supp1y is used as a reference for phase, that vo1tage stated as “xxx
vo1ts at 0 degrees.” Any other AC vo1tage or current in that circuit yi11 have its phase shift
expressed in terms re1ative to that source vo1tage.
This is yhat makes AC circuit ca1cu1ations more comp1icated than DC. When app1ying
Ohm’s Lay and Kirchhoff’s Lays, quantities of AC vo1tage and current must reflect phase
shift as ye11 as amp1itude. Mathematica1 operations of addition, subtraction, mu1tip1ication,
and division must operate on these quantities of phase shift as ye11 as amp1itude. Fortunate1y,

22. 22
A B
Phase shift = 90 degrees
A is ahead of B
(A "leads" B)
B A
Phase shift = 90 degrees
B is ahead of A
(B "leads" A)
A
B
Phase shift = 180 degrees
A and B waveforms are
mirror-images of each other
A B
Phase shift = 0 degrees
A and B waveforms are
in perfect step with each other
Figure 1.26:

23. 23
there is a mathematica1 system of quantities ca11edgomplex numbers idea11ysuited for this
task of representing amp1itude and phase.
Because the subject of comp1ex numbers is so essentia1 to the understanding of AC circuits,
the next chapter yi11 be devoted to that subject a1one.
● REVIEW:
● Phase shi†t is yhere tyo or more yaveforms are out of step yith each other.
● The amount of phase shift betyeen tyo yaves can be expressed in terms of degrees, as
defined by the degree units on the horizonta1 axis of the yaveform graph used in p1otting
the trigonometric sine function.
● A leading yaveform is defined as one yaveform that is ahead of another in its evo1ution.
A lagging yaveform is one that is behind another. Examp1e:
A B
Phase shift = 90 degrees
A leads B; B lags A
●
● Ca1cu1ations for AC circuit ana1ysis must take into consideration both amp1itude and
phase shift of vo1tage and current yaveforms to be comp1ete1y accurate. This requires
the use of a mathematica1 system ca11edgomplexnumbers.
1.& Primgip1es of radio
One of the more fascinating app1ications of e1ectricity is in the generation of invisib1e ripp1es
of energy ca11ed radio vaves. The 1imited scope of this 1esson on a1ternating current does not
permit fu11exp1oration of the concept, some of the basic princip1es yi11 becovered.
With Oersted’s accidenta1 discovery of e1ectromagnetism, it yas rea1ized that e1ectricity and
magnetism yere re1ated to each other. When an e1ectric current yas passed through a conduc-
tor, a magnetic fie1d yas generated perpendicu1ar to the axis of floy. Likeyise, if a conductor
yas exposed to a change in magnetic flux perpendicu1ar to the conductor, a vo1tage yas pro-
duced a1ong the 1ength of that conductor. So far, scientists kney that e1ectricity and magnetism
a1yays seemed to affect each other at right ang1es. Hoyever, a major discovery 1ay hidden just
beneath this seeming1y simp1e concept of re1ated perpendicu1arity, and its unvei1ing yas one
of the pivota1 moments in modern science.
This breakthrough in physics is hard to overstate. The man responsib1e for this concep-
tua1 revo1ution yas the Scottish physicist James C1erk Maxye11 (1831-18F9[, yho “unified” the
study of e1ectricity and magnetism in four re1ative1y tidy equations. In essence, yhat he dis-
covered yas that e1ectric and magnetic }elds yere intrinsica11y re1ated to one another, yith or
yithout the presence of a conductive path for e1ectrons to floy. Stated more forma11y, Maxye11’s
discovery yas this:

24. 24
A ghamgimg e1egtrig fie1d produges a perpemdigu1ar magmetig fie1d, and
A ghamgimg magmetig fie1d produges a perpemdigu1ar e1egtrig fie1d.
A11of this can take p1ace in open space, the a1ternating e1ectric and magnetic fie1ds support-
ing each other as they trave1 through space at the speed of 1ight. This dynamic structure of
e1ectric and magnetic fie1ds propagating through space is better knoyn as an elegtromagnetig
vave.
There are many kinds of natura1 radiative energy composed of e1ectromagnetic yaves. Even
1ight is e1ectromagnetic in nature. So are X-rays and “gamma” ray radiation. The on1y dif-
ference betyeen these kinds of e1ectromagnetic radiation is the frequency of their osci11ation
(a1ternation of the e1ectric and magnetic fie1ds back and forth in po1arity[. By using a source of
AC vo1tage and a specia1 device ca11ed an antenna, ye can create e1ectromagnetic yaves (of a
much 1oyer frequency than that of 1ight[ yith ease.
An antenna is nothing more than a device bui1t to produce a dispersing e1ectric or magnetic
fie1d. Tyo fundamenta1 types of antennae are the dipole and the loop: Figure 1.2F
Basic antenna designs
DIPOLE LOOP
Figure 1.2F:
Whi1e the dipo1e 1ooks 1ike nothing more than an open circuit, and the 1oop a short circuit,
these pieces of yire are effective radiators of e1ectromagnetic fie1ds yhen connected to AC
sources of the proper frequency. The tyo open yires of the dipo1e act as a sort of capacitor
(tyo conductors separated by a die1ectric[, yith the e1ectric fie1d open to dispersa1 instead of
being concentrated betyeen tyo c1ose1y-spaced p1ates. The c1osed yire path of the 1oop antenna
acts 1ike an inductor yith a 1arge air core, again providing amp1e opportunity for the fie1d to
disperse ayay from the antenna instead of being concentrated and contained as in a norma1
inductor.
As the poyered dipo1e radiates its changing e1ectric fie1d into space, a changing magnetic
fie1d is produced at right ang1es, thus sustaining the e1ectric fie1d further into space, and so on
as the yave propagates at the speed of 1ight. As the poyered 1oop antenna radiates its
changing magnetic fie1d into space, a changing e1ectric fie1d is produced at right ang1es, yith
the same end-resu1t of a continuous e1ectromagnetic yave sent ayay from the antenna. Either
antenna achieves the same basic task: the contro11ed production of an e1ectromagnetic fie1d.
When attached to a source of high-frequency AC poyer, an antenna acts as a transmitting
device, converting AC vo1tage and current into e1ectromagnetic yave energy. Antennas a1so
have the abi1ity to intercept e1ectromagnetic yaves and convert their energy into AC vo1tage
and current. In this mode, an antenna acts as a regeiving device: Figure 1.28

25. 25
AC voltage
produced
AC current
produced
electromagnetic radiation electromagnetic radiation
Radio receivers
Radio transmitters
Figure 1.28:
Whi1e there is mugh more that may be said about antenna techno1ogy, this brief introduction
is enough to give you the genera1 idea of yhat’s going on (and perhaps enough information to
provoke a fey experiments[.
● REVIEW:
● James Maxye11 discovered that changing e1ectric fie1ds produce perpendicu1ar magnetic
fie1ds, and vice versa, even in empty space.
● A tyin set of e1ectric and magnetic fie1ds, osci11ating at right ang1es to each other and
trave1ing at the speed of 1ight, constitutes an elegtromagnetig vave.
● An antenna is a device made of yire, designed to radiate a changing e1ectric fie1d or
changing magnetic fie1d yhen poyered by a high-frequency AC source, or intercept an
e1ectromagnetic fie1d and convert it to an AC vo1tage orcurrent.
● The dipole antenna consists of tyo pieces of yire (not touching[, primari1y generating an
e1ectric fie1d yhen energized, and secondari1y producing a magnetic fie1d in space.
● The loop antenna consists of a 1oop of yire, primari1y generating a magnetic fie1d yhen
energized, and secondari1y producing an e1ectric fie1d in space.
1.t Comtributors
Contributors to this chapter are 1isted in chrono1ogica1 order of their contributions, from most
recent to first. See Appendix 2 (Contributor List[ for dates andcontact information.
Harvey Lew (February F, 2004[: Corrected typographica1 error: “circuit” shou1d have been
“circ1e”.

26. 26
Duame Damiamo (February 25, 2003[: Pointed out magnetic po1arity error in DC generator
i11ustration.
Ma rk D. Zare11a (Apri1 28, 2002[: Suggestion for improving exp1anation of “average” yave-
form amp1itude.
Johm €ymomds (March 28, 2002[: Suggestion for improving exp1anation of the unit “Hertz.”
Jasom €targk (June 2000[: HTML document formatting, yhich 1edto a much better-
1ooking second edition.