Here is the "Electricity - Basic Navy Training Courses"
in its entirety. It should provide one of the Internet's best resources for people seeking
a basic electricity course - complete with examples worked out. See
Table of Contents. • U.S. Government Printing Office; 1945 - 618779
All college curricula seem to have a number
of particular "weeding out" courses that
cull the herd - so to speak - from the eventual graduating class.
The unfortunate victims are then faced with either dropping out of college (not
always such a dooming fate) or choosing a different major. For mechanical engineers
(MEs) it was often statics; for electrical engineers (EEs) it was
AC circuits - the topic of this article. DC is relatively simple because voltage
and current is always in phase, thus no "hard" vector math is involved, but throw
in reactance with its attendant non-zero phase angles and suddenly the student is
faced with trigonometry - the kiss of death to
mathphobes. My experience in engineering school
showed that for MEs who lived through statics,
dynamics provided the next level of weeding out (it nearly got
me). For EEs it was Fourier
and Laplace transforms.
Level three for MEs was thermodynamics (thermogodda**ics was a popular
alternate title), and for EEs it was
control theory. Somehow, I lived through it all and managed
to graduate with a BSEE degree*. After more than four decades in the craft,
this stuff comes much easier than it did in my days of yore.
AC Circuits - Some Surprises
know the fundamental differences between d.c. and a.c. But a.c. has some special
peculiarities all its own. You might say that d.c. plows along like a steady old
battlewagon whereas a.c. cuts-up like a frisky P. T.
You may be surprised by the way a.c. acts in some circuits. For example, did
you know that an a-c coil can be built with only one ohm of resistance and yet pass
practically no current at 120 volts? And on the other hand, a condenser, which is
made of insulator material, will conduct large alternating currents?
A Few Whys
The basic reason for this behavior lies in the a-c voltage. Look at figure 170.
It's only a simple sine wave of a-c voltage. But that sine wave tells you plenty.
To begin with - it's NOT a picture of a.c. Don't get the idea that a.c. humps
along like a caterpillar on a wire. It doesn't! Alternating current flows just exactly
the way its voltage pushes. And you know that the push reverses its direction every
so often. That means the current flows first one way and then the other. The sine
wave tells you about this reversal and it also tells you the amount of push at any
Figure 170. - A-C voltage.
Look again at figure 170. Imagine that this voltage is impressed on a lamp of
100 ohms resistance. At instant 1, there is zero current because, I = 0/100 = 0.
At instant 2, the current is I = 85/100 = 0.85 ampere. And at instant 3 the current
is I = 170/100 = 1.7 amperes, or maximum. Notice what was happening between instant
1 and instant 3. The voltage increased from zero to 170 volts. And at the same time,
the current increased from zero to 1. 7 amperes. This is the first outstanding characteristic
of a.c. A.c. IS CONSTANTLY CHANGING IN VALUE.
If you wanted to find the current in an a-c circuit you'd have to apply Ohm's
law at thousands of instants. But that would be impossible in a practical circuit,
so you use an EFFECTIVE VALUE of a-c voltage and a-c current. The effective voltage
is equal to the maximum voltage multiplied by 0.707.
Eeff. = 0.707 x Emax.
In the example just used, the lamp would have 170 X 0.707 = 120 volts of effective
emf impressed. And the effective current would be 120/100 = 1.2 amperes.
You're wondering what the term "effective value" means and where it comes from.
It means the amount of a.c. that produces the same heating effect that a given d.c.
produces. Here's the problem: You can't take instantaneous readings of a-c current
and voltage for every instant on the sine wave. You've got to have some value of
a.c. that's a true picture of its ability to do work - that corresponds to d-c values.
The maximum value is easiest to determine but it won't do because it's the CORRECT
value for only TWO INSTANTS of each cycle.
The heating effect of currents is easily measured and this effect is used to
establish a comparison between a.c. and d.c. It is found that if the maximum value
of the alternating current (Imax) is multiplied by 0.707 the result is
the a-c current value corresponding to the d-c current in .heat producing ability.
For example, 10 amperes of d.c. produces a certain heat; 10 amperes, EFFECTIVE VALUE,
of a.c. produces the same heat. BUT you get this value - 10 amperes of a.c.-by multiplying
Imax by 0.707. In this case, 14.14 amperes (Imax) times 0.707
gives you the effective value - 10 amperes. Thus a 10 ampere current in a.c. has
a maximum value of 14.14 amperes. But usually this maximum value will cause you
no headaches - ALL A-C METERS READ IN EFFECTIVE VALUES.
Figure 171. - A.c. - d.c. compared.
The point you must understand, and remember, is that, although an a-c meter reads
a steady current or voltage, NEITHER THE CURRENT NOR THE VOLTAGE IS ACTUALLY STEADY.
Both go up and down in value according to their sine waves.
The second outstanding characteristic of a.c. is that it CHANGES DIRECTION AT
You noticed in the sine wave of figure 170 that half the time the voltage was
positive and half the time it was negative. Positive and negative indicate direction.
They simply mean that the voltage first pushes in one direction and then in the
other. For example, if you had the ordinary D-C circuit shown in figure 171, current
would flow from the negative terminal to the positive terminal - ALL THE TIME. But
suppose you impress A.C. on this d-c circuit - the current flows from negative to
positive HALF THE TIME and from positive to negative HALF THE TIME. The lamp is
just as bright on a.c. as d.c. Just as much work is done - just as much power is
consumed - provided the a-c effective values equal the d-c values.
Three Pure Circuits
There are three things that limit the flow of current in an a-c circuit- RESISTANCE,
INDUCTIVE REACTANCE, AND CAPACITIVE REACTANCE. That's two more items than you had
in d.c. Remember that resistance ALONE limits current in a d-c circuit.
When you have only one factor ALONE - resistance, inductive reactance, or capacitive
reactance - you have a PURE circuit. Say you have only resistance in an a-c circuit-then
it's a PURE RESISTANCE CIRCUIT. But pure circuits don't happen very often! In fact
it's almost impossible to get one. However, by studying the action of pure circuits
with anyone of these - resistance, inductive reactance, or capacitive reactance
- you get the best picture of how each one of these things affects current. You'll
have to remember, though, that most PRACTICAL CIRCUITS are combinations of all three.
Figure 172. - Pure resistance.
Figure 173. - Pure inductive reactance.
This one is easy. Just like a d-c circuit, in fact. Figure 172 shows a nearly
pure resistance circuit and the sine waves of current and voltage. The voltage impressed
on this circuit is shown by the solid line. The current flowing is shown by the
dotted line. Just what you'd expect. The current obeys Ohm's law: I = E/R for every
instant. Since the resistance is constant, the current rises and falls with the
The sine waves of figure 172 show one very important thing. Voltage and current
are exactly IN PHASE - in time. When the voltage is zero, so is the current. When
the voltage is maximum, the current is maximum. Pure resistance circuits are IN
Pure Inductive Reactance
This one is not so easy, because inductive circuits always contain a voltage
of self induction. That means a coil and probably an iron core. To make as pure
an inductive circuit as possible, you'd wind a many turn coil on a soft iron core
- like figure 173.
In an inductive reactance circuit, this is what happens - the expanding and contracting
flux, set up by the a.c., produces a voltage of self-induction. In a pure circuit,
this self-induced voltage Esi is just as strong as the applied voltage
Ea. But the Esi IS NOT IN PHASE WITH THE Ea. Figure
174 shows the first step in understanding a pure inductive circuit.
Notice that the Ea and Esi are 90° put of phase. This out
of phaseness was caused by the expanding and contracting flux. Be sure to note that
this is the FIRST CONDITION. The complete picture is given in figure 177.
Figure 174. - First condition.
Figure 175. - Second condition.
Figure 176. - Third condition.
Figure 177. - Pure inductive reactance circuit.
Figure 178. - Practical inductive circuit.
Figure 179. - Current and voltage for figure 178.
Now you have TWO voltages controlling current Ea and Esi.
The result is a current out of phase with both. In fact, the current's phase is
midway between Ea and Esi. That makes the current 45° out
of phase with its applied voltage. Since the current reaches its maximum AFTER the
voltage, THE CURRENT LAGS ITS APPLIED VOLTAGE.
But this is not the WHOLE picture. The current, by its field, produced the Esi.
And if the current moves out of phase - lagging, then the Esi is forced
further out of phase, as in figure 175. Notice that the Esi is now opposing
the Ea more than half the time. You'll have to look at figure 175 to
see what's going on. During the time labeled 1, the two voltages are opposing each
other - Esi is negative and Ea is positive. The result is
a lowered current because the voltages that should be pushing current are wearing
themselves out bucking each other. This same condition is true for the time labeled
3. But, during 2 and 4, the two voltages are aiding each other - the current is
pushed in the same direction by both voltages.
Which condition has the upper hand - 1 and 3, where the voltages oppose or 2
and 4, where they aid ? Well, which lasts the longest time ? You can see that the
opposing condition lasts longer than the aiding. Therefore, the CURRENT IS ACTUALLY
REDUCED BY THE OPPOSITION OF THE Esi.
Not only is the current reduced - but it's shoved further out of phase. Current
is midway between Ea and Esi, so it must be 67-1/2° lagging
The third and FINAL condition is shown in figure 176. The current, by moving
further out of phase, forces the Esi further out of phase. In turn, the
Esi forces the current out of phase. And so on. This is like the question,
"Which comes first, the chicken or the egg?" "Which does the forcing out of phase,
the Esi or the current?" That's a good question - except -you can't answer
it! Each works on the other. Current sets up the field that makes Esi;
and Esi always stays 90° away from its current. The Esi helps
to push the current, so as Esi gets further out of phase, it carries
the current further out of phase. And, as the current gets further out of phase,
it forces the Esi still further out of phase because Esi is
always 90° from the current.
Where is the end to all this pushing further and further out of phase? When the
Esi and Ea are 180° out of phase - that's figure 176. Notice
that Esi and Ea are opposing each other ALL THE TIME. And,
if they're equal - Esi = Ea - the total voltage is zero. Therefore,
in a pure inductive reactance circuit, the two voltages - Ea and Esi-and
the current would have the phases shown by figure 177.
Inductive reactance does two things to current - REDUCES THE AMOUNT OF CURRENT
AND THROWS IT OUT OF PHASE, LAGGING.
Practical Inductive Circuit
If a pure inductive circuit could be built - and it can't be - the current would
be lagging 90°. Further, the voltage of self induction would exactly cancel the
applied voltage. A pure inductive circuit cannot be built because EVERY CIRCUIT
CONTAINS SOME RESISTANCE. Therefore, all practical inductive circuits contain two
factors controlling current - RESISTANCE (R) and INDUCTIVE REACTANCE (XL).
Both limit current - in this respect they are alike. And both are measured in ohms.
But RESISTANCE tends to keep current IN PHASE. And INDUCTIVE REACTANCE tends to
force current OUT OF PHASE.
A practical inductive circuit - a REAL circuit - contains both inductive reactance
and resistance. Look at figure 178-this is a practical circuit. The coil has 12
ohms of resistance (R = 12 Ω) and 12 ohms of inductive reactance (XL
= 12 Ω). The inductive reactance (XL) does just as much to limit current
as the resistance (R). And the XL exerts just as much force to send the
current 90° out of phase as the resistance does to keep it exactly in phase. Result
- the current is half way between 90° out of phase, and exactly in phase - it is
45° out of phase, lagging. Figure 179 shows the sine waves of current and voltage
for this circuit.
You can conclude that, in all inductive circuits, the CURRENT IS REDUCED AND
LAGS OUT OF PHASE.
Pure Capacitive Reactance
This is another one that is not so easy. Because capacitive circuits contain
condensers (capacitors) - and condensers do some strange things.
First, you should know how condensers are built. They're made up of alternate
layers of conductor and dielectric (insulator) materials. Half of the conductor
plates are-connected to one terminal and half to the other terminal. Between every
two conductor plates is a layer of dielectric.
Many materials will serve as conductors and dielectrics in condensers. But waxed
paper is a common dielectric and tin foil is a common conductor. Figure 180 shows
a waxed paper and tin foil condenser. Although this condenser is made of only six
plates, you'll find many condensers having hundreds of plates.
Figure 181 shows a condenser with a.c. impressed across its terminal. The "innards"
are highly magnified so that you can see what happens inside. During the first quarter
of the cycle - that's the first 90° - the condenser is being CHARGED. Voltage is
pushing into the condenser from the left (solid arrows). Current is flowing WITH
this voltage (dotted arrows). The electrons of the current pile up on the surface
of the conductor plates. This gives these plates a negative charge. Repulsion occurs
between the conductors negative charge and the electrons in the molecules of the
dielectric. The dielectric electrons strain to get away-they move just as far from
the conductor's negative charge as they can. This warps the dielectric molecules
out of shape. Instead, of nice symmetrical molecules, they're all lopsided - with
their electron-congested sides AWAY from the negative conductor plate.
Notice, in figure 181, how this builds up a negative charge all along one side
of the dielectric plates. Now, compare this to current flow - just about the same,
except that the dielectric has NO FREE ELECTRONS to flow. If the dielectric had
been a conductor, current would flow in the normal way.
So far you've got electrons all piled up along the side of the plates away from
the voltage force. The final act comes when the strained dielectric forces electrons
out of the conductor plates connected to the right-hand side. Current flows. Electrons
came in on the left side-piled up on the plates - repelled the electrons of the
dielectric, which in turn repelled the electrons in the plates of the right-hand
side. Current flows out of the right-hand side conductor plates. All this is true
for the first 90° of the cycle, because voltage is increasing. And as long as voltage
is increasing, electrons continue to pile up on the left-hand plates. You can say,
that as long as the voltage is INCREASING current flows across a condenser IN THE
DIRECTION OF VOLTAGE.
Figure 180. - Simple condenser.
Figure 181. - Condenser action - No. 1.
Figure 182. - Condenser action - No. 2.
Exactly at the 90° point of the sine wave, everything stands still. Voltage is
at its maximum. The condenser is charged. The voltage is no longer increasing, so
it can't force any more electrons onto the plates. Current stops.
CURRENT IS STOPPED - BUT EVERYTHING IS STRAINED. The left-hand plates have too
many electrons. The dielectric's molecules are lopsided, and the right-hand plates
have too few electrons. This strained condition is maintained by the maximum voltage
at the 90° point in the cycle.
Now, see what happens during the next quarter cycle - the second 90°. Figure
182 shows the same condenser, but during the second quarter of a cycle.
When the voltage decreases - from 90° to 180° the strain is relieved - the force
maintaining the strain is gradually removed. Every thing returns to normal. And
in returning to normal - here's what takes place. The left side loses its
excessive electrons. These electrons flow through the external circuit to the right
side. Here they fill up the right-hand plates. The dielectric no longer has a charge
against it so its molecules spring back to normal symmetrical shapes. The condenser
is DISCHARGED. And look what happens during this discharge. In figure 182, you can
see that the VOLTAGE is in the same direction as in figure 181 - from LEFT to RIGHT.
But CURRENT is from RIGHT TO LEFT (follow the dotted arrows).
That's right - current IS flowing AGAINST the applied voltage. And the reason
is found in the strained dielectric of the condenser. When that dielectric was being
strained by the INCREASING voltage, it was storing energy (much like an emf). When
the voltage decreased, the voltage wasn't strong enough to hold the energy in the
condenser. Electrons streamed out - backed by the energy of the strained dielectric.
These electrons make a CURRENT AGAINST THE VOLTAGE DIRECTION.
These two facts stand out. The current is in the same direction as voltage, as
long as voltage is increasing. And the current is in the opposite direction to the
voltage, as long as voltage is decreasing. Figure 183 shows you the current and
voltage relationships in a pure capacitive circuit. Notice that current LEADS the
voltage by 90°.
Capacitive reactance (XC) does two things to a current. XC
limits current like a resistance and causes current to be out of phase with its
voltage LEADING. XC, like XL, is measured in ohms.
Practical Capacitive Circuit
A practical capacitive circuit - a real circuit - is bound to have some resistance.
You can't have any circuit without some resistance. Look at figure 184. The circuit
has a condenser with 12 ohms of XC and 12 ohms of R.
Figure 183. - Pure capacitive circuit.
Figure 184. - Practical capacitive circuit.
Figure 185. - Current and voltage for figure 184.
Figure 186. - Practice circuit.
R and XC are equal. They both reduce current flow and the R tends
to keep current in phase while the XC tends to force it 90° out of phase-leading.
Result-the current is midway between 90° leading and exactly in phase - it is 45°
out of phase, leading. The current and voltage relationship is shown in figure 185.
All Three Together
Many circuits are combinations of XL, XC, and R. Ana all
of them - XL, XC, and R - have their own individual effect
on the current. There is a certain method of combining these three items to give
you the IMPEDANCE. Impedance (Z) is the total opposition to the flow of current
in an a-c circuit. It corresponds to resistance in a d-c circuit.
When you are determining the impedance of an a-c circuit, the first step is to
combine the two reactances. They're opposite in action - XL makes current lag and
XC makes current lead. Therefore, when they're combined, the action of
one cancels the action of the other.
If a circuit has 15 ohms of XL and 24 ohms of XC, then
the total reactance (X) is 24 - 15 = 9 ohms. And the current will LEAD the voltage
because XC is stronger than XL.
If a circuit has 30 ohms of XL and 19 ohms of XC, the X
is 30 - 19 = 11 ohms. And the current LAGS the voltage because XL is
stronger than XC.
After you have combined XL, and XC, the total reactance
X must be added to the resistance R to get the impedance Z. Here's how you add X
and R -
Z = SQRT (R2 + X2)
Take a practice circuit. The one in figure 186 is a good example. In this drawing
the resistance and reactance values are given. You can find out HOW MUCH current
is flowing, and whether the current is LEADING OR LAGGING.
First, how much total reactance?
X = XL - XC.
X = 9 - 6 = 3 ohms.
Second, how much impedance, Z?
Z = SQRT (R2 + X2).
Z = SQRT (16 + 9) = SQRT(25) = 5 ohms.
By Ohm's law (but using Z instead of R for - an a-c circuit) you find the current
I = E/Z = 120/5 = 24 amps.
And the current is LAGGING because XL is larger than Xc.
Where They Are
You'll find circuits involving XL, XC and R almost everywhere
you find a.c. This is only the beginning. Circuits containing a-c induction motors
have a high inductive reactance. This makes the current lag too far behind the voltage.
So condensers are put in the circuit to increase the XC and offset the
XL. Condensers are used in vacuum tube circuits and across switches.
Induction coils are used in radio circuits to choke down current.
If you keep the three actions straight, you can figure out the effect of each
in a circuit. Remember - All three, XL, XC and R limit current.
And the total opposition to current flow in a.c. is Z. And Z is made up of XL, XC,
R tends to keep current in phase with voltage.
XL tends to make current lag voltage.
XC tends to make current lead voltage.
* University of Vermont, 1989, Magna Cum Laude, top of
Chapter 17 Quiz
Posted May 1, 2019