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(NAVPERS 10622)
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Table of Contents. • U.S. Government Printing Office; 1945  618779
AC Circuits  Some Surprises
You 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. cutsup 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 ac 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 ac voltage. Look at figure 170. It's
only a simple sine wave of ac 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 instant.
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.
Figure 170.  AC voltage.
If you wanted to find the current in an ac 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 ac voltage and ac current. The effective voltage is equal
to the maximum voltage multiplied by 0.707. Or 
E_{eff.} = 0.707 x E_{max.}
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 ac 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 dc 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 (I_{max}) is multiplied by 0.707 the result is the ac current value
corresponding to the dc 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 I_{max} by 0.707.
In this case, 14.14 amperes (I_{max}) 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 AC METERS READ IN EFFECTIVE
VALUES.
The point you must understand, and remember, is that, although an ac 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 REGULAR
INTERVALS.
Figure 171.  A.c.  d.c. compared.
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 DC 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 dc 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 ac effective values
equal the dc values.
THREE PURE CIRCUITS
There are three things that limit the flow of current in an ac 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 dc 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 ac circuitthen
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.
PURE RESISTANCE
This one is easy. Just like a dc 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 voltage.
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 PHASE circuits.
Figure 172.  Pure resistance.
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 selfinduction. In a pure circuit, this
selfinduced voltage E_{si} is just as strong as the applied voltage E_{a}.
But the E_{si} IS NOT IN PHASE WITH THE E_{a}. Figure 174 shows the first
step in understanding a pure inductive circuit.
Notice that the E_{a} and E_{si} 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 173.  Pure inductive reactance.
Now you have TWO voltages controlling current E_{a} and E_{si}. The
result is a current out of phase with both. In fact, the current's phase is midway between
E_{a} and E_{si}. 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 E_{si}.
And if the current moves out of phase  lagging, then the E_{si} is forced further
out of phase, as in figure 175. Notice that the E_{si} is now opposing the E_{a}
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  E_{si} is negative
and E_{a} 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.
Figure 174.  First condition.
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 E_{si}.
Figure 175.  Second condition.
Figure 176.  Third condition.
Not only is the current reduced  but it's shoved further out of phase. Current is
midway between E_{a} and E_{si}, so it must be 671/2° lagging its E_{a}.
The third and FINAL condition is shown in figure 176. The current, by moving further
out of phase, forces the E_{si} further out of phase. In turn, the E_{si}
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 E_{si} 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 E_{si}; and E_{si} always
stays 90° away from its current. The E_{si} helps to push the current, so as
E_{si} 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 E_{si} still further
out of phase because E_{si} is always 90° from the current.
Figure 177.  Pure inductive reactance circuit.
Where is the end to all this pushing further and further out of phase? When the E_{si}
and E_{a} are 180° out of phase  that's figure 176. Notice that E_{si}
and E_{a} are opposing each other ALL THE TIME. And, if they're equal  E_{si}
= E_{a}  the total voltage is zero. Therefore, in a pure inductive reactance
circuit, the two voltages  E_{a} and E_{si}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 (X_{L}). 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.
Figure 178.  Practical inductive circuit.
A practical inductive circuit  a REAL circuit  contains both inductive reactance
and resistance. Look at figure 178this is a practical circuit. The coil has 12 ohms
of resistance (R = 12 Ω) and 12 ohms of inductive reactance (X_{L} = 12 Ω). The
inductive reactance (X_{L}) does just as much to limit current as the resistance
(R). And the X_{L} 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.
Figure 179.  Current and voltage for figure 178.
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 areconnected
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 180.  Simple condenser.
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 awaythey 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 electroncongested 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 righthand side. Current flows. Electrons came
in on the left sidepiled up on the plates  repelled the electrons of the dielectric,
which in turn repelled the electrons in the plates of the righthand side. Current flows
out of the righthand 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 lefthand plates. You can say, that as long as the voltage
is INCREASING current flows across a condenser IN THE DIRECTION OF VOLTAGE.
Figure 181.  Condenser action  No. 1.
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 lefthand plates have too many
electrons. The dielectric's molecules are lopsided, and the righthand plates have too
few electrons. This strained condition is maintained by the maximum voltage at the 90°
point in the cycle.
Figure 182.  Condenser action  No. 2.
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 righthand
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.
Figure 183.  Pure capacitive circuit.
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 (X_{C}) does two things to a current. X_{C} limits
current like a resistance and causes current to be out of phase with its voltage LEADING.
X_{C}, like X_{L}, is measured in ohms.
Figure 184.  Practical capacitive circuit.
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 X_{C} and 12 ohms of R.
Figure 185.  Current and voltage for figure 184.
R and X_{C} are equal. They both reduce current flow and the R tends to keep
current in phase while the X_{C} tends to force it 90° out of phaseleading.
Resultthe 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 X_{L}, X_{C}, and R. Ana all of
them  X_{L}, X_{C}, 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 ac circuit. It corresponds
to resistance in a dc circuit.
When you are determining the impedance of an ac circuit, the first step is to combine
the two reactances. They're opposite in action  XL makes current lag and X_{C}
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 X_{L} and 24 ohms of X_{C}, then the total
reactance (X) is 24  15 = 9 ohms. And the current will LEAD the voltage because X_{C}
is stronger than X_{L}.
If a circuit has 30 ohms of X_{L} and 19 ohms of X_{C}, the X is 30
 19 = 11 ohms. And the current LAGS the voltage because X_{L} is stronger than
X_{C}.
After you have combined X_{L}, and X_{C}, 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 (R^{2} + X^{2})
PRACTICE CIRCUIT
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.
Figure 186.  Practice circuit.'
First, how much total reactance?
X = X_{L } X_{C}.
X = 9  6 = 3 ohms.
Second, how much impedance, Z?
Z = SQRT (R^{2} + X^{2}).
Z = SQRT (16 + 9) = SQRT(25) = 5 ohms.
By Ohm's law (but using Z instead of R for  an ac circuit) you find the current
 I = E/Z = 120/5 = 24 amps.
And the current is LAGGING because X_{L} is larger than Xc.
WHERE THEY ARE
You'll find circuits involving X_{L}, X_{C} and R almost everywhere
you find a.c. This is only the beginning. Circuits containing ac 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 X_{C} and offset the X_{L}.
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, X_{L}, X_{C} and R limit current.
And the total opposition to current flow in a.c. is Z. And Z is made up of XL, X_{C},
and R.
R tends to keep current in phase with voltage.
X_{L} tends to make current lag voltage.
X_{C} tends to make current lead voltage.
Chapter 17 Quiz
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