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Table of Contents.
¶ U.S. GOVERNMENT PRINTING OFFICE; 1945  618779
CHAPTER 17 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
(click
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