Resistors, Capacitors, and Inductors in AC Circuits
This paper is not intended to give sufficient information to do circuit analysis or design on ac
circuits
but rather to give an indication of how the basic circuit elements of resistors, capacitors,
and
inductors
can
CONTROL
the voltage and current in ac circuits.
It is important to remember that ac circuits are continuously changing sine waves of current and
voltage. Unless informed otherwise it is easy to imagine that these sine waves are “in step
–
ter
med
in phase” everywhere in these circuits. This is not true in general and there are ways to
control the
relative phase of the current and voltage signals to the advantage of the
experimenter. The website
mentioned below has
animations
of how the signals
behave.
Resistors:
Ohm’s Law holds for ac circuits in the most
obvious
fashion and the voltage signal and the current signal
are in phase
at every instant
within
and
across
the resistor.
The ability to
control the current flow is available regardless of
th
e frequency of
the signal. The diagram taken from the URL
http://www.physclips.unsw.edu.au/site_map.htm#AC
Portrays
the two quantities in phase (maximum of one occurs at
the
same time as
the maximum of the other).
Capacitors:
While there is a relationship similar to Ohm’s law
for capacitors the voltage across the
capacitors terminals is
not in phase with the current through the
capacitor.
Remember that a capacitor will completely block
the flow of
dc current and as current goes to zero the capacitor achieves
maximum voltage across its terminals. In ac circuits the
phase angle
between the current and voltage values for
capacitors is 900 out of
phase. The current is said to
lead
the
voltag
e and the maximum in the
current sine curve occurs ¼
of a cycle before the voltage signal
maximizes. In the diagram at the right notice that the current
is zero at
time = 0 but the voltage zero occurs at a later time. One important thing to remember
is tha
t
capacitors can be used to change
(control)
the relative phase between the current and
voltage in ac
circuits. This may be useful at times.
Inductors:
Inductors (coils) are in some sense the opposite of
capacitors in ac circuits. While
capacitors tend to
block current
flow at low frequencies and shift the phase of
the current to
lead the phase of the voltage, inductors tend to block the flow
of
current at high frequencies and to shift the phase of current
behind the phase of
the voltage. The inductor can
be
used to
control the relative phase and
amplitude of current and
voltage signals
in ac circuits.
Other circuit elements
: There are other circuit elements in ac circuits that assist in controlling
the
phase, amplitude, and shape of ac signals but one can
see the potential for control from
these three
devices alone.
The Transformer and Power Transmission
The transformer's ability to step AC voltage up or down with ease gives AC an
advantage unmatched
by DC in the realm of power distribution shown in the
figure
below. When transmitting electrical power
over long distances, it is far more efficient to
do so with stepped

up voltages and stepped

down
currents (smaller

diameter wire with
less resistive power losses), then step the voltage back down
and the cur
rent back up
for industry, business, or consumer use.
Transformers enable efficient long distance high voltage transmission of electric energy.
Transformer technology has made long

range electric power distribution practical.
Without the ability
to effic
iently step voltage up and down, it would be cost

prohibitive to
construct power systems for
anything but close

range (within a few miles at most) use.
Example Calculation: Power Considerations
Assume that the resistance of the wires from the power plant t
o your house is 100
Ohms, that your
average power usage is 1,000 watts, and that the voltage needed is
110

120 volts. In rough numbers
the average current used is (I = P/V) 8.7 amps.
Power loss using direct current transferred at 115 volts
–
(P=I
2
R) =
7500
W
att
or more
than is used
in the house. Most of the energy is lost in the transmission line.
Power loss using
AC
with current transferred at 10,000 volts and stepped down with a
transformer.
The current will be 0.1 amp and the power lost in the lines is
1.15
W
att,
which may be tolerable.
Another disadvantage
of
DC
is that either every item in the house must use the same
voltage
(remember that transformers in the computer will not work) or separate lines
must be used for each
voltage used in the house.
Whi
le all plug

in items
in the house
use 115 volts
AC
, many have a transformer
inside to adjust
to
the voltage
requirements
for that
device
.
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