1034
I
n this chapter we describe alternating current (AC) circuits. Every time we turn on a
television set, a stereo, or any of a multitude of other electrical appliances in a home,
we are calling on alternating currents to provide the power to operate them. We begin
our study by investigating the characteristics of simple series circuits that contain
resistors, inductors, and capacitors and that are driven by a sinusoidal voltage. We shall
ﬁnd that the maximum alternating current in each element is proportional to the
maximum alternating voltage across the element. In addition, when the applied
voltage is sinusoidal, the current in each element is also sinusoidal, but not necessarily
in phase with the applied voltage. The primary aim of this chapter can be summarized
as follows: if an AC source applies an alternating voltage to a series circuit containing
resistors, inductors, and capacitors, we want to know the amplitude and time character-
istics of the alternating current. We conclude the chapter with two sections concerning
transformers, power transmission, and electrical ﬁlters.
33.1
AC Sources
An AC circuit consists of circuit elements and a power source that provides an alternat-
ing voltage
±
v
. This time-varying voltage is described by
±
v
²±
V
max
sin
³
t
where
±
V
max
is the maximum output voltage of the AC source, or the
voltage
amplitude.
There are various possibilities for AC sources, including generators, as
discussed in Section 31.5, and electrical oscillators. In a home, each electrical outlet
serves as an AC source.
From Equation 15.12, the angular frequency of the AC voltage is
where
f
is the frequency of the source and
T
is the period. The source determines the
frequency of the current in any circuit connected to it. Because the output voltage of
an AC source varies sinusoidally with time, the voltage is positive during one half of the
cycle and negative during the other half, as in Figure 33.1. Likewise, the current in any
circuit driven by an AC source is an alternating current that also varies sinusoidally
with time. Commercial electric-power plants in the United States use a frequency of
60 Hz, which corresponds to an angular frequency of 377 rad/s.