Page 365 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 29

Alternating-Current

Circuits

ALTERNATING CURRENT

The frequency of an alternating current is the number of complete back-and-forth cycles it goes through each
second (Fig. 29-1). As in the case of harmonic motion, the unit of frequency is the hertz (Hz), where 1 Hz =
1 cycle/s.
An alternating emf of frequency f whose maximum value is V max varies with time according to the formula
V = V max sin 2π ft = V max sin ωt

The quantity ω = 2π f is the angular frequency of the emf in radians per second. Similarly, an alternating current
(ac) of frequency f whose maximum value is I max varies with time according to the formula

I = I max sin 2π ft = I max sin ωt

Fig. 29-1

EFFECTIVE VALUES
Because an alternating current changes continuously, its maximum value I max does not indicate its ability to do
work or to produce heat, as the magnitude of a direct current does. A 5-A direct current is not equivalent to an
alternating current in which I max = 5 A. It is therefore customary to define an effective current I eff such that a direct
current with this magnitude does work or produces heat at the same rate as the corresponding alternating current.
The rate at which energy is dissipated in a resistance R by an alternating current is, at any time t,
2
2
I R = I 2 sin ωt
max
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