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548 ⏐⏐⏐ SINUSOIDAL ALTERNATING WAVEFORMS
12
i (mA)
0 1s
(a)
t
12
0
which, in words, states that to find the effective value, the function i(t)
must first be squared. After i(t) is squared, the area under the curve is
found by integration. It is then divided by T, the length of the cycle or
the period of the waveform, to obtain the average or mean value of the
squared waveform. The final step is to take the square root of the mean
value. This procedure gives us another designation for the effective
value, the root-mean-square (rms) value. In fact, since the rms term is
the most commonly used in the educational and industrial communities,
it will used throughout this text.
EXAMPLE 13.19 Find the rms values of the sinusoidal waveform in
each part of Fig. 13.53.
i (mA)
1s 2 s
(b)
FIG. 13.53
Example 13.19.
t
v
169.7 V
Solution: For part (a), I rms � 0.707(12 � 10 �3 A) � 8.484 mA.
For part (b), again I rms � 8.484 mA. Note that frequency did not
change the effective value in (b) above compared to (a). For part (c),
V rms � 0.707(169.73 V) � 120 V, the same as available from a home
outlet.
EXAMPLE 13.20 The 120-V dc source of Fig. 13.54(a) delivers
3.6 W to the load. Determine the peak value of the applied voltage
(E m) and the current (I m) if the ac source [Fig. 13.54(b)] is to
deliver the same power to the load.
I dc
E 120 V P = 3.6 W
Load
(a)
e
E m
(c)
FIG. 13.54
Example 13.20.
+
–
I m
i ac
(b)
t
P = 3.6 W
Load