CURRENT IN A PERSONAL COMPUTER
The plate on the back of a personal computer says that it draws 2.7 A from a 120-V, 60-Hz line. For this computer, what are (a) the average current, (b) the average of the square of the current, and (c) the current amplitude?
IDENTIFY and SET UP:
This example is about alternating current.
In part (a) we find the average, over a complete cycle, of the alternating current. In part (b) we recognize that the 2.7-A current draw of the computer is the rms value I_{rms} —that is, the square root of the mean (average) of the square of the current, (i^2)_{av}. In part (c) we use Eq. (31.4) to relate I_{rms} to the current amplitude.
I_{\mathrm{rms}}=\frac{I}{\sqrt{2}} (31.4)
EXECUTE:
(a) The average of any sinusoidally varying quantity, over any whole number of cycles, is zero.
(b) We are given I_{rms} = 2.7 A. From the definition of rms value,
(c) From Eq. (31.4), the current amplitude I is
I=\sqrt{2} I_{\mathrm{rms}}=\sqrt{2}(2.7 \mathrm{~A})=3.8 \mathrm{~A}Figure 31.6 shows graphs of i and i^2 versus time t.
EVALUATE: Why would we be interested in the average of the square of the current? Recall that the rate at which energy is dissipated in a resistor R equals i^2 R. This rate varies if the current is alternating, so it is best described by its average value (i^2)_{av}R = I_{rms}^2R . We’ll use this idea in Section 31.4.
