Most of the examples dealt with so far, and particularly those utilizing batteries, have constant voltage sources. Once the current is established, it is thus also a constant. Direct current (DC) is the flow of electric charge in only one direction. It is the steady state of a constant-voltage circuit. Most well-known applications, however, use a time-varying voltage source. Alternating current (AC) is the flow of electric charge that periodically reverses direction. If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating current circuit. Examples include the commercial and residential power that serves so many of our needs. Figure 1 shows graphs of voltage and current versus time for typical DC and AC power. The AC voltages and frequencies commonly used in homes and businesses vary around the world.

Figure 2 shows a schematic of a simple circuit with an AC voltage source. The voltage between the terminals fluctuates as shown, with the AC voltage given by

where *, *

where

Current in the resistor alternates back and forth just like the driving voltage, since

**Making Connections: Take-Home Experiment—AC/DC Lights: **

Wave your hand back and forth between your face and a fluorescent light bulb. Do you observe the same thing with the headlights on your car? Explain what you observe. *Warning: Do not look directly at very bright light*.

We are most often concerned with average power rather than its fluctuations—that 60-W light bulb in your desk lamp has an average power consumption of 60 W, for example. As illustrated in Figure 3, the average power

This is evident from the graph, since the areas above and below the

and

where rms stands for root mean square, a particular kind of average. In general, to obtain a root mean square, the particular quantity is squared, its mean (or average) is found, and the square root is taken. This is useful for AC, since the average value is zero. Now,

which gives

as stated above. It is standard practice to quote

To summarize, when dealing with AC, Ohm’s law and the equations for power are completely analogous to those for DC, but rms and average values are used for AC. Thus, for AC, Ohm’s law is written

The various expressions for AC power

and

### Example 1: **Peak Voltage and Power for AC**

(a) What is the value of the peak voltage for 120-V AC power? (b) What is the peak power consumption rate of a 60.0-W AC light bulb?

*Strategy*

We are told that

*Solution for (a)*

Solving the equation

*Discussion for (a)*

This means that the AC voltage swings from 170 V to

*Solution for (b)*

Peak power is peak current times peak voltage. Thus,

We know the average power is 60.0 W, and so

*Discussion*

So the power swings from zero to 120 W one hundred twenty times per second (twice each cycle), and the power averages 60 W.

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