## Summary

- Direct current (DC) is the flow of electric current in only one direction. It refers to systems where the source voltage is constant.
- The voltage source of an alternating current (AC) system puts out \(V={V}_{0}\phantom{\rule{0.25em}{0ex}}\text{sin 2}\pi \text{ft}\), where \(V\) is the voltage at time \(t\), \({V}_{0}\) is the peak voltage, and \(f\) is the frequency in hertz.
- In a simple circuit, \(I=\text{V/R}\) and AC current is \(I={I}_{0}\phantom{\rule{0.25em}{0ex}}\text{sin 2}\pi \text{ft}\), where \(I\) is the current at time \(t\), and \({I}_{0}={V}_{0}\text{/R}\) is the peak current.
- The average AC power is \({P}_{\text{ave}}=\cfrac{1}{2}{I}_{0}{V}_{0}\).
- Average (rms) current \({I}_{\text{rms}}\) and average (rms) voltage \({V}_{\text{rms}}\) are \({I}_{\text{rms}}=\cfrac{{I}_{0}}{\sqrt{2}}\) and \({V}_{\text{rms}}=\cfrac{{V}_{0}}{\sqrt{2}}\), where rms stands for root mean square.
- Thus, \({P}_{\text{ave}}={I}_{\text{rms}}{V}_{\text{rms}}\).
- Ohm’s law for AC is \({I}_{\text{rms}}=\cfrac{{V}_{\text{rms}}}{R}\).
- Expressions for the average power of an AC circuit are \({P}_{\text{ave}}={I}_{\text{rms}}{V}_{\text{rms}}\), \({P}_{\text{ave}}=\cfrac{{V}_{\text{rms}}^{\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}2}}{R}\), and \({P}_{\text{ave}}={I}_{\text{rms}}^{\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}2}R\), analogous to the expressions for DC circuits.

## Glossary

### direct current

(DC) the flow of electric charge in only one direction

### alternating current

(AC) the flow of electric charge that periodically reverses direction

### AC voltage

voltage that fluctuates sinusoidally with time, expressed as *V = V*_{0} sin 2*πft*, where *V* is the voltage at time *t, V*_{0} is the peak voltage, and *f* is the frequency in hertz

### AC current

current that fluctuates sinusoidally with time, expressed as *I = I*_{0} sin 2*πft*, where *I* is the current at time *t, I*_{0} is the peak current, and *f* is the frequency in hertz

### rms current

the root mean square of the current, \({I}_{\text{rms}}={I}_{0}/\sqrt{2}\), where *I*_{0} is the peak current, in an AC system

### rms voltage

the root mean square of the voltage, \({V}_{\text{rms}}={V}_{0}/\sqrt{2}\), where *V*_{0} is the peak voltage, in an AC system