Physics » Electric Current, Resistance, and Ohm's Law » Alternating Current versus Direct Current

# Summarizing Alternating Current Versus Direct Current

## 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 = V0 sin 2πft, where V is the voltage at time t, V0 is the peak voltage, and f is the frequency in hertz

### AC current

current that fluctuates sinusoidally with time, expressed as I = I0 sin 2πft, where I is the current at time t, I0 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 I0 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 V0 is the peak voltage, in an AC system