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