Editing Alternating current (section)

=== Power ===
{{Main|AC power}}

The relationship between voltage and the power delivered is:
:<math>p(t) = \frac{v^2(t)}{R}</math>,

where <math>R</math> represents a load resistance.

Rather than using instantaneous power, <math>p(t)</math>, it is more practical to use a time-averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a [[root mean square]] (RMS) value, written as <math>V_\text{rms}</math>, because
:<math>P_\text{average} = \frac{{V_\text{rms}}^2}{R}.</math>

;Power oscillation: <math>\begin{align} v(t) &= V_\text{peak}\sin(\omega t) \\ i(t) &= \frac{v(t)}{R} = \frac{V_\text{peak}}{R}\sin(\omega t) \\ p(t) &= v(t)i(t) = \frac{(V_\text{peak})^2}{R}\sin^2(\omega t) = \frac{(V_\text{peak})^2}{2 R} \ (1 - \cos(2 \omega t) ) \end{align}</math>
For this reason, AC power's waveform becomes [[Rectifier#Full-wave rectification|Full-wave rectified]] sine, and its fundamental frequency is double that of the voltage's.