Alternating Current

Power

$$p(t)=\frac{v^2(t)}{R}$$ $$P_{avg}=\frac{V_{rms}^2}{Z}$$ $$v(t)=V_{peak}\sin (\omega t)$$ $$i(t)=\frac{v(t)}{R}=\frac{V_{peak}}{R}\sin (\omega t)$$ $$p(t)=v(t)i(t)=\frac{V_{peak}^2}{R}{\sin }^2(\omega t)=\frac{V_{peak}^2}{2R}(1-\cos (2\omega t))$$