# AC Circuits

Circuits where voltage changes polarity or current changes direction periodically are called alternating current (AC) circuits. In AC circuits, voltage and current most often travel in sinusoidal waveforms.

\begin{aligned} v(t) &= V_{peak}cos( \omega t + \theta_{v} ) = V_{peak}sin( \omega t + \phi_{v} ) \\ i(t) &= I_{peak}cos( \omega t + \theta_{i} ) = I_{peak}sin( \omega t + \phi_{i} ) \\ \end{aligned}

Where:

v(t) = voltage drop across two points as a function of time in volts.

i(t) = current as a function of time in amperes.

V_{peak} = peak voltage of voltage waveform in volts.

I_{peak} = peak current waveform in amperes.

\theta_{v} = \phi_{v} + \frac{\pi}{2} = phase shift of voltage waveform in rad.

\theta_{i} = \phi_{i} + \frac{\pi}{2} = phase shift of current wave form in rad.

\omega = angular frequency of waveforms in rad/s.