Question

Show that the current leads the voltage by an angle $\frac{\pi }{2}$ in an ac circuit containing a pure capacitor.

Answer 1

$V=V_{0}sin\omega t$

$q=CV=C{V}_{0}sin\omega t$

$I=\frac{dq}{dt}=\omega C{V}_{0}cos\omega t$

$I=\omega C{V}_{0}sin\omega t+\frac{\pi }{2}$