Chapter 8, Problem 12P

The current flowing through a capacitor shown in Fig P8.12 is given by $i\left(t\right)=C\frac{dv\left(t\right)}{dt}$. If $C=500\mu F$ and $v\left(t\right)=250\sin \left(200\pi t\right)\text{V}$ ,

(a) Find the current $i\left(t\right)$.

(b) Find the power $p\left(t\right)=v\left(t\right)i\left(t\right)$ and its maximum value $P_{\max }$.