Chapter 8, Problem 14P

The current flowing through the capacitor shown in Fag. P8.12 is given by

$i\left(t\right)=C\frac{dv\left(t\right)}{dt}$. If $C=2\mu F$ and $v\left(t\right)=t^2{e}^{-10}\text{V}$.

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

(b) Find the value of the voltage when the current is zero.

(c) Use the given information to sketch $v\left(t\right)$.