Problem $3$:$$ An AC power supply is connected to a capacitor of capacitance $8\mathrm{.}5$ F$.$ At time t $=0$ the power supply is switched on and starts providing a time$-$dependent voltage v$($t$)=$ V$0$ cos$($t$)$ across the capacitor, where V$0=4\mathrm{.}6$ V and $=380$ rad$/$s$.$ The capacitor is initially uncharged.