An AC voltage source described by $V=10 \cos (\mathrm{\pi }/2) \mathrm{t}$ is connected to a $1\mu F$ capacitor as shown in figure. The key $K$ is closed at $t=0$. The time $(t>0)$ after which the magnitude of current $I$ reaches its maximum value for the first time is

Angular frequency $\omega =\frac{\mathrm{\pi }}{2} \mathrm{rad}/\mathrm{s}$.

Current will lead the voltage by $90°$.

Hence current  $i=I_0\cos \left(\frac{\mathrm{\pi }}{2}t+\frac{\mathrm{\pi }}{2}\right)=-I_0\sin \left(\frac{\mathrm{\pi }}{2}t\right)$, which is shown in the figure.

Magnitude of the current will reach maximum value for the first time at time t₀ given by

$\begin{array}{rcl}{t}_0& =& \frac{T}{4}=\frac{(2\mathrm{\pi }/\mathrm{\omega })}{4}=\frac{\mathrm{\pi }}{2\omega }=\frac{\mathrm{\pi }}{2(\mathrm{\pi }/2)}=1 \mathrm{s}\end{array}$.