The rms current in a circuit connected to a 50 Hz ac source is 15 A. The value of the current in the circuit (1/600)s after the instant the current is zero, is:

Let AC current equation be I=I₀ sin $\omega$t
Now, let's find the time/instant when current becomes zero.
So, $0={\mathrm{I}}_0\sin \mathrm{\omega t}\Rightarrow \sin \mathrm{\omega t}=0\Rightarrow \mathrm{\omega t}=\mathrm{\pi }\Rightarrow \mathrm{t}=\frac{\mathrm{\pi }}{\mathrm{\omega }}=\frac{\mathrm{\pi }}{2\mathrm{\pi v}}=\frac{1}{2\mathrm{v}}$
$[\mathrm{v}=50\mathrm{Hz}]\mathrm{t}=\frac{1}{2\mathrm{v}}=\frac{1}{100}\sec$
Now: As we have to find current $\left(\frac{1}{600}\right)$ sec after the instant the current is zero
So time is ${\mathrm{t}}^{\mathrm{\prime }}={\mathrm{I}}_0\sin \left(\mathrm{\omega }\times \frac{7}{600}\right)\left[\because {\mathrm{I}}_0={\mathrm{I}}_{\text{r.m.s }}\sqrt{2}=15\sqrt{2}\mathrm{A}\right]$
$={\mathrm{I}}_0\sin \left(2\mathrm{\pi v}\times \frac{7}{600}\right)={\mathrm{I}}_0\sin \left(2\mathrm{\pi }\times 50\times \frac{7}{600}\right)={\mathrm{I}}_0\sin \frac{7\mathrm{\pi }}{6}=15\sqrt{2}\times \frac{1}{2}=\frac{15}{\sqrt{2}}\mathrm{A}$