The ac current in a circuit is given by 3 sin($\omega$t) ampere. The time taken by the current to drop from rms value to zero is

RMS value of current is $\frac{i_0}{\sqrt{2}}=\frac{3}{\sqrt{2}} A$

At RMS curent, 

$\frac{3}{\sqrt{2}}=3\sin \omega t$

$\Rightarrow t=\frac{\pi }{4\omega }, \frac{3\pi }{4\omega }....$

Current drops to zero at $t=\frac{\pi }{\omega }$ again.

Time taken is 

$∆t=\frac{\pi }{4\omega }$