A $10\Omega$ resistance is connected across $220V-50Hz$ AC supply. The time taken by the current to change from its maximum value to the rms value is:

$\mathrm{V}=220\mathrm{V}/50\mathrm{Hz}$

$\Rightarrow i=i_0\sin \omega t$

When $i=i_0$

$i=i_0\sin \omega t_1\Rightarrow \omega t_1=\frac{\pi }{2}\dots ..\left(i\right)$

When  $i=\frac{i_0}{\sqrt{2}}$

$\frac{i_0}{\sqrt{2}}=i_0\sin \omega t_2\Rightarrow \omega t_2=\frac{\pi }{4}$........(ii)

Time taken by current from maximum value to rms value

$\Rightarrow (t_1-t_2)=\frac{\pi }{2\omega }-\frac{\pi }{4\omega }=\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}=\frac{1}{8\times 50}=\frac{1}{400}\sec =2.5\mathrm{ms}$