A resistance of $20\Omega$ is connected to a source of an alternating potential V=220sin$\left(100\pi t\right)$ . The time taken by the current to change from the peak value to rms value, is

Both voltage and current are in the same phase. So, let us calculate the time taken by the voltage to change from peak value of rms value.

Now, 220=220sin$100\pi t_1$ .

Or $100\pi t_1=\frac{\pi }{2}$ or $t_1=\frac{1}{200}s$

Again, $\frac{200}{\sqrt{2}}=200\sin 100\pi t_2$

 $or\frac{1}{\sqrt{2}}=\sin 100\pi t_2$o r $100\pi t_2=\frac{\pi }{4}$

Or $t_2=\frac{1}{400}s$

Required time =$t_1-t_2$

$=\frac{1}{200}-\frac{1}{400}=\frac{2-1}{400}=\frac{1}{400}s$

=$2.5\times {10}^{-3}s$