A 10Ω resistance is connected across 220V - 50Hz AC supply. The...

$⇒ i = {i}_{0}sin\omegat$

When $i = {i}_{0}$

${i}_{0} = {i}_{0}sin\omega{t}_{1} ⇒ \omega{t}_{1} = \dfrac{\pi}{2} \ldots ( 1 )$

When $i = \dfrac{{i}_{0}}{\sqrt{2}}$

$\dfrac{{i}_{0}}{\sqrt{2}} = {i}_{0}sin\omega{t}_{2} ⇒ \omega{t}_{2} = \dfrac{\pi}{4} \ldots ( 2 )$

Time taken by current from maximum value to rms value, $⇒ \left({t}_{1} - {t}_{2}\right) = \dfrac{\pi}{2\omega} - \dfrac{\pi}{4\omega} = \dfrac{\pi}{4\omega} = \dfrac{\pi}{4 \times 2\pif}$

$= \dfrac{1}{8 \times 50}$

$= \dfrac{1}{400}sec$

$= 2 . 5ms$