A resistance of 40Ω is connected to a source of alternating current...

The current in AC is of the form of $i = {i}_{0}sin\omegat$. The maximum current is ${i}_{0}$ and rms current is $\dfrac{{i}_{0}}{\sqrt{2}}$. The change in the phase when current change from maximum to rms value is $\dfrac{\pi}{4}rad$. Therefore, the time taken for the same will be,

$t = \dfrac{∆ ϕ}{\omega} = \dfrac{\pi}{4 \times 2\pi \times 50} = 2 . 5ms$.