Q 12-07-091JEE MainJEE Main 2022 (24 Jun, Shift 1)Medium
A resistance of $40\ \Omega$ is connected to a source of alternating current rated $220\ \text{V}, 50\ \text{Hz}$. Find the time taken by the current to change from its maximum value to the rms value:
Answer: (A) $2.5\ \text{ms}$
Write $i = i_0\cos\omega t$, maximum at $t = 0$. The current equals $\dfrac{i_0}{\sqrt2}$ when $\omega t = \dfrac{\pi}{4}$:
$$t = \frac{\pi/4}{2\pi f} = \frac{1}{8f} = \frac{1}{400}\ \text{s} = 2.5\ \text{ms}$$
Solution by Sreeraj P, M.Sc Physics