Q 12-06-108JEE MainJEE Main 2021 (18 Mar, Shift 2)Easy
The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance $R$, inductance $L$ is connected to a battery, is:
Answer: (C) $\frac{L}{R}\ln2$
$U \propto i^2$, so 25% of the maximum energy means $i = \dfrac{I_0}{2}$:
$$1 - e^{-Rt/L} = \frac12 \Rightarrow t = \frac{L}{R}\ln 2$$
Solution by Sreeraj P, M.Sc Physics