JEE PYQ: Magnetic Effects Of Current Question 7
Question 7 - 2021 (18 Mar 2021 Shift 2)
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:
(1) $\frac{L}{R} \ln 5$
(2) infinite
(3) $\frac{L}{R} \ln 2$
(4) $\frac{L}{R} \ln 10$
Show Answer
Answer: (3) $\frac{L}{R} \ln 2$
Solution
Magnetic energy $= \frac{1}{2}Li^2 = 25%$ of max $\Rightarrow i = \frac{i_0}{2}$. For charging: $i = i_0(1 - e^{-Rt/L})$. Setting $i = i_0/2$: $t = \frac{L}{R} \ln 2$.
BETA
