Question:
The time taken for the magnetic energy to reach $25 \%$ of its maximum value, when a solenoid of resistance $\mathrm{R}$, inductance $\mathrm{L}$ is connected to a battery, is :
Correct Option: , 3
Solution:
Magnetic energy $=\frac{1}{2} \mathrm{Li}^{2}=25 \%$
$\mathrm{ME} \Rightarrow 25 \% \Rightarrow \mathrm{i}=\frac{\mathrm{i}_{0}}{2}$
$\mathrm{i}=\mathrm{i}_{0}\left(1-\mathrm{R}^{-\mathrm{R} / \mathrm{L}}\right)$ for charging
$\mathrm{t}=\frac{\mathrm{L}}{\mathrm{R}} \ln 2$
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