A coil of inductance $300 \mathrm{mH}$ and resistance $2 \Omega$ is connected to a source of voltage 2V. The…

A coil of inductance $300 \mathrm{mH}$ and resistance $2 \Omega$ is connected to a source of voltage 2V. The current reaches half of its steady state value in
  1. $0.05 \mathrm{~s}$
  2. $0.1 \mathrm{~s}$
  3. $0.15 \mathrm{~s}$
  4. $0.3 \mathrm{~s}$

Solution

$\mathrm{I}=\mathrm{I}_{\circ}\left(1-\mathrm{e}^{-\frac{\mathrm{R}}{\mathrm{L}}\mathrm{t}}\right)$ $0.693=\frac{\mathrm{R}}{\mathrm{L}} \mathrm{t}$ $\mathrm{t}=\frac{.3 \times 0.693}{2}=0.1 \mathrm{sec}$

Asked in: JEE Main 2005

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