question_answer

A coil of inductance 300 mH and resistance\[2\Omega \]. are connected to a source of voltage 2V. The current reaches half of its steady state value in                                    [AIEEE 2005]

A) 0.05s

B) 0.1s 

C) 0.15s

D) 0.3s

Correct Answer: B

Solution :

[b] The current at any instant is given by

\[l={{l}_{0}}\,(1-{{e}^{-Rt/L}})\,\Rightarrow \,\frac{{{l}_{0}}}{2}\,={{l}_{0}}\,(1-{{e}^{-Rt/L}})\]

\[\frac{Rt}{L}\,=\ln \,2\]

\[\therefore \,\,\,t=\frac{L}{R}\,\ln 2\,=\frac{300\times {{10}^{-3}}}{2}\times 0.693\]