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  Solved  Paper-2005

A) 0.05s     

B)        0.1s       

C)        0.15s     

D)        0.3s

Correct Answer: B

Solution :

The current at any instant is given by \[l={{l}_{0}}\,(1-{{e}^{-Rt/L}})\,\Rightarrow \,\frac{{{l}_{0}}}{2}\,={{l}_{0}}\,(1-{{e}^{-Rt/L}})\]   \[\frac{Rt}{L}\,=\ln \,2\] \[\therefore \,\,\,t=\frac{L}{R}\,\ln 2\,=\frac{300\times {{10}^{-3}}}{2}\times 0.693\]