question_answer

A coil of inductance 300 m H and resistance \[2\,\Omega \] is connected to a source of voltage 2 V. The current reaches half of its steady state value in

A)  0.05 s                                   

B)  0.1 s

C)  0.15s                                    

D)  0.3s

Correct Answer: B

Solution :

The current at any instant is given by \[I={{I}_{0}}(1-{{e}^{-Rt/L}})\] \[\frac{{{I}_{0}}}{2}={{I}_{0}}(1..{{e}^{-Rl/L}})\] \[=\frac{1}{2}=(1-{{e}^{-Rt/L}})\] \[{{e}^{-Rt/L}}=1/2\] \[\frac{Rt}{L}=\] In 2                 \[\therefore \]  \[t=\frac{L}{R}\] In \[2=\frac{300\times {{10}^{-3}}}{2}\times 0.693\]                                 \[150\times 0.693\times {{10}^{-3}}\]                                 \[=0.10395s=0.1s\]