A coil of inductance 300 mH and resistance 2 0 is connected to a source of voltage 2 V. The current reaches half of its steady state value in

0.05 s

0.1 s

0.15 s

0.3 s

Solution

0.1 s

The current at any instant is given by

I = I_o ( 1 - e^{-R t /L} )

$\frac{I_{o}}{2} = I_{o} (1 - e^{\frac{- R t}{L}}) \frac{1}{2} = (1 - e^{\frac{R t}{L}})$

e^-Rt/L = 1/ 2

$\frac{Rt}{L} = \ln 2$

$∴ t = \frac{L}{R} \ln 2 = \frac{300 \times 10^{- 3}}{2} \times 0.693 = 150 \times 0.693 \times 10^{- 3} ∴ t = 0.10395 s \Rightarrow t = 0.1 s$

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