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

Options

A. `0.1 s`
B. `0.05 s`
C. `0.3 s`
D. `0.15 s`

Answer

A

Explanation

The charging of inductance given by,
`i = i_(0)(1 - e^(-(Rt)/(L))) " (i_(0))/(2) = i_(0)(1 - e ^((-Rt)/(L))) Rightarrow e^((-Rt)/(L)) = 1/2`
Taking log on both the sides,
`-(Rt)/(L) = log 1 - log 2`
`Rightarrow t = (L)/(R) log 2 = (300 xx 10^(-3))/(2) xx 0.69 = 0.1 sec`