A coil of inductance `8.4 mH` and resistance `6` `Omega` is connected to a `12 V` battery. The current in the coil is `1.0 A` at approximately the time.

Options

A. `500 s`
B. `20 s`
C. `35 s`
D. `1 ms`

Answer

D

Explanation

The current-time `(i-t)` equation in `L -R` circuit is given by [Growth of current in `L-R` circuit]
`i = i_(0)(1-e^(-i//t_(L)))` -----(i)
Where `i_(0) = (V)/(R ) = (12)/(6) = 2A` and `t_(L) = (L)/(R ) = (8.4 xx 10^(-3))/(6)`
and `I = 1A , t = ?`
Substituting these values in Eq. (i), we get
`t = 0.97 xx 10^(-3) s` or `t = 0.97 ms t = 1m s`