An e.m.f. of `15` volt is applied in a circuit containing `5` henry inductance and `10` ohm resistance. The ratio of the current at time `t=oo` and at `t=1` second is

Options

A. `(e^(1/2))/(e^(1/2-1))`
B. `(e^(2))/(e^(2) - 1)`
C. `1 - e^(-1)`
D. `e^(-1)`

Answer

B

Explanation

`i = i_(0) (1 - e^(-Rt/L))`
`i_(0) = (E)/(R)` (Steady current) when `t = infty`
`i_(infty) = (E)/(R)(1 - e^(-infty)) = (15)/(10) = 1.5`
`i_(1) = 1.5 (1 - e^(-R/L)) = 1.5 (1 - e^(-2))`
`Rightarrow (i_(infty))/(i_(1)) = (1)/(1 - e^(-2)) = (e^(2))/(e^(2) - 1)`