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=(E)/(R)(1-e^(-(Rt)/(L)))`
`t=1s` , `i_(1)=(15)/(10)(1-e^((-(10xx1))/(5)))`
`t=prop` , `i_(2)=(15)/(10)`
`(i_(1))/(i_(2))=1-e^(-2)=1-(1)/(e^(2))=(e^(2))/(1-e^(2))`