An inductance `L` and and a resistance `R` are connected in series to a battery of voltage `V` and negligible internal resistance through a switch. The switch is closed at `t = 0`. The charge that passes through the battery in one time constant is [`e` is base of natural logarithms]

Options

A. `(e R^(2)V)/(L)`
B. `(VL)/(R )`
C. `(VL)/(eR^(2))`
D. `(eL)/(VR)`

Answer

C

Explanation

`q = int i dt = int i_(0)(1-e^((-R )/(L)t))dt`