In the circuit shown in figure switch `S` is closed at time `t=0`. The charge which passes through the battery in one time constant is

Options

A. `(eR^(2)E)/(L)`
B. `E((L)/(R ))`
C. `(EL)/(eR^(2))`
D. `(eL)/(ER)`

Answer

C

Explanation

The current at time `t` is given by
`i = i_(0) (1 - e^(-t//tau))`
Here `i_(0) = (E)/(R )` and `tau = (L)/(R )`
`:. q = int_(0)^(tau) idt = int_(0)^(t) (1 - e^(-t//tau)) dt`
`= (i_(0) tau)/(e) =(((E)/(R ))((L)/(R )))/(e) = (EL)/(eR^(2))`