In the circuit shown if Fig. the switch S is closed at time t = 0. The current through the capacitor and inductor will be equal at time t equal (given `R = sqrt(L//C)`

Options

A. RC
B. `RC log_(e) 2`
C. `(1)/(R log_(e))`
D. LR

Answer

B

Explanation

In Fig. when switch S is is closed current through L grows and current throught C decays.
As `I_(C ) = I_(L)`
`:. (V)/(R ) e^(-t//RC) = (V)/(R ) (1 - e^((-Rt)/(L)))`
As `R = sqrt((L)/(C )) :. R^(2) C = L` or `RC = (L)/(R )`
From (i), `e^(-t//RC) = 1 - e^(-t//RC)`
`2 e^(-t//RC) = 1`
`e^(-t//RC) = (1)/(2)`
`t = RC log_(e) 2`