In the circuit shown below, the key K is closed at t = 0. The current through the battery is

Options

A. `(VR_(1)R_(2))/(sqrt(R_(1)^(2) + R_(2)^(2))) at t = 0` and `(V)/(R_(2)) at t = infty`
B. `(V)/(R_(2))` at t - 0 and `(V(R_(1) + R_(2)))/(R_(1)R_(2))` at `t = infty`
C. `(V)/(R_(2)` at t = 0 and `(VR_(1)R_(2))/(sqrt(R_(1)^(2) + R_(2)^(2)))` at `t = infty`
D. `(V(R_(1) + R_(2)))/(R_(1)R_(2))` at t = 0 and `(V)/(R_(2))` at `t - infty`

Answer

C

Explanation

At t = 0, no current will flow through L and `R_(1)`
`therefore` Current through battery = `(V)/(R_(2))`
At `t = infty`
effective resistance, `R_(eff) = (R_(1)R_(2))/(R_(1) + R_(2))`
`therefore` Current through battery = `(V)/(R_(eff) = (V(R_(1)) + R_(2))/(R_(1)R_(2))`