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=oo`
B. `(V)/(R^(2))` at `t=0` and `(V(R_(1)+R_(2)))/(R_(1)R_(2))` at `t=oo`
C. `(V)/(R^(2))` at `t=0` and `(VR_(1)R_(2))/(sqrt(R_(1)^(2)+R_(2)^(2)))` at `t=oo`
D. `(v(R_(1)+R_(2)))/(R_(1)R_(2))` at `t=0` and `(V)/(R_2)` at `t=oo`

Answer

B

Explanation

(c) At t-0, no current will flow through L and `(R_(1))`
`:. Current through battery `(V)/(R^2)`
At `t=(oo)`,
effective resistnace, (R_eff)=(R_(1)R_(2))/(R_(1)+R_(2))`
`:. Current through battery `(V)/R_(eff))=(V(R_(1)=R_(2))/(R_(1)R_(2))`.