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

Options

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

Answer

C

Explanation

At t = 0 ionductor behaves as broken wire, then `i=(V)/(R_(2))`.

At `i=oo`, inductor behaves as a conducting wire,
`i=(V)/(R_(1)R_(2)//(R_(1)+R_(2)))=(V(R_(1)+R_(2)))/(R_(1)R_(2))`