In the circuit shows in Fig switch `S` is shifed to position `2` from position `1` at `t = 0`, having been on position `1` for a long time. The current in the circuit just after shifting of switch will be (battery and both the inductors are ideal)

Options

A. `(4)/(5) (E)/(R )`
B. `(5)/(4) (E)/(R )`
C. `(5)/(9) (E)/(R )`
D. `(E)/(R )`

Answer

C

Explanation

Let `i_(1)` be the current in the circuit before shifting
`i_(1) = (E)/(R )` (i)
Since the flux associated with the inductors will be same just before and juse after shifting, therefore
`i_(1) 5L = i_(2) 9L`
`i_(2) = (5)/(9) (E)/(R )`