In the following circuit (Fig.) the switch is closed at `t = 0`. Find the current `i_(1),i_(2),i_(3)` and `di_(3)//dt` at `t = 0` and at `t = oo`. Initially, all current are zero.

Explanation

At `t=0`
`i_(3)` is zero since current cannot suddenly change due to the inductor.
`therefore i_(1)=i_(2)`(from `KCL`)
applying `KCL` in the part `ABEF` we get `i_(1)=i_(2)=epsilon/(2R)`
At `t=oo`
`i_(3)` will become constant and hence potential difference across the inductor will be zero.It is just like a simple wire and the circuit can be solved assuming it to be like shown in the following diagram.
` i_(2)=i_(3)=epsilon/(3R) i_(1)=(2epsilon)/(3R)`