Question

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.

Answer 1

At t=0
`i_(3)` is zero, since current cannot suddenly change due to the inductor.
`:. i_(1)=i_(2)`(from KCL)
applying KVL in the part ABEF we get `i_(1)=i_(2)=(epsi)/(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)=(epsi)/(3R),i_(1)=(2epsi)/(3R)`