Sol. Let I 0 be the initial current in the steady state condition before shifting the switch.

∴ I 0 =

Let be the current in the circuit at time t = 0, when the switch is shifted to position 2.

Since the flux associated with inductors will be same just before and just after the shifting of switch, otherwise the induced emf would be infinite.

φ = I 0 L = (L + 2L)

or = =

If I is the instantaneous current in the circuit at time t, then

E – 3L – IR = 0

or 3L = E – IR

or =

or ln =

or = e –2R/3L

or E – IR = e –2R/3L

or I =