# Solved Problems-10

Problems-10
In the network shown in the figure, the switch is closed at time t = 0. Assuming all the initial currents and voltages as zero, find the current through the inductor L2 by the use of Nortonâ€™s theorem.

Solution
The network for t > 0 in Laplace domain is shown in the figure below.

The equivalent network reduces to one as shown below.

To find the current in L2, we have to find Theveninâ€™s equivalent circuit across the terminals A and B. The impedance between terminals A and B is given as,

Short circuit current flowing from A to B is given as,

Therefore, the Nortonâ€™s equivalent circuit is shown in the figure below.

Hence the current,

By partial fraction expansion,

Where,
âˆ´

Taking inverse Laplace transform, we get the required current as,