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Solved 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 Norton’s theorem.
Description: 2431.png
The network for t > 0 in Laplace domain is shown in the figure below.
Description: 2437.png
The equivalent network reduces to one as shown below.
Description: 2444.png
To find the current in L2, we have to find Thevenin’s equivalent circuit across the terminals A and B. The impedance between terminals A and B is given as,
Description: 5647.png
Short circuit current flowing from A to B is given as,
Description: 5653.png 
Therefore, the Norton’s equivalent circuit is shown in the figure below.
Hence the current,
Description: 5663.png
Description: 979.png
By partial fraction expansion,
Description: 5669.png
Description: 5675.png
Description: 5681.png
Description: 5687.png
Description: 5693.png
∴ Description: 5702.png
Taking inverse Laplace transform, we get the required current as,
Description: 5708.png

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