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Solved Problems-4

Problems-4
In the network shown in the figure, the switch S is closed and a steady state is attained. At t = 0, the switch is opened. Determine the current through the inductor for t > 0.
 
Description: Description: 2785.png
 
Solution
When the switch S is closed and the steady-state exists, the current through the inductor is,
i(0 –) = Description: Description: 7322.png = 2 A
 
The voltage across the capacitor, VC (t) = 0 as it is shorted.
 
For t > 0, the switch is opened. By KVL,
Description: Description: 7331.png
 
Taking Laplace transform,
Description: Description: 7340.png
or Description: Description: 7346.png
 
Putting the values,
Description: Description: 7352.png
 
Taking inverse Laplace transform,
Description: Description: 7358.png 
 




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