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Question

In the circuit shown aside, the switch S is closed for long time and at t = 0 s, S is opened. The current at t s (> 0) through the resistance R is:

A
1.5 (1 + e3t) A
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B
3.0 (1 - e3t) A
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C
3.0 (1 + e3t) A
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D
1.5 (1 - e3t) A
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Solution

The correct option is A 1.5 (1 + e−3t) AWhen switch is closed t=0s1H is shorted in steady state.Therefore, current through $1 H$,Io=31=3AWhen S is opened, at t=0s, current through R=Io=3AAs t=∞, If=32=1.5ANow time constant =ReqL=31=3s−1At time t, let i(t)=a+be−3tat t=0 3=a+bat t=∞ a=1.5Therefore i(t)=1.5(1+e−3t)A

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