GATE 2017 EC (EC2) – Question 41

Networks, Signals and Systems · Time and Frequency Domain Analysis of Linear Circuits · 2 marks · Numerical answer

The switch in the circuit shown was open for a long time and is closed at t=0. The current $i(t)$ through the switch, in amperes, at t=0.5 s is ________.

Diagram for GATE 2017 EC (EC2) question 41

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Correct answer: 8.0 to 8.3

Explanation

Before switching, the inductor is a DC short. The two 5 Ω branches share the 10 A source equally, so the inductor current is $i_L(0^-)=5$ A. Inductor current is continuous at switching.

Closing the switch shorts the branch terminals. The separate 5 Ω resistor then carries zero current, and the inductor–resistor branch has natural response $i_L(t)=5e^{-Rt/L}=5e^{-2t}$ A.

KCL gives switch current $i(t)=10-i_L(t)$. At 0.5 s this is $10-5e^{-1}=$ **8.1606 A**, within the official 8.0–8.3 A interval.

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