GATE 2023 EC – Question 44
The switch $S_1$ was closed and $S_2$ was open for a long time. At $t=0$, switch $S_1$ is opened and $S_2$ is closed, simultaneously. The value of $i_c(0^+)$, in amperes, is
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Correct answer: (B) -1
Explanation
Before $t=0$ (DC steady state) the capacitor is open and the inductor is a short. The 1 A source divides between the 25 Ω and the 100 Ω + inductor branch: the inductor current is $1\times\dfrac{25}{125}=0.2$ A and the capacitor voltage is $0.2\times100=20$ V. At $t=0^+$, $S_1$ opens (source removed) and $S_2$ shorts the 100 Ω, but the inductor current stays 0.2 A and the capacitor voltage stays 20 V. KCL at the top node (downward currents): $i_c+0.2+\dfrac{20}{25}=0$, so $i_c(0^+)=-1$ A.