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GATE 2018 EC – Question 46

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

For the circuit given in the figure, the magnitude of the loop current (in amperes, correct to three decimal places) 0.5 second after closing the switch is ________.

Diagram for GATE 2018 EC question 46

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Correct answer: 0.31 to 0.33

Explanation

The loop has the 1 V source and $1\ \Omega+1\ \Omega$ in series with the $1$ H inductor, so $\tau=\frac LR=0.5$ s and $i(t)=\frac12\left(1-e^{-2t}\right)$. At $t=0.5$ s, $i=0.5(1-e^{-1})=0.316$ A.