GATE 2016 EC (EC2) – Question 44

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

The switch has been closed for a long time and opens at $t=0$, remaining open. The diode has zero forward drop and zero reverse current. The steady-state magnitude of capacitor voltage $V_C$ in volts is ________.

Diagram for GATE 2016 EC (EC2) question 44

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Correct answer: 99 to 101

Explanation

Before opening, the inductor is a DC short and carries $I_0=10/1=10$ A; the capacitor is uncharged. After the source is disconnected, the inductor transfers its stored energy to the capacitor through the ideal diode.

At the first inductor-current zero, the diode blocks reversal and traps the capacitor voltage. Energy conservation gives $\tfrac12LI_0^2=\tfrac12CV_C^2$.

Thus $|V_C|=10\sqrt{(1\mathrm{\ mH})/(10\mathrm{\ \mu F})}=$ **100 V**.

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