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GATE 2021 EE – Question 24

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Numerical answer

In the given circuit, the value of capacitor C that makes current $I=0$ is ________ $\mu$F.

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Correct answer: 20

Explanation

At $\omega=5$ krad/s, $I=0$ requires the impedance seen by the source to be infinite. The shunt inductor $j5\ \Omega$ is in parallel with the branch $j5\ \Omega$ in series with the capacitor ($-jX_C$), so the parallel impedance is infinite when the two susceptances cancel: $j5+j(5-X_C)=0$, i.e. $X_C=10\ \Omega$. Then $C=\frac{1}{\omega X_C}=\frac{1}{5000\times10}=20\ \mu$F.