GATE 2021 EE – Question 31

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

A signal generator having a source resistance of $50\ \Omega$ is set to generate a 1 kHz sinewave. Open circuit terminal voltage is 10 V peak-to-peak. Connecting a capacitor across the terminals reduces the voltage to 8 V peak-to-peak. The value of this capacitor is ________ $\mu$F. (Round off to 2 decimal places.)

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Correct answer: 2.30 to 2.50

Explanation

The capacitor forms a divider with the source resistance: $\frac{X_C}{\sqrt{50^2+X_C^2}}=\frac{8}{10}=0.8$. So $X_C^2=0.64(2500+X_C^2)$, giving $0.36X_C^2=1600$ and $X_C=66.67\ \Omega$. Then $C=\frac{1}{2\pi\times1000\times66.67}=2.39\ \mu$F.