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GATE 2020 EE – Question 55

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 · 2 marks · Numerical answer

A resistor and a capacitor are connected in series to a 10 V dc supply through a switch. The switch is closed at $t=0$, and the capacitor voltage is found to cross 0 V at $t=0.4\tau$, where $\tau$ is the circuit time constant. The absolute value of percentage change required in the initial capacitor voltage if the zero crossing has to happen at $t=0.2\tau$ is ________ (rounded off to 2 decimal places).

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Correct answer: 54.00 to 56.00

Explanation

The capacitor voltage is $v(t)=10+(V_0-10)e^{-t/\tau}$. The zero crossing at $0.4\tau$ gives $V_0=10(1-e^{0.4})=-4.918$ V, and at $0.2\tau$ it needs $V_0'=10(1-e^{0.2})=-2.214$ V. The change is $\frac{4.918-2.214}{4.918}=55\%$.