GATE 2025 IN – Question 64
A signal $V_M=5\sin(\pi t/3)$ V is applied to the shown switch-and-capacitor circuit with $C=0.1\ \mu\mathrm F$. Output $V_x$ feeds an ADC whose input is 10 MΩ in parallel with 0.1 μF. If S opens at $t=0.5$ s, $V_x$ at $t=1.5$ s is ______ V (rounded to two decimal places). Assume ideal components.
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Correct answer: 1.50 to 1.54
Explanation
At opening, $V_x=5\sin(\pi\times0.5/3)=2.5$ V.
The hold capacitor and ADC input capacitor are in parallel, giving $C_{total}=0.2\ \mu\mathrm F$.
The discharge time constant is $RC=(10\times10^6)(0.2\times10^{-6})=2$ s.
The elapsed time is $1.5-0.5=1$ s.
Thus $V_x=2.5e^{-1/2}=1.5163\ldots$ V, giving **1.52 V**.