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GATE 2018 EC – Question 45

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Multiple choice

For the circuit given in the figure, the voltage $V_c$ (in volts) across the capacitor is

Diagram for GATE 2018 EC question 45
  1. $1.25\sqrt2\sin(5t-0.25\pi)$
  2. $1.25\sqrt2\sin(5t-0.125\pi)$
  3. $2.5\sqrt2\sin(5t-0.25\pi)$
  4. $2.5\sqrt2\sin(5t-0.125\pi)$

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Correct answer: (C) $2.5\sqrt2\sin(5t-0.25\pi)$

Explanation

The two $100\ \text{k}\Omega$ resistors total $200\ \text{k}\Omega$ in series with the $1\ \mu$F capacitor, whose reactance at $\omega=5$ is $\frac{1}{5\times10^{-6}}=200\ \text{k}\Omega$. The divider gives $\frac{V_c}{V_s}=\frac{-j200}{200-j200}=\frac{1}{\sqrt2}\angle-45^\circ$, which for the source of amplitude 5 V gives $\frac{5}{\sqrt2}=2.5\sqrt2$ V amplitude at $-0.25\pi$.