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GATE 2019 EC – Question 40

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

In the circuit shown, if $v(t)=2\sin(1000t)$ volts, $R=1\ \text{k}\Omega$ and $C=1\ \mu$F, then the steady-state current $i(t)$, in milliamperes (mA), is

Diagram for GATE 2019 EC question 40
  1. $\sin(1000t)+\cos(1000t)$
  2. $2\sin(1000t)+2\cos(1000t)$
  3. $3\sin(1000t)+\cos(1000t)$
  4. $\sin(1000t)+3\cos(1000t)$

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Correct answer: (C) $3\sin(1000t)+\cos(1000t)$

Explanation

At $\omega=1000$ rad/s, $\omega RC=1$, so every capacitor has a reactance of $1\ \text{k}\Omega$, equal to $R$. Reducing the delta network of these equal impedances gives an input admittance of $(1.5+j0.5)$ mS, so with $V=2\angle0^\circ$ (sine reference) the current is $(3+j1)$ mA, which is $3\sin(1000t)+\cos(1000t)$.