GATE 2023 EC – Question 18

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Multiple choice

A series $RLC$ circuit has a quality factor $Q$ of 1000 at a center frequency of $10^6$ rad/s. The possible values of $R$, $L$ and $C$ are

$R=1\ \Omega,\ L=1\ \mu H$ and $C=1\ \mu F$
$R=0.1\ \Omega,\ L=1\ \mu H$ and $C=1\ \mu F$
$R=0.01\ \Omega,\ L=1\ \mu H$ and $C=1\ \mu F$
$R=0.001\ \Omega,\ L=1\ \mu H$ and $C=1\ \mu F$

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Correct answer: (D) $R=0.001\ \Omega,\ L=1\ \mu H$ and $C=1\ \mu F$

Explanation

For a series RLC circuit $Q=\dfrac{\omega_0L}{R}$ with $\omega_0=1/\sqrt{LC}$. With $L=1\ \mu$H and $C=1\ \mu$F, $\omega_0=10^6$ rad/s, so $\omega_0L=1\ \Omega$. Then $Q=1/R=1000$ gives $R=0.001\ \Omega$.