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GATE 2015 EC – Question 16

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Numerical answer

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ________.

A source $10\cos\omega t$ V in series with a $4\ \Omega$ resistor, a $0.1$ mH inductor and a $1\ \mu$F capacitor.

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Correct answer: 24 to 26

Explanation

At resonance $\omega = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{10^{-4} \times 10^{-6}}} = 10^5$ rad/s. The current is limited only by the resistance, so $I = \frac{10}{4} = 2.5$ A. The capacitor reactance is $\frac{1}{\omega C} = 10\ \Omega$, so the capacitor voltage is $2.5 \times 10 = 25$ V.