GATE 2020 IN – Question 43

Electrical Circuits and Machines · AC circuits and resonance: Peak, average and rms values, apparent, active and reactive power, power factor, phasor analysis, impedance and admittance, series and parallel resonance, locus diagrams, basic filters with R, L and C elements · 2 marks · Numerical answer

The series circuit shown has R = 100 Ω, L = 100 mH, C = 10 μF and source $100\sqrt2\cos(1000t)$ V. Find the RMS current in A.

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Correct answer: 1 to 1

Explanation

At $\omega=1000$ rad/s, inductive reactance is $\omega L=100$ Ω and capacitive reactance is $1/(\omega C)=100$ Ω. They cancel, leaving purely resistive impedance 100 Ω. The source RMS voltage is 100 V because its peak is $100\sqrt2$ V. Thus RMS current is $100/100=1$ A.

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