Home › Previous year questions › GATE 2016 EC (EC2) › Question 18GATE 2016 EC (EC2) – Question 18 Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Numerical answer
The figure shows a parallel RLC circuit with a sinusoidal current source. At resonance, the ratio $|I_L|/|I_R|$ of the inductor and resistor current phasor magnitudes is ________.
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Show answer and explanation Correct answer: 0.30 to 0.34
Explanation At parallel resonance, $\omega_0=1/\sqrt{LC}$. All three branches have the same voltage magnitude V, so $|I_L|/|I_R|=R/(\omega_0L)$.
With R=10 Ω, L=10 mH and C=10 μF, $\omega_0=3162.28$ rad/s. Thus the ratio is $10/(3162.28\cdot0.01)=$ **0.31623**, within 0.30–0.34.
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