GATE EC 2016 Set 2 — Question 18
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Network Theory → Transient & AC Analysis → Resonance in RLC Circuits
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Question
The figure shows an RLC circuit with a sinusoidal current source.
At resonance, the ratio , i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________
Correct answer
0.3 to 0.34
Solution
In a parallel RLC circuit, the resonant frequency is given by:Given:
Calculating :At resonance, the impedance of the parallel combination is purely resistive and equal to . The voltage across the parallel branches is:The magnitude of the current through the inductor is:The required ratio is:The value is approximately 0.316, which falls within the specified range of 0.30 to 0.34.
Calculating :At resonance, the impedance of the parallel combination is purely resistive and equal to . The voltage across the parallel branches is:The magnitude of the current through the inductor is:The required ratio is:The value is approximately 0.316, which falls within the specified range of 0.30 to 0.34.
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