GATE EC 2025 Set 1 — Question 39
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Network Theory → Transient & AC Analysis → Resonance in RLC Circuits
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Question
In the circuit below, is an ideal AC voltmeter and is an ideal AC ammeter. The source voltage (in Volts) is .
What should be the value of the variable capacitor such that the RMS readings on and are and , respectively?
Correct answer
(A) \(25 μF\)
Solution
The source voltage is , so the angular frequency is .
The voltmeter measures the RMS voltage across the load branch, .
The ammeter measures the RMS current through the load branch, .
The impedance of the load branch (consisting of , , and in series) is:
.The complex impedance is .
For , the imaginary part must be zero (resonance condition):
.
Correct option is (A).
The voltmeter measures the RMS voltage across the load branch, .
The ammeter measures the RMS current through the load branch, .
The impedance of the load branch (consisting of , , and in series) is:
.The complex impedance is .
For , the imaginary part must be zero (resonance condition):
.
Correct option is (A).
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