GATE EC 2026 Set 1 — Question 31
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Network Theory → Transient & AC Analysis → Resonance in RLC Circuits
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Question
Consider the circuit shown in the Figure, where the input is in Volt.The average power (in mW) dissipated in the load resistance of at the resonant frequency is __.(rounded off to two decimal places)
Correct answer
71.5 to 72.5
Solution
In the given circuit, the voltage source is connected directly in parallel with the capacitor (), the inductor (), and the load resistor ().
1.Identify the voltage across the resistor: Since the resistor is in parallel with the ideal voltage source, the voltage across the resistor is .
2.Calculate the RMS voltage: The peak voltage is . The RMS voltage is given by:
3.Calculate the average power: The average power dissipated in a resistor is given by .
4.Convert to mW:
Note: At the resonant frequency, the parallel combination of and has infinite impedance (it acts as an open circuit), so the total current from the source is equal to the current through the resistor. However, because it is an ideal voltage source, the power dissipated in the resistor is independent of the frequency and the other parallel components.Continue learning with Success Tracker
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