GATE EC 2014 Set 2 — Question 40
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Network Theory → Transient & AC Analysis → Resonance in RLC Circuits
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Question
A series LCR circuit is operated at a frequency different from its resonant frequency. The operating frequency is such that the current leads the supply voltage. The magnitude of current is half the value at resonance. If the values of , and are 1 H, 1 F and 1 , respectively, the operating angular frequency (in rad/s) is ________.
Correct answer
0.45 to 0.47
Solution
In a series LCR circuit, the current at resonance is .
At any angular frequency , the current magnitude is .
Given , we have:Since the current leads the supply voltage, the circuit is capacitive ():Substituting :Using the quadratic formula :Since , we take the positive root:
At any angular frequency , the current magnitude is .
Given , we have:Since the current leads the supply voltage, the circuit is capacitive ():Substituting :Using the quadratic formula :Since , we take the positive root:
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