GATE 2014 EC (EC2) – Question 40
A series LCR circuit operates off resonance with current leading supply voltage. Current magnitude is half its resonant value. Given L = 1 H, C = 1 F and R = 1 Ω, find operating angular frequency (rad/s).
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Show answer and explanation
Correct answer: 0.45 to 0.47
Explanation
At resonance the impedance is R=1Ω. Half the resonant current requires |Z|=2Ω, giving|ω−1/ω|=√3 for L=C=1. Current leads voltage, so reactance is negative:ω−1/ω=−√3. Solving ω²+√3ω−1=0 gives **ω=(√7−√3)/2=0.456850rad/s**.