GATE 2021 IN – Question 51
An air-cored coil of winding resistance 10 $\Omega$ is in series with variable capacitor $C_x$. A 10 V sinusoidal source has angular frequency 1000 rad/s. As capacitance varies, the maximum capacitor voltage observed is 30 V. Neglect skin effect. The coil inductance is ______ mH.
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Show answer and explanation
Correct answer: 30 to 30
Explanation
The official key uses the resonance approximation: at XL=XC the series current is V/R=10/10=1 A. With VC=30 V this gives XC=XL=30 Ω, hence L=30/1000=0.03 H=**30 mH**. Strict maximization over capacitance at fixed frequency gives VC,max/V=√[1+(ωL/R)²] and L=28.28 mH; the official scoring answer 30 is retained.