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An air cored coil having a winding resistance of 10 Ω is connected in series with a variable capacitor Cx. The series circuit is excited by a 10 V sinusoidal voltage source of angular frequency 1000 rad/s. As the value of the capacitor is varied, a maximum voltage of 30 V was observed across it. Neglecting skin-effect, the value of the inductance of the coil in millihenry is ________

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Magnitude of  maximum Voltage across capacitor is

VCmax = QV

⇒ 30 = Q 10

⇒ Q = 3 = quality factor

⇒ Q = factor of a coil is Q = ωL/R


L = inductance of the circuit

R = Resistance of the circuit

⇒ 3 = (10× L)/10

L = 30 mH

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