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The quality factor of the coil for a series circuit having R = 10Ω, L = 0.1H, C = 10µF.

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The quality factor of the coil for a series circuit having R = 10Ω, L = 0.1H, C = 10µF.

(a) 1

(b) 5

(c) 10

(d) 15

This question was posed to me by my college director while I was bunking the class.

This key question is from Bandwidth of an RLC Circuit topic in portion Resonance & Magnetically Coupled Circuit of Network Theory

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Correct answer is (c) 10

Easy explanation: The resonant frequency is given by fr = 1/(2π√LC)=1/(2π√(0.1×10×10^-6))=159.2 Hz. The relation between quality factor, resonant frequency and bandwidth is Q = fr/BW = 2πfrL/R = (6.28×159.2×0.1)/10=10.

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