Question

For the series resonant circuit given below, the value of the quality factor is ___________

(a) 15

(b) 36

(c) 25

(d) 10

This question was addressed to me by my school principal while I was bunking the class.

Query is from Problems of Series Resonance Involving Quality Factor topic in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

The correct choice is (d) 10

The explanation: Resonant Frequency, FR = \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(5 × 10^{-3})(0.02 × 10^{-6})}}\)

= \(\frac{1}{6.28\sqrt{10^{-10}}}\)

= \(\frac{1}{6.28 × 10^{-5}}\) = 15.9 kHz.

Inductive Reactance, XL = 2πfL = (6.28) (15.92 × 10^3)(5 × 10^-6)

= 0.5 kΩ

∴ Quality factor Q = \(\frac{X_L}{R} = \frac{0.5 kΩ}{50}\) = 10.