Question

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

(a) 35.156

(b) 56.118

(c) 50.294

(d) 46.128

This question was addressed to me in final exam.

The above asked question is from Problems of Parallel Resonance Involving Quality Factor in portion Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right choice is (d) 46.128

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

= \(\frac{1}{6.28\sqrt{(4.7×10^{-3})(0.001×10^{-6})}}\)

= \(\frac{1}{6.28\sqrt{4.7×10^{-12}}}\)

= \(\frac{1}{1.362×10^{-5}}\) = 73.412 kHz

Inductive Reactance, XL = 2πfL = (6.28) (73.142 × 10^3)(4.7 × 10^-6)

= 2.168 kΩ

Quality factor Q = \(\frac{X_L}{R} = \frac{2.168 kΩ}{47}\) = 46.128.