Question

For the series resonant circuit given below, the bandwidth is ____________

(a) ±351 Hz

(b) ±796 Hz

(c) ±531 Hz

(d) ±225 Hz

The question was asked in an online quiz.

This is a very interesting question from Problems of Series Resonance Involving Quality Factor topic in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct option is (b) ±796 Hz

Easiest 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

∴ ∆F = \(\frac{f}{Q} = \frac{15.9 kHz}{10}\) = 1.592 kHz

∴ Bandwidth = \(\frac{∆F}{2}\) = ±796 Hz.