Question

For the parallel resonant circuit, the bandwidth of the circuit is ____________

(a) ±6.25 kHz

(b) ±8.56 kHz

(c) ±10.35 kHz

(d) ±6.37 kHz

I got this question in exam.

I'm obligated to ask this question of Problems of Parallel Resonance Involving Quality Factor in chapter Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Right choice is (a) ±6.25 kHz

Explanation: Resonant Frequency, f = \(\frac{1}{2π\sqrt{LC}} \)

= \(\frac{1}{6.28\sqrt{(100×10^{-6})(162.11×10^{-12})}}\)

= \(\frac{1}{6.28\sqrt{1.621×10^{-14}}}\)

= \(\frac{1}{799×10^{-9}}\) = 1.25 MHz.

Inductive Reactance, XL = 2πfL = (6.28) (1.25×10^6)(100×10^-6)

= 785.394 Ω

Q = \(\frac{X_L}{R} = \frac{785.394}{7.85}\) = 100.05

∴ ∆F = \(\frac{f}{Q} = \frac{1.25 × 10^6}{100.05}\) = 12.5 kHz

Hence, bandwidth = \(\frac{∆F}{2}\) = 6.25 kHz.