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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 kHzI 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» 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.


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