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 Select the correct answer from above options network theory questions and answers, network theory questions pdf, network theory question bank, network theory gate questions and answers pdf, mcq on network theory pdf, gate network theory questions and solutions, network theory mcq Test , ies network theory questions, Network theory Questions for GATE EC Exam, Network Theory MCQ (Multiple Choice Questions)

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.