Question

A 50 μF capacitor, when connected in series with a coil having a resistance of 40Ω, resonates at 1000 Hz. The inductance of the coil for the resonant circuit is ____________ (a) 2.5 mH (b) 1.2 mH (c) 0.5 mH (d) 0.1 mH The question was asked in an international level competition. This key question is from Problems of Series Resonance Involving Quality Factor in portion 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

Correct choice is (c) 0.5 mH To explain: At resonance, XL = XC Or, 2πfL = \frac{1}{2πfC} ∴ L = \frac{1}{4π^2 f^2 C} = \frac{1}{4π^2 × (1000)^2 × 50 × 10^{-6}} = \frac{1}{39.46×50} = 0.0005 So, L = 0.5 mH.