Question

A 50 μF capacitor, when connected in series with a coil having resistance of 40Ω, resonates at 1000 Hz. The circuit is in resonating condition. The voltage across the coil is __________ (a) 100.31 V (b) 200.31 V (c) 300.31 V (d) 400.31 V The question was asked in examination. This interesting question is from Advanced Problems on Resonance in section 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

The correct choice is (a) 100.31 V To explain: At resonance, | I | = \frac{V}{Z} = \frac{V}{R} Given that, R = 40Ω and V = 100 V ∴ | I | = \frac{100}{40} = 2.5 A XL = ωL = 2π × 1000 × 0.5 × 10^-3 = 2π × 0.5 = 3.14 Ω ∴ VCOIL = I Z (At resonance) = 2.5 \sqrt{40^2 + 3.14^2} = 2.5 × 40.122 = 100.31 V.