Question

For the circuit shown in the figure below, the value of R for critical damping will be? (a) 10.5 Ω (b) 8.57 Ω (c) 3.5 Ω (d) 3 Ω I got this question by my college professor while I was bunking the class. My question is based upon Advanced Problems on Resonance in division 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 answer is (b) 8.57 Ω Easiest explanation: For a parallel RLC circuit, \frac{d^2 V}{dt^2} + \frac{1}{RC} \frac{dV}{dt} + \frac{V}{LC} = 0 Solving the 2nd order differential equation, we get, 2rωn = \frac{1}{RC} and ωn = \frac{1}{\sqrt{LC}} As, r=1, ∴ R = \frac{1}{2} \sqrt{\frac{L}{C}} = \frac{1}{2} \sqrt{\frac{7}{\frac{1}{42}}} = \frac{1}{2} × 17.15 = 8.57 Ω.