Question

For the series circuit given below, the value of the voltage across the capacitor and inductor are _____________ (a) VC = 16.306 V; VL = 16.306 V (b) VC = 11.268 V; VL = 11.268 V (c) VC = 16.306 V; VL = 16.306 V (d) VC = 14.441 V; VL = 14.441 V I have been asked this question at a job interview. This intriguing question comes from Problems of Parallel 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

Right option is (c) VC = 16.306 V; VL = 16.306 V Best explanation: Resonant Frequency, \(\frac{1}{2π\sqrt{LC}} \) = \(\frac{1}{6.28\sqrt{(4.7×10^{-3})(0.001×10^{-6})}}\) = \(\frac{1}{6.28\sqrt{4.7×10^{-12}}}\) = \(\frac{1}{1.362×10^{-5}}\) = 73.412 kHz Inductive Reactance, XL = 2πfL = (6.28) (73.142 × 10^3)(4.7 × 10^-6) = 2.168 kΩ Capacitive Reactance, XC = \(\frac{1}{2πfC} = \frac{1}{(6.28)(73.142×10^3)(0.001×10^{-6})}\) = \(\frac{1}{4.613×10^{-4}}\) = 2.168 kΩ ZEQ = R = 47 Ω IT = \(\frac{V_{in}}{Z_{EQ}} = \frac{V_{in}}{R} = \frac{0.3535}{47}\) = 7.521 mA ∴ Voltage across the capacitor, VC = XCIT = (2.168 kΩ)(7.521 mA) = 16.306 V ∴ Voltage across the inductor, VL = XLIT = (2.168 kΩ)(7.521 mA) = 16.306 V.