Question

For the series resonant circuit given below, the value of the equivalent impedance of the circuit is ________ (a) 55 Ω (b) 47 Ω (c) 64 Ω (d) 10 Ω I got this question in a national level competition. I want to ask this question from Problems of Parallel Resonance Involving Quality Factor topic 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

Right answer is (b) 47 Ω Easy 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 We see that, XC = XL are equal, along with being 180° out of phase. Hence the net reactance is zero and the total impedance equal to the resistor. ∴ ZEQ = R = 47 Ω.