Question

For the series resonant circuit given below, the value of the inductive and capacitive reactance is _________ (a) XL = 5.826 kΩ; XC = 5.826 kΩ (b) XL = 2.168 kΩ; XC = 2.168 kΩ (c) XL = 6.282 kΩ; XC = 6.282 kΩ (d) XL = 10.682 kΩ; XC = 10.682 kΩ I have been asked this question in my homework. I'm obligated to ask this question of Problems of Parallel Resonance Involving Quality Factor topic 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

The correct option is (c) XL = 6.282 kΩ; XC = 6.282 kΩ The best I can explain: 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.