Question

A coil (which can be modelled as a series RL circuit) has been designed for a high Quality Factor (Q) performance. The voltage is rated at and a specified frequency. If the frequency of operation is increased 10 times and the coil is operated at the same rated voltage. The new value of Q factor and the active power P will be? (a) P is doubled and Q is halved (b) P is halved and Q is doubled (c) P remains constant and Q is doubled (d) P decreases 100 times and Q is increased 10 times The question was posed to me during an internship interview. This question is from Problems of Series Resonance Involving Quality Factor topic 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

Correct option is (d) P decreases 100 times and Q is increased 10 times The best explanation: ω2 L = 10 ω1 LR will remain constant ∴ Q2 = \frac{10 ω_1 L}{R} = 10 Q1 That is Q is increased 10 times. Now, I1 = \frac{V}{ω_1 L} For a high Q coil, ωL >> R, I2 = \frac{V}{10 ω_1 L} = \frac{I_1}{10} ∴ P2 = R (\frac{I_1}{10})^2 = \frac{P_1}{100} Thus, P decreases 100 times and Q is increased 10 times.