Question

In the figure below, the values of the resistance R1 and inductance L1 of a coil are to be calculated after the bridge is balanced. The values are _________________ (a) 375 Ω and 75 mH (b) 75 Ω and 150 mH (c) 37.5 Ω and 75 mH (d) 75 Ω and 75 mH I have been asked this question in an international level competition. This key question is from Problems Involving Coupling Coefficient in chapter 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 choice is (a) 375 Ω and 75 mH To elaborate: Applying the usual balance condition relation, Z1 Z4 = Z2 Z3 We have, (R1 + jL1 ω) \frac{R_4/jωC_4}{R_4+1/jωC_4} = R2 R3 Or, R1 R4 + jL1 ωR4 = R2 R3 + j R2 R3 R4 C4 ω ∴ R1 = 2000 × \frac{750}{4000} = 375 Ω ∴ L1 = 2000 × 750 × 0.5 × 10^-6 = 75 mH.