1.

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 mHI 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

Answer»

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.



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