Question

In the circuit given below, the magnitudes of VL and VC are twice that of VK. Calculate the inductance of the coil, given that f = 50.50 Hz.

(a) 6.41 mH

(b) 5.30 mH

(c) 3.18 mH

(d) 2.31 mH

I have been asked this question during a job interview.

The origin of the question is Problems of Series Resonance Involving Frequency Response of Series Resonant Circuit in division Resonance & Magnetically Coupled Circuit of Network Theory

Answer 1

Correct option is (c) 3.18 mH

To explain I would say: VL = VC = 2 VR

∴ Q = \(\frac{V_L}{V_R}\)  = 2

But we know, Q = \(\frac{ωL}{R} = \frac{1}{ωCR}\)

∴ 2 = \(\frac{2πf × L}{5}\)

Or, L = 3.18 mH.