Question

In the circuit given below, the series circuit shown in figure, for series resonance, the value of the coupling coefficient, K will be?

(a) 0.25

(b) 0.5

(c) 0.1

(d) 1

The question was posed to me in an online interview.

Question is from Advanced Problems on Application of Laplace Transform in chapter Application of the Laplace Transform in Circuit Analysis of Network Theory

Answer 1

Right choice is (a) 0.25

Explanation: Mutual inductance wm = ω k \(\sqrt{L_1 L_2}\)

Or, m = k.2.8 j^2

= 4k.j

At resonance, Z = 20 – j10 + j2 + j6 + 2.4kj – 2j + 8kj = 0

Or, -2 = -8k

Or, k = \(\frac{1}{4}\) = 0.25.