Question

In 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. 0.999
• D. 1.0

Answer 1

The correct option is A 0.25

At resonance

$X_L-X_C=0$

$|X_L|=|X_C|$

$|X_L|=|j12|$

$X_L=j12$

$X_L=X_{L_1}+X_{L_2}+2k\sqrt{X_{L_1}\times X_{L_2}}$

$X_L=j2+j8+2k\sqrt{j2\times j8}=j12$

$2kj4=j2$

$k=0.25$