Question

Consider the following series circuit shown in figure. For series resonance, the value of coupling coefficient, k will be

• A. 1
• B. 0.999
• C. 0.25
• D. 5

Answer 1

The correct option is C 0.25

For series resonance

$|X_L|=|X_C|$

$X_C=-j12\Omega$

$X_L=j2+j8+j2M$

$X_L=j10+j2k\sqrt{16}(M=k\sqrt{L_1{L}_2})$

$X_L=j10+j8k$

$j2=j10+j8k$

$j2=j8k$

$\Rightarrow k=\frac{2}{8}=0.25$