Question

Two impedances $Z_1$ and $Z_2$ are connected in series with the primary and secondary winding of an ideal transformer as shown in the figure below, where the primary coil has $j6\Omega$ and secondary coil has $j9\Omega$ reactance. The mutual inductance if $\omega =1000$ rad/sec is ____ $mH$

• A. 7.35

Answer 1

The correct option is A 7.35
For an ideal trnasformer, $K=1$
$\therefore M=\sqrt{L_1{L}_2}$
Given, $X_{L1}=j\omega L_1=6j$ and
$X_{L2}=j\omega L_2=9j$
$\therefore M=\sqrt{\frac{6j}{j\omega }\times \frac{9j}{j\omega }}=\frac{1}{\omega }\sqrt{6\times 9}$
$=\frac{7.35}{\omega }=\frac{7.35}{1000}=7.35mH$