# GATE 2015 EE - SET 1 Question 22

Solution :

$L_{1}$ = 800 m H ,$L_{2}$ =600 m H , m = 480 m H

$L_{eff}$ = ?

$X_{L_{(eff)}}$ = $\left [ jX_{1} +\frac{w^{2}M^{2}}{jX_{2}}\right ]$

$X_{L}$ = $j \left [ X_{1}-\frac{w^{2}M^{2}}{X_{2}} \right ]$

$X_{1}$ = 2$\pi f L_{1}$  = 2 * 3.14 *50*0.8 = 251.2

$X_{2}$  = 2$\pi f L_{2}$ = 2 * 3.14 *50*0.6 = 188.4

$\omega$ = 2$\pi f$= 314

$X_{L_{(eff)}}$ = $\left [ jX_{1} +\frac{w^{2}M^{2}}{jX_{2}}\right ]$

$X_{L}$= j$\left [ 251.2-\frac{(314)^{2}(0.48)^{2}}{188.4} \right ]$

$X_{L}$ = j 130.624

j 2$\pi f L_{eff}$ = j 130.624

$L_{eff}$ = $\frac{130.624}{314}$  = 0.416 = 416 *  $10^{-3}$ = 416 m H