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