Home » Uncategorized » GATE 2015 EE - SET 1 Question 22

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

 

 

Translate »