# GATE 2015 EE – SET 2 – Question 47

Solution :

$$N_{1}$$ = 100 , $$N_{2}$$=50 ,$$N_{3}$$ = 50

$$I_{2}$$ = 2$$\angle 30^{0}$$
$$I_{3}$$ = 2$$\angle 150^{0}$$
$$I_{1}$$ = ?

I $$\alpha$$$$\frac{1}{N}$$
$$\frac{I_{A}}{I_{B}}$$ = $$\frac{N_{B}}{N_{A}}$$

$$I_{A}$$ = $$\frac{N_{B}}{N_{A}} * I_{B}$$

$$I_{1}$$ = $$\frac{N_{2}}{N_{1}}*I_{2} + \frac{N_{3}}{N_{1}}*I_{3}$$

$$I_{1}$$ =$$\frac{50}{100}\left [2\angle 30^{0}\right ] + \frac{50}{100}\left [ 2\angle 150^{0} \right ]$$

$$I_{1}$$ =1$$\angle 30^{0}+1\angle 150^{0}$$

$$I_{1}$$ = (0.87 + 0.5j) + (-0.87 +0.5j)

$$I_{1}$$ = 1J = 1$$\angle 90^{0}$$