GATE 2015 EE - SET 2 - Question 6

Solution :

 cos\phi = 0.707
\phi = cos^{-1}(0.707)= 45^{0}

W_{1}+ W_{2} = 5kW   --------------- (1)

tan\phi = \frac{\sqrt{3}(W_{1}-W_{2})}{W_{1}+W_{2}}

tan 45   = \frac{\sqrt{3}(W_{1}-W_{2})}{5}

W_{1} - W_{2} = \frac{5}{\sqrt{3}}  --------------------(2)

W_{1} + W_{2} = 5

W_{1}-W_{2}\frac{5}{\sqrt{3}}

Solving the two equations above

W_{1} = 3.94 kW

W_{2} = 1.06 kW