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