2 Wattmeter are used to measure power in a 3ø balanced star connected load using the 2 wattmeter method. The reading of the 2 wattmeter are 8kw & 4kw. Calculate total power consumed by the 3ø load and the power factor. -

$w_1=8kw \hspace{2cm} w_2=4kw \\ P=w_1+w_2=12kw \\ \text{Assume logging pf} \\ \emptyset=\tan^{-1}\bigg[\sqrt3\bigg(\dfrac{w_1-w_2}{w_1+w_2}\bigg)\bigg] \\ =\tan^{-1}\bigg[\sqrt3\bigg(\dfrac{4}{12}\bigg)\bigg] \\ =\tan^{-1}\bigg[\bigg(\dfrac{1}{\sqrt3}\bigg)\bigg] \\ =30^0 \\ \cos \emptyset=0.866(logging)$