Appologies, this isn't actually a homework problem, but I thought that this may be the best place to get academic input. Which is the correct way to solve this? Find the total VA and PF for a circuit with the two loads: Apparent Load 1 = 250 VA w/ 0.75 PF Apparent Load 2 = 150 VA w/ 0.90 PF Method 1 Real Power 1 = 0.75 * 250 = 187.5 W Real Power 2 = 0.90 * 150 = 135 W Total Apparent Load = 250 VA + 150 VA = 400 VA Total Real Power = 187.5 + 135 = 322.5 W Resulting Power Factor = 322.5 / 400 = 0.80625 Method 2 Real Power 1 = 0.75 * 250 = 187.5 W Real Power 2 = 0.90 * 150 = 135 W Total Real Power = 187.5 + 135 = 322.5 W Reactive Power 1 = sqrt(250^2 187.5^2) = 165.36 VAR Reactive Power 2 = sqrt(150^2 135^2) = 65.38 VAR Total Reactive Power = 230.7 VAR Total Apparent Power = sqrt(322.5^2 + 230.74^2) = 396.55 VA Resulting Power Factor = 322.5 / 396.55 = 0.813
Thanks, t_n_k. I found this http://www.ccontrolsys.com/w/Electrical_Measurement_Math that confirms. I'm looking for any other references that confirm this... if you happen to be aware of anything else, I'd be interested.
How about just doing the math from the definitions. Do you know about complex power? If so, things are very easy. If not, then things are a bit harder, but not too much.
You are neglecting to take into account whether the power factor is leading or lagging. If both are leading or both are lagging, then you will get the results in Method 2. But if one is leading and the other is lagging, which is precisely the case when you are doing power factor correction, then you have to take that into account.