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
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