Complex Imaginary Exam 1 Prob 34

[ElecPwrPEOct11]

This is a simple problem with two 5kVA motors in parallel, one with PF=0.75 and the second with PF=0.65 both lagging. The question asks to find the total system power factor. The relevant answers are:

B ) 0.69

C) 0.71

The right way to do this problem is find the complex power for each and add them. 5 <41.41 + 5 <49.458= 9.97 <45.434. Cos 45.434 = 0.7017. Ideally I'd say the answer is neither B nor C but 0.7. But the book answer is C.

Common sense tells me it should be a straight average of the two PFs, so 0.7. Carrying 4 decimals through the calc I get the PF= 0.7017. I want to make sure I'm doing this right as I was certainly pulling hairs while taking this practice test. This test's answers are so close together that rounding can cause an incorrect answer. Does the PE play this game?

 

[Flyer_PE]

I get 0.701 for the power factor of the system. However, an average of the two power factors won't get you there since power factor is not a linear function (cosine of an angle).

 

[ElecPwrPEOct11]

I get 0.701 for the power factor of the system. However, an average of the two power factors won't get you there since power factor is not a linear function (cosine of an angle).

OK my common sense of taking a straight average is wrong. Thanks for calling me out on that Flyer_PE. Do you remember questions on the PE that had answers choices that so closely 'straddled' the calculated answer like this problem?

 

[Flyer_PE]

^Not really. I think they try to put a couple of wrong answers that you would get if you forget about applying a multiplier or something. I wouldn't expect anything to require you to carry all the digits in the calculator to arrive at the correct answer.

 

[ElecPwrPEOct11]

^Not really. I think they try to put a couple of wrong answers that you would get if you forget about applying a multiplier or something. I wouldn't expect anything to require you to carry all the digits in the calculator to arrive at the correct answer.

Phew, thanks Flyer_PE. That seems like a more reasonable exam approach.