New Member, need help

[tmccord]

I cannot for the life of me figure out how to solve this problem:

An induction motor ( lagging pf ) draws 37.1 amps from a 440_v 60_cps line. A resistance across ( parallel to the motor ) the line draws 19 amps. An ammeter connected to the line reads a total of 53.6 amps.

A) What is the pf of the motor?

The answer given in the back of the book is .805

Any ideas?

Thanks

 

[Laplace]

Draw a phasor diagram of the given currents. There is the 19 A resistor current at zero phase angle; the 37.1 A motor current at some lagging phase angle (the cosine of this angle will be the power factor); and the total current of 53.6 A at some phase angle between the other two. The essential fact here is that at some particular phase angle for the 37.1 phasor the difference between the 37.1 and 53.6 phasors will exactly equal 19+j0. Find that angle and take the cosine. You may be able to do this with trigonometric identities but I used a numerical approximation technique to estimate the angle as 36.3444 degrees. Interestingly, arcos(0.805)=36.39 degrees. The book answer is pretty close to being correct.

 

[Laplace]

It turns out that the trigonometric solution using phasor algebra is extremely simple because of the fact that: sin^2 + cos^2 =1. This confirms the book solution.