NCEES Problem 523

Can someone please offer an alternate solution/explanation for Problem 523?

If I hadn't seen this problem ever before, and suppose it appears for the first time on the exam next week, it would not have dawned upon me that I would have approached this using their solution of drawing out the full-load and half-load current phasor diagrams.

I guess I'm looking for suggestions on solving this from another perspective, if anyone can offer one.

I'm having a hard time trying to understand how they weaved together the principles of AC motor half-load/full-load current draws and power factor.

Thanks!

This is a "fun with the power triangle" question.

At no-load, the apparent power consumed by the motor will be mostly reactive. This value will remain constant regardless of the load placed on the motor. This will be the reactive side of the triangle.

They then give you the magnitude of the full load current. This is the hypotenuse (sp?) of the triangle.

You need to find the the "real" current for the motor at full load in order to determine the real current at half load.

The two sides of the triangle you have then are the real current at half-load and the 28amps reactive that are always there.

Once you have these values, you can determine the angle and the power factor.

Not sure if this helps or I'm just repeating what NCEES did.

Jim