Parallel R-L circuits, modeled motor

[Bradracer18]

Homework Statement

A 0.5hp motor is observed to draw 1000W and 10 A when connected across a 120V, 60 Hz source.

The motor can be modeled as a parallel R-L circuit. Sketch the phasor diagram and find the values for R and L.

---There are more questions to this, but I might be able to do them, so want to start here. I can't understand how to get the answers in the back of the book(both in Ohms).

The answers are 14.4 and 21.7 Ohms.

Homework Equations

Not sure yet...

The Attempt at a Solution

My phasor diagram has voltage(E=120V) leading Current(I=10A) by 90 degrees. So, in other words, the voltage arrow points in the + x direction and the I points somewhere down at an angle between 0 and -90 degrees(on a conventional x-y axis).


I can't even get started...so any help to get me started would be great!

Brad

 

[Astronuc]

For reference here is some info on a parallel R-L circuit.

Parallel resistor-inductor circuits
http://www.allaboutcircuits.com/vol_2/chpt_3/4.html


Is there a discussion in one's textbook regarding real, reactive and apparent power?

 

[Bradracer18]

yeah, I have the equations for them.

Total Power VA = IE

Actual Power = P = IEcos(theta)

Reactive Power = Pr = IEsin(theta)I don't see how these help though, I tried to use them, and solved for theta...and got 33.6 degrees...but how does that help, and is that even correct??

 

[Astronuc]

Well how about 1000 W? This is the Real Power!

So P = V²/R => R = V²/P = (120 V)² / (1000 W)

Then Apparent or Total Power = (120 V)(10A) = 1200 VA = S

and S² = P² + Q², where Q is Reactive Power,

and Q = V²/X, where X is the Reactance = $\omega$L for a pure inductive load, and $\omega$ = 2$\pi$f

http://www.allaboutcircuits.com/vol_2/chpt_3/2.html