# Parallel R-L circuits, modeled motor

## 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.

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!

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Astronuc
Staff Emeritus
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
Staff Emeritus
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