# Expressing motor loads in polar form

1. Oct 25, 2009

### dumbkiwi

1. The problem statement, all variables and given/known data
I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v.

Express the motor loads as impedances in polar and complex number forms assuming the motors are operating at 400v. This "express" has me baffled and have spent 4 hours trying to get past this bit of the problem. My notes are not clear on the form this should take and I am now stuck as it were.

2. Relevant equations

3. The attempt at a solution
I have worked out that 80% of 2.8 Kw is 2.24kw which with a voltage of 400v gives a current of 7amps. With a power factor of 0.8 I get a Cos of 36.86 degrees. The current is lagging. If current is expressed as 7xCos38.86 is voltage then 400xCos38.86? My notes are not very clear on these two expressions and can't progress until I have this information.

Many thanks, Dumbkiwi.

2. Oct 25, 2009

### tiny-tim

Welcome to PF!

Hi dumbkiwi! Welcome to PF!
The impedance of a load (a combination of components) in an AC current is a complex number Z = R + jX where R is the resistance of the load and X is its reactance.

For a load for which the voltage leads the current by a phase angle φ:

Z = |Z|cosφ + j|Z|sinφ.​

Polar form is the form re, or in this case Z = |Z|e

3. Oct 25, 2009

### dumbkiwi

Hi Tiny Tim,

Thanks for your reply, I think it will help but I am too tired to try and work through it just now but will post again when I have had time to look at.

Regards Dumbkiwi.

4. Oct 27, 2009

### salvparla

hello dumbkiwi,

Is that you Calum If it is im struggling on this assignment too! fancy meeting up and putting our heads together?

salv

5. Oct 28, 2009

### dumbkiwi

Hey Salv,

Yeah could do that. I'll send you a pm with my phone number.

See you soon mate.

Regards Callum.