Calculating impedance in complex number and polar form

[dumbkiwi]

Homework Statement

I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging.

A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75 lagging.

They are fed by a generator which has an output resistance of 0.2 ohms and an output inductance of 1mH. 400volts.

I am stuck trying to answer - In complex number form and polar form calculate the overall impedance for the two motors in parallel. It appears to me that I have no value for the jX portion of the complex number so does that mean it is 0 or should I already know where this should have been calculated from. Our previous class examples have given values to calculate the inductive or capacitive values.

However our notes also state that a current lagging at phase angle to voltage then I in complex number form can be expressed as a - jb and v +j0. Where do a and b come from?

Now it may well be I am thick but I cannot see for the life of me where these missing pieces come from and no information I have read over the last 12 hours of study has enlightened me so some assistance would be gratefully received.

Many thanks in advance.

Dumbkiwi.

Homework Equations

The Attempt at a Solution

Had I the information I seek I may well have supplied this bit.

 

[tiny-tim]

I have a motor with a full load output rating of 2.8 kW with an effciency off 70% and at 80% of full load runs with a Power Factor of 0.8 lagging.

A second motor has afull load output of 4.2kW with an effciency of 85% and at 80% of full load runs with a PF of 0.75 lagging.
…
It appears to me that I have no value for the jX portion of the complex number so does that mean it is 0 or should I already know where this should have been calculated from.
…
However our notes also state that a current lagging at phase angle to voltage then I in complex number form can be expressed as a - jb and v +j0. Where do a and b come from?

Hi dumbkiwi!

The "jX portion" (of R + jX) has been given to you, since you can work it out from the power factor.

The power factor is the cosφ in the polar form Z = |Z|cosφ + j|Z|sinφ.

In other words, R= |Z|cosφ, and X = |Z|sinφ.

(and be careful of the + or - sign for sinφ, which depends on whether the current or the voltage is lagging)

 

[dumbkiwi]

Hi Tiny Tim,

Ah ha - I was thinking that's all it could be but was finding it difficult to find confirmation but easy to pull my hair out.

Lets hope I can now get this kicked into touch.

Many thanks.

Regards Dumbkiwi.