Calculating impedance in complex number and polar form

In summary, the conversation discusses the specifications of two motors and a generator, and the question of calculating the overall impedance for the two motors in parallel using complex number and polar form. The missing value for the jX portion of the complex number can be calculated from the power factor, which is the cosφ in the polar form Z = |Z|cosφ + j|Z|sinφ. The conversation ends with the hope of being able to solve the problem now.
  • #1
dumbkiwi
5
0

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.
 
Physics news on Phys.org
  • #2
dumbkiwi said:
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! :smile:

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. :wink:

(and be careful of the + or - sign for sinφ, which depends on whether the current or the voltage is lagging)
 
  • #3
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.
 

1. What is impedance in complex number and polar form?

Impedance is a measure of the opposition to current flow in an electrical circuit. In complex number and polar form, it is represented as a combination of resistance and reactance, where resistance is the real part and reactance is the imaginary part of the complex number.

2. How do you calculate impedance in complex number and polar form?

To calculate impedance in complex number and polar form, you can use the formula Z = R + jX, where Z is the impedance, R is the resistance, and X is the reactance. R and X can be determined using Ohm's Law and the properties of inductors and capacitors.

3. What is the difference between complex number and polar form?

Complex number form represents a complex number as a combination of a real part and an imaginary part, usually in the form a + bi. On the other hand, polar form represents a complex number as a combination of magnitude and angle, usually in the form |z|∠θ.

4. Why is it important to calculate impedance in complex number and polar form?

Calculating impedance in complex number and polar form is important because it allows us to analyze and understand the behavior of electrical circuits. It helps in designing and troubleshooting circuits and also in determining the efficiency and power requirements of a circuit.

5. What are the applications of calculating impedance in complex number and polar form?

Calculating impedance in complex number and polar form has various applications in electrical engineering, such as in designing filters, antennas, and transmission lines. It is also used in power systems for determining voltage and current distribution and in audio systems for equalizing sound signals.

Similar threads

  • Calculus and Beyond Homework Help
Replies
14
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
2K
  • Precalculus Mathematics Homework Help
Replies
12
Views
884
  • General Math
Replies
15
Views
3K
Replies
10
Views
327
Replies
6
Views
506
  • Calculus and Beyond Homework Help
Replies
14
Views
2K
Back
Top