Power Factor Proof: Avoid Poor PF < 0.8

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Homework Help Overview

The discussion revolves around generalizing the circumstances required to avoid a poor power factor, defined as being less than 0.8, in electrical circuits. Participants are exploring the relationship between real power, apparent power, and the components of the circuit, including resistors, inductors, and capacitors.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to express the power factor in terms of resistance, inductance, and capacitance. There are questions about how to make apparent power approach real power and discussions on the implications of setting inductive and capacitive reactance equal.

Discussion Status

The discussion is active, with participants sharing equations and reasoning. Some have suggested that proving the relationship between power factors and circuit components may be possible through mathematical expressions, while others express uncertainty about how to formalize this proof.

Contextual Notes

There are indications of urgency in the discussion, with participants seeking timely assistance. Some posts reiterate the homework statement and equations, suggesting a focus on clarifying understanding rather than providing direct solutions.

physics97
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Homework Statement


Hi guys, I am having trouble with my homework, it states to generalise the circumstances required to avoid a poor power factor (assumed to be less then 0.8) of a circuit, this generalisation must then be proved. Any help would be greatly appreciated.


Homework Equations


Power Factor = Real Power / Apparent Power
Real Power = I^2*R
Apparent Power = I^2*Z
Z=sqrt(R^2+(Xl-Xc)
Where:
R is resistor
Xl is inductor
Xc is capacitor
in ohms

The Attempt at a Solution

 
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What happens if you use your equations to express the power factor with R, Xl and Xc?
 
mfb said:
What happens if you use your equations to express the power factor with R, Xl and Xc?
Simplifies down to:
PF = R / sqrt(R^2+(xl-xc)^2) ?
 
Getting to the point where this is urgent, anyone able to help?
 
How do you make the value of the apparent power approach the value of the real power?
 
SteamKing said:
How do you make the value of the apparent power approach the value of the real power?
When Xl=Xc the power factor is equal to 1 (easily proven), so i suppose that as Xl-Xc approaches zero, the apparent power approaches the value of the real power. My problem is I am truly stumped on how i could prove it, any suggestions?
 
physics97 said:

Homework Statement


Hi guys, I am having trouble with my homework, it states to generalise the circumstances required to avoid a poor power factor (assumed to be less then 0.8) of a circuit, this generalisation must then be proved. Any help would be greatly appreciated.


Homework Equations


Power Factor = Real Power / Apparent Power
Real Power = I^2*R
Apparent Power = I^2*Z
Z=sqrt(R^2+(Xl-Xc)
Where:
R is resistor
Xl is inductor
Xc is capacitor
in ohms

The Attempt at a Solution


Error in an equation * Z=sqrt((R^2)+((Xl-Xc)^2))
 
physics97 said:
When Xl=Xc the power factor is equal to 1 (easily proven), so i suppose that as Xl-Xc approaches zero, the apparent power approaches the value of the real power. My problem is I am truly stumped on how i could prove it, any suggestions?

Didn't you just prove it? I think even EEs must accept a mathematical proof as sufficient.
 
SteamKing said:
Didn't you just prove it? I think even EEs must accept a mathematical proof as sufficient.

Thanks for your help mate, greatly appreciated
 

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