Power Factor Proof: Avoid Poor PF < 0.8

[physics97]

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

 

[mfb]

What happens if you use your equations to express the power factor with R, Xl and Xc?

 

[physics97]

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) ?

 

[physics97]

Getting to the point where this is urgent, anyone able to help?

 

[SteamKing]

How do you make the value of the apparent power approach the value of the real power?

 

[physics97]

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]

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))

 

[SteamKing]

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.

 

[physics97]

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

Thanks for your help mate, greatly appreciated