Power Factor Proof: Avoid Poor PF < 0.8

AI Thread Summary
To avoid a poor power factor of less than 0.8 in a circuit, the relationship between real power and apparent power must be optimized. The power factor can be expressed as PF = R / sqrt(R^2 + (Xl - Xc)^2), indicating that when the inductive reactance (Xl) equals the capacitive reactance (Xc), the power factor reaches its maximum of 1. This condition occurs when Xl - Xc approaches zero, thus making apparent power equal to real power. A mathematical proof of this relationship is deemed sufficient for validation. Understanding these principles is crucial for effective circuit design and energy efficiency.
physics97
Messages
6
Reaction score
0

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

 
Physics news on Phys.org
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
 

Similar threads

Power Factor of an L-C-R curcuit
Replies
10
Views
5K
What circuit element should be placed in series to raise power factor?
Replies
13
Views
3K
The potential difference across an inductor
Replies
9
Views
10K
Current through source in AC circuit with R & LC in parallel
Replies
2
Views
3K
Change in Capacitor for largest possible Current
Replies
2
Views
2K
Adjusting the Power Factor of an RLC circuit
Replies
20
Views
2K
RLC Circuit Homework: Find L, Z, I, and P
Replies
8
Views
2K
What Is the Maximum Induced EMF in the Inductor?
Replies
8
Views
2K
Finding Maximum Power in an AC Circuit
Replies
12
Views
5K
Generator from a power plant delivering electric power
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top