RLC series circuit: Determine C so that P.F.=X

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Discussion Overview

The discussion revolves around determining the capacitance needed in an RLC series circuit to achieve a specific power factor, transitioning from an initial power factor of 0.6 to a target of 0.8. Participants explore the relationships between resistance, inductive reactance, and power factor, engaging in technical reasoning and calculations related to circuit theory.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes using three equations involving reactive power (Q), impedance (Z), and power factor (Y) to solve for the necessary values to adjust the power factor.
  • Another participant asks for known values such as resistance (R), inductance (L), and frequency to better understand the problem.
  • There is a discussion about how changes in inductive reactance (XL) and resistance (R) affect power (P) and the power factor.
  • One participant asserts that installing a compensating capacitor does not change resistance, suggesting a need for deeper understanding of power factor theory.
  • Another participant mentions finding a solution in a referenced figure, indicating a specific capacitance value (C = 2.422 µF) needed to achieve the desired power factor.
  • There is a clarification about the definitions of apparent power (S), reactive power (Q), and effective power (P) in the context of the power triangle.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the relationships between power, resistance, and reactance, but there is disagreement on the clarity of the referenced figure and its implications for solving the problem. The discussion remains unresolved regarding the best approach to determine the required capacitance without a consensus on the definitions and relationships involved.

Contextual Notes

Limitations include the lack of specific numerical values for resistance and inductance, which are necessary for precise calculations. There is also ambiguity in the definitions and relationships among power, reactance, and power factor that may affect the conclusions drawn by participants.

EVriderDK
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Hey.

If a a circuit is too inductive, and has a power factor of 0.6, how would i find a capacitor in series or parallel that would give a power factor of 0.8?

I think that i could do it with 3 equations and 3 unkowns like this:

1: Q=XL*I^2
Z=X*I^2
2: tan(P/Q)=[itex]\varphi[/itex]
tan(P/Z)=Y
3: cos(Y)=0.8

Then solve for X and Y and Z?

Please help.
 
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EV,

What are your knowns? R? L? Frequency? What?

Ratch
 
I found out. See pic :)
 

Attachments

  • PFC.jpg
    PFC.jpg
    25 KB · Views: 479
EV,

What is L? What is R? How about a phasor diagram.

Ratch
 
Ratch

L is the size of the inductor (self inductance), and R is the size of the resistor (resistance)

L would be L=(Q/(I^2))/(2*∏*f) Where Q/(I^2) = X_L the inductive reactance
R would be P/(I^2)
 
Last edited:
EV,

So if you know the inductive reactance Xl, and the resistance R, and they compute to a power factor of 0.6, can you firgure out what the reduction in inductive reactance should be to get a 0.8 power factor?

Ratch
 
Well, when XL change, Q change, and when R change, P change, so that should be possible.

I cannot see how though.
 
EV,

Installing a compensating cap does not change R. I think you need to study the theory behind the power factor some more.

Ratch
 
Ratch.

I know, as you can see in the picture. P stays the same.

If P does not change, then R does not change.
 
  • #10
EV,

I know, as you can see in the picture. P stays the same.

What picture?

If P does not change, then R does not change.

What is P, the apparent power?

Ratch
 
  • #11
PFC.jpg in #3

No. S is apparent, Q is reactive and P is the effective
 
  • #12
EVriderDK said:
PFC.jpg in #3

No. S is apparent, Q is reactive and P is the effective
Here's the figure !

attachment.php?attachmentid=48504&d=1340232919.jpg
 
  • #13
EV,

A power triangle diagram would have been nice. I just noticed, the page you referenced gives the solution you want. C = 2.422 uf in the lower right corner. What else do you want to know?

Ratch
 
  • #14
Ratch said:
EV,

A power triangle diagram would have been nice. I just noticed, the page you referenced gives the solution you want. C = 2.422 uf in the lower right corner. What else do you want to know?

Ratch

Nothing. As i wrote, i found out :)
 
  • #15
SammyS,

Call it a figure if you wish. That is a list of values for a bunch of undefined quantities. It wasn't until he explained which quantities defined the power triangle that I understood how everything was related, and the answer was already present.

Ratch
 
  • #16
Ratch said:
SammyS,

Call it a figure if you wish. That is a list of values for a bunch of undefined quantities. It wasn't until he explained which quantities defined the power triangle that I understood how everything was related, and the answer was already present.

Ratch

Sorry, thourght P, Q and S was standard.
 

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