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

  1. Jun 19, 2012 #1
    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.
     
  2. jcsd
  3. Jun 20, 2012 #2
    EV,

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

    Ratch
     
  4. Jun 20, 2012 #3
    I found out. See pic :)
     

    Attached Files:

    • PFC.jpg
      PFC.jpg
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  5. Jun 20, 2012 #4
    EV,

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

    Ratch
     
  6. Jun 20, 2012 #5
    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: Jun 20, 2012
  7. Jun 20, 2012 #6
    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
     
  8. Jun 21, 2012 #7
    Well, when XL change, Q change, and when R change, P change, so that should be possible.

    I cannot see how though.
     
  9. Jun 21, 2012 #8
    EV,

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

    Ratch
     
  10. Jun 21, 2012 #9
    Ratch.

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

    If P does not change, then R does not change.
     
  11. Jun 21, 2012 #10
    EV,

    What picture?

    What is P, the apparent power?

    Ratch
     
  12. Jun 21, 2012 #11
    PFC.jpg in #3

    No. S is apparent, Q is reactive and P is the effective
     
  13. Jun 21, 2012 #12

    SammyS

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    Here's the figure !

    attachment.php?attachmentid=48504&d=1340232919.jpg
     
  14. Jun 21, 2012 #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
     
  15. Jun 21, 2012 #14
    Nothing. As i wrote, i found out :)
     
  16. Jun 21, 2012 #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
     
  17. Jun 21, 2012 #16
    Sorry, thourght P, Q and S was standard.
     
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