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Power Factor Proof

  1. Mar 4, 2013 #1
    1. The problem statement, all variables and given/known data
    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.

    2. Relevant equations
    Power Factor = Real Power / Apparent Power
    Real Power = I^2*R
    Apparent Power = I^2*Z
    R is resistor
    Xl is inductor
    Xc is capacitor
    in ohms

    3. The attempt at a solution
  2. jcsd
  3. Mar 4, 2013 #2


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    What happens if you use your equations to express the power factor with R, Xl and Xc?
  4. Mar 5, 2013 #3
    Simplifies down to:
    PF = R / sqrt(R^2+(xl-xc)^2) ?
  5. Mar 5, 2013 #4
    Getting to the point where this is urgent, anyone able to help???
  6. Mar 5, 2013 #5


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    How do you make the value of the apparent power approach the value of the real power?
  7. Mar 5, 2013 #6
    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 truely stumped on how i could prove it, any suggestions?
  8. Mar 5, 2013 #7
    Error in an equation * Z=sqrt((R^2)+((Xl-Xc)^2))
  9. Mar 5, 2013 #8


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    Didn't you just prove it? I think even EEs must accept a mathematical proof as sufficient.
  10. Mar 5, 2013 #9
    Thanks for your help mate, greatly appreciated
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