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Find The value of impedance

  1. Jun 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Find Z R=10Ω
    Vs=120v
    (PF)=0.72 Lagging

    2. Relevant equations

    I=P/Vs(PF)
    Z=Vs/I

    3. The attempt at a solution




    I have I=P/Vs(PF) and transpose for I to get 4.34A
    Then to find Z Z=Vs/I which gives 27.65ohm
    When I put this back into (PF)=R/Z to confirm i dont get the right answer


    Any help would be great
     
  2. jcsd
  3. Jun 16, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    What value do you use for P in your equations?

    As an alternative, consider that the power factor is the cosine of the angle of the apparent power phasor, and that the impedance will have the same angle. Here the PF is 0.72 and is said to be lagging, which means the impedance will appear to have an inductive reactance component. You can draw the triangle for the impedance:

    attachment.php?attachmentid=59591&stc=1&d=1371387227.gif

    You should be able to write an expression to relate XL to given cosine of the angle θ.
     

    Attached Files:

  4. Jun 16, 2013 #3
    Thanks for getting back, so

    arcos( 0.72 ) = 43.95deg
    Tanθ o/a
    Tan 43.95 * XL/10 transpose for XL
    XL = Tan 43.95*10 = 9.64 ohm
    using trig Z^2 = R^2 + XL^2
    = Drum roll..................... 13.89 ohm

    Does this seem closer to the mark? it works when i put it into a known equation

    P was from a earlier part of the question which i used to find I

    Thank you, its much appriciated
     
  5. Jun 16, 2013 #4

    gneill

    User Avatar

    Staff: Mentor

    Looks good!
     
  6. Jun 16, 2013 #5
    Awesome, Thanks a lot
     
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