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Power factor and frequency change

  1. Nov 25, 2010 #1
    1. The problem statement, all variables and given/known data
    240V,50 Hz electrical appliance is rated at 2KW and has a lagging power factor of0.7.
    a)Determine the appliance's power factor when it is used on a 60Hz supply?
    b)Calculate the supply voltage required to maintain the appliance at its rated power when operated off a 60Hz supply?

    2. Relevant equations
    S^2=P^2+Q^2 to obtain Q
    S=VsI to obtain I
    Z=Vs/I to obtain Z
    p.f. = R/Z to obtain R
    Z^2=R^2+Xl^2 to obtain Xl
    Xl=2pifL to obtain L at 50Hz

    3. The attempt at a solution

    I have done the above then used the value for L in Xl=2pifL at 60 Hz but not sure were to go from here.
  2. jcsd
  3. Nov 26, 2010 #2
    As you have already found Xl at 60 Hz you can find power factor at 60 Hz from value of new Z and R (Note R is unchanged)

    Since you know Z and P (rated power) you can find V
  4. Nov 26, 2010 #3
    Thanks, I get the first section now but I don't see how I can work out the supply voltage using the new Z and the rated power.
  5. Nov 26, 2010 #4
    should i be using P=V^2/Z
  6. Nov 26, 2010 #5
    Note V^2/Z gives the apparent power S.
  7. Nov 26, 2010 #6
    I'm confused now, how do I calculate the supply voltage required to maintain the appliance at its rated power at 60Hz.

    I have the rated power and the impedence at 60Hz.
  8. Nov 26, 2010 #7
    Hi, you know P and Z, from Z you can find p.f.
    From above values you can find S. Once you know S you can find V.
  9. Nov 26, 2010 #8
    I have worked out the pf to be 0.63
    P(rated power) = 2000 w
    Z=22.31 ohms

    Would it be correct to use P(rated power)= V^2/R as R remains the same to obtain V(supply voltage)
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