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Questions on Ac power.

  1. May 9, 2013 #1
    1. The problem statement, all variables and given/known data

    I have some questions about powers in AC circuit. What is the maximum and minimum current power on resistor and inductance.

    2. Relevant equations

    Um = U / V2
    Im = I / V2

    3. The attempt at a solution
    prmax = U*I=(Um/V2)*(Im/V2)=(Um*Im)/2. But answer seems to actually be that prmax = Um*Im, how can that be? And for plmax = 1/2 Um * Im plmin=- 1/2 Um *Im
     
  2. jcsd
  3. May 9, 2013 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi 0fibonacci1! :smile:

    your notation is difficult to understand :redface:

    here's an extract from the pf library on impedance
    Power:

    Power = work per time = voltage times charge per time = voltage times current:

    [tex]P = VI =\ V_{max}I_{max}\cos(\omega t + \phi/2)\cos(\omega t - \phi/2)[/tex]
    [tex]=\ V_{max}I_{max}(\cos\phi + \cos2\omega t)/2[/tex]​
    (because [itex]2cosAcosB = cos(A-B) + cos(A+B))[/itex])
    [tex]=\ V_{rms}I_{rms}(\cos\phi + \cos2\omega t)[/tex]
    [tex]=\ \left(V_{rms}^2\left/|Z|\right.\right)(\cos\phi + \cos2\omega t)[/tex]​

    So (instantaneous) power is the constant part, [itex]P_{av} = V_{rms}I_{rms}\cos\phi[/itex] (the average power), plus a component varying with double the circuit frequency, [itex]V_{rms}I_{rms}\cos2\omega t[/itex] (so a graph of the whole power is a sine wave shifted by a ratio [itex]\cos\phi[/itex] above the x-axis).​
     
  4. May 10, 2013 #3

    NascentOxygen

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    Staff: Mentor

    It almost seems that you might be using V2 as denoting 2 ?
     
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