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Homework Help: EMF expression in electrical generator

  1. Aug 25, 2012 #1
    Hi all!

    I'm studying electrical generators, and while I was trying to come up to the expression of EMF induced in a conductor I got two different results following two different ways, and I can't find the error.

    With sinusoidal B, with [tex]e=bvl[/tex] I get an RMS value [tex]E=2K_{f}f\phi[/tex], while with [tex]e=\frac{d\Lambda}{dt}[/tex] I get [tex]E=\pi K_{f}f\phi[/tex]

    Following the calculations; can you please tell me where the error is?

    Case 1:

    p = polar pairs
    r = radius
    ƒ = frequency
    Kf = form factor

    [tex]\tau=\frac{\pi r}{p}[/tex]
    [tex]v=2f\tau[/tex]
    [tex]E=K_{f}B_{m}lv=K_{f}\frac{\phi}{\tau l}l2f \tau=2K_{f}f\phi[/tex]

    Case 2:

    [tex]e=\frac{d\Lambda}{dt}=\frac{1}{2}\frac{d\phi}{dt}[/tex]
    [tex]E_{M}=\sqrt{2}E=\frac{1}{2}\phi_{M}\omega=\frac{1}{2}\sqrt{2}K_{f}\phi2\pi f=\pi f\sqrt{2}K_{f}\phi[/tex]
    [tex]E=\pi K_{f}f\phi[/tex]

    I thought it could be a [tex]\frac{2}{\pi}[/tex] due to a mean value, but the flux is the same in both the expressions...
     
    Last edited: Aug 25, 2012
  2. jcsd
  3. Aug 28, 2012 #2
    Just adding some notation and clarifications about my calculations:

    [tex]v = conductor\; velocity[/tex]
    [tex]\tau = polar\; pitch[/tex]
    [tex]l=rotor\; and\; conductor\; length[/tex]
    [tex]\Lambda=magnetic\; flux\; of\; B\; linked\; with\; the\; coils[/tex]
    [tex]\phi = polar\; magnetic\; flux[/tex]
    [tex]B_{m} = mean\; value\; of\; B[/tex]

    [tex]B_{m}=\frac{\phi}{\tau l}[/tex]

    And the passage from Λ to 0.5Φ:

    [tex]e=\frac{d\Lambda}{dt}=\frac{1}{2}\frac{d\phi}{dt}[/tex]

    is because with one conductor I've half a coil.

    I can't solve it, if you've any ideas it'd be great.
     
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