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Equation relating rotational velocity and output electrical power

  1. Mar 13, 2012 #1
    What is the equation that relates the angular velocity of an alternator rotor with its output electrical power, voltage and frequency (not necessarily just one equation) .
    And for a DC generator?
    I know that when you calculate the power generated by a turbine you multiply its efficiency of conversion and the theoretical power that you can extract from a flow with that swept area by the turbine. I assume that in that efficiency is the factor of conversion to electrical power. How does that work?
    regards
     
  2. jcsd
  3. Mar 14, 2012 #2
    Start with Maxwell's equation in differential form
    [tex] curl\space E = - dB/dt [/tex]
    Integrate to get Faraday's Law:
    [tex] \oint E\space d\ell= - \frac{d}{dt}\int_{A}^{}B\cdot n \space dA [/tex]
    The induced voltage in an N-turn loop around the perimeter of an area A is equal to minus the time derivative of the perpendicular magnetic field integrated over the area inside the loop. Either the magnetic field or the area can be a function of time. If an N-turn loop of area A(t) = Aosin(ωt) rotates in a dc magnetic field B0 with angular frequency ω, then the rms output voltage is
    [tex] V= \frac{\omega NA_0 B_0}{\surd 2}[/tex]

    Bob S
     
    Last edited: Mar 14, 2012
  4. Mar 14, 2012 #3

    jim hardy

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    That's a kinda general question...
    like asking what make a centrifugal pump work..

    Here's a fairly scholarly article on automobile alternators and where they are going
    www.rle.mit.edu/per/JournalPapers/JPtpemay04p618.pdf

    and the Wikipedia page really is pretty good
    http://en.wikipedia.org/wiki/Alternator

    Alternators in cars have widely varying efficiency at various speeds and loads. Take 50-60% as ballpark.
    Utility central station alternators can be, as you doubtless know, 99% efficient.
     
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