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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?
  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

    and the Wikipedia page really is pretty good

    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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