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AC electrical generator

  1. Oct 31, 2007 #1
    1. The problem statement, all variables and given/known data
    An alternating current electrical generator has a fixed internal impedance [tex]R_{g}+iX_{g}[/tex] and is used to supply power to a passive load that has an impedance [tex]R_{g} +iX_{l}[/tex], where [tex]i = \sqrt{-1}[/tex], [tex]R_{g}\neq 0[/tex], and [tex]X_{g} \neq 0 [/tex]. For maximum power transfer between the generator and the load, [tex]X_{l}[/tex] should be equal to...

    The answer is [tex]X_{l}=X_{g}[/tex].

    However, I don't know how come up with this answer. It seems that the maximum power transmission occur with the imaginary part of the total impedance of the system vanishes. But Why??

    Thanks a lot=)
     
  2. jcsd
  3. Nov 1, 2007 #2

    George Jones

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    From your last sentence above, it seems that you forgot a negative sign in the equation above.

    It's a two variable max/min problem from mutivariable calculus.

    The power delivered to the load is [itex]P=|I^2| R_l[/itex]. What is I?
     
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