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Calculating Maximum Average Power of AC Circuit

  1. Apr 1, 2014 #1
    1. The problem statement, all variables and given/known data

    L7Qf3n9.png

    2. Relevant equations



    3. The attempt at a solution

    The text in the black box looks wrong to me. The method below is how I would do it. Why is it wrong?

    $$To\quad maximize\quad power,\quad \overrightarrow { Z_{ L } } =\overrightarrow { { { Z }_{ th } }^{ * } } \\ \\ \overrightarrow { { { Z }_{ th } } } =9.412+22.35j\\ \overrightarrow { { { Z }_{ th } }^{ * } } =9.412-22.35j\\ \overrightarrow { Z_{ L } } =9.412-22.35j\\ \overrightarrow { Z_{ L } } ={ R }_{ L }+{ X }_{ L }j\\ \\ Therefore,\quad { R }_{ L }=9.412Ω$$

    This is how they did it in the previous example: KbR7EuY.png
     
  2. jcsd
  3. Apr 1, 2014 #2

    rude man

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    Because ZL is not what you said. ZL = RL. It's real only. You don't have the freedom to add a reactive component = ZTH* to RL to maximize the power in RL.

    In general, if a voltage source has a series impedance Z = ReZ + jImZ, picking the load resistance RL = |Z| maximizes power dissipation in RL.
     
    Last edited: Apr 1, 2014
  4. Apr 4, 2014 #3
    Oh, thank you. I didn't realize the load is purely real. Frustration has been removed. :)
     
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