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Maximum Power Transfer Theorem

  1. Aug 3, 2012 #1

    JJBladester

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    Gold Member

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

    "If the load voltage at the output of a circuit keeps going up as the load resistance is increased, why doesn’t the load power keep going up as well?"

    2. Relevant equations

    The maximum power transfer theorem states:
    A load will receive maximum power from a network when its resistance is exactly equal to the Thevenin resistance of the network applied to the load. That is,

    RL=Rth

    max_power.JPG

    RL = Load resistance

    PL = Power dissipated by load

    Rth = Thevenin resistance

    [tex]I_L=\frac{E_{th}}{R_{th}+R_L}=\frac{E_{th}}{R_{th}+R_{th}}=\frac{E_{th}}{2R_{th}}[/tex]

    [tex]P_{L_{max}}=I_{L}^{2}R_L=\left (\frac{E_{th}}{2R_{th}} \right )^{2}\left (R_{th} \right )=\frac{E_{th}^{2}R_{th}}{4R_{th}^{2}}=\frac{E_{th}^{2}}{4R_{th}}[/tex]

    3. The attempt at a solution

    Here's how I answered this question.

    That's how I answered the question, but I'm not fully satisfied with my answer. Maybe I'm actually not satisfied with the wording of the original question... A Thevenin voltage source wouldn't change; it would be fixed, right? Thus, this question is sort of mis-stated in my opinion.

    Doesn't the maximum power transfer theorem assumes a fixed source voltage?
     
  2. jcsd
  3. Aug 3, 2012 #2

    berkeman

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    Staff: Mentor

    I think your answer is fine. When the load resistance increases past the source resistance, less current flows throught the load, reducing the power dissipated.

    BTW, have you learned yet that for circuits with reactive components (like inductors and capacitors), the maximum power transfer occurs when the load impedance is the complex conjugate of the source impedance? When the circuit only has resistors, there is no imaginary component to the impedances, so maximum power is transfered when the resistances are equal.
     
  4. Aug 3, 2012 #3

    JJBladester

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    Gold Member

    Thank you. I'm still curious whether the maximum power transfer theorem is applicable if the source voltage is allowed to increase. My understanding of a Thevenin circuit was that Eth was *fixed*.

    Berkeman, I haven't learned this yet. We just got into capacitors. I'm excited to learn about the M.P.T.T. for cases other than simply resistors!
     
  5. Aug 3, 2012 #4

    berkeman

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    Staff: Mentor

    The source is usually a fixed value for these calculations. I'm not sure what it means for the source voltage to be "allowed" to increase. Sources are usually fixed, unless they have some strange behavior. They can be current limited, for example, as many real power supplies are. But that will result in a decrease in output voltage if the current limit is reached...
     
  6. Aug 3, 2012 #5

    gneill

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    Staff: Mentor

    The initial statement of the problem said that the load voltage rises as the load resistance rises, which is perfectly true for even a fixed value of Eth; in the limit as RL approaches infinite resistance the load voltage approaches Eth.
     
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