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As I understand it, should maximum power transfer be when $$ R_L=R_{th} $$ then $$ P_L= P_{L(max)} $$

So that this should do the trick:

$$ P_{L}=\frac{V_{th} ^2}{R_{th}} $$

But it seems that I am doing something wrong.

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It's a simple error in your reasoning. When the load resistance is equal to the Thevenin resistance, the voltage across the load is precisely 1/2 the Thevenin voltage.

Thus,

\$P_{L,max} = \dfrac{V^2_{th}}{4R_{th}} \$

Your calculation would be correct if the entire Thevenin voltage appeared across the load but that isn't the case.

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  • \$\begingroup\$ I see, that explains a lot. \$\endgroup\$ – Faux_Clef Aug 10 '13 at 13:03

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