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Maximum Power Transfer

When a load is connected to a circuit with an internal (Thévenin) resistance, the power delivered to the load is greatest when the load resistance equals the source's internal resistance. Under this condition the efficiency is only 50%, since just as much power is lost in the source itself – maximum power and good efficiency are therefore not the same thing.

P_{max}=\dfrac{U_{th}^2}{4R_{th}}\ \text{at}\ R_L=R_{th}

maximum power delivered to the load

Symbols

$R_L$	load resistance	$\Omega$
$R_{th}$	source's (Thévenin) resistance	$\Omega$
$U_{th}$	Thévenin voltage	V

Example

$U_{th}=10$ V, $R_{th}=5$ Ω:

$P_{max}=10^2/(4\cdot5)=5$ W at $R_L=5$ Ω.

R_L=R_{th}

gives maximum power to the load, not the best efficiency – that is then only 50%.

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