Maximum power transfer theorem

In <a href="/facts/Electrical_engineering/YYXW1KLW">electrical engineering</a>, the maximum power transfer theorem states that, to obtain maximum external <a href="/facts/Electric_power/w61ID9yQ">power</a> from a power source with <a href="/facts/Internal_resistance/2PexRRay">internal resistance</a>, the <a href="/facts/Electrical_resistance/hxSt0UAj">resistance</a> of the <a href="/facts/Electrical_load/IX0XBAqB">load</a> must equal the <a href="/facts/Output_impedance/80brK3Cv">resistance of the source</a> as viewed from its output terminals. <a href="/facts/Moritz_von_Jacobi/eYTfnSQh">Moritz von Jacobi</a> published the maximum power (transfer) theorem around 1840; it is also referred to as "Jacobi's law".
The <a href="/facts/Theorem/f2Pe1FMD">theorem</a> results in maximum power transfer from the power source to the load, but not maximum <a href="/facts/Efficiency/azCNkIzY">efficiency</a> of useful power out of total power consumed. If the load resistance is made larger than the source resistance, then efficiency increases (since a higher percentage of the source power is transferred to the load), but the magnitude of the load power decreases (since the total circuit resistance increases). If the load resistance is made smaller than the source resistance, then efficiency decreases (since most of the power ends up being dissipated in the source). Although the total power dissipated increases (due to a lower total resistance), the amount dissipated in the load decreases.
The theorem states how to choose (so as to maximize power transfer) the load resistance, once the source resistance is given. It is a common misconception to apply the theorem in the opposite scenario. It does not say how to choose the source resistance for a given load resistance. In fact, the source resistance that maximizes power transfer from a voltage source is always zero (the hypothetical <a href="/facts/Ideal_voltage_source/aAIbDymf">ideal voltage source</a>), regardless of the value of the load resistance.
The theorem can be extended to <a href="/facts/Alternating_current/qxICS3xa">alternating current</a> circuits that include <a href="/facts/Electrical_reactance/LnvyrUnM">reactance</a>, and states that maximum power transfer occurs when the load <a href="/facts/Electrical_impedance/I06NSXtN">impedance</a> is equal to the <a href="/facts/Complex_conjugate/7TEaoQDe">complex conjugate</a> of the source impedance.
The mathematics of the theorem also applies to other physical interactions, such as:

<ul><li>mechanical collisions between two objects,</li>
<li>the sharing of charge between two capacitors,</li>
<li>liquid flow between two cylinders,</li>
<li>the transmission and reflection of light at the boundary between two media.</li></ul>

Maximum power transfer theorem open-in-new

Maximum power transfer theorem