## Maximum Power from a Real Voltage Source, power adjustment

The power output from a real voltage source is calculated to:

P_{out} = U_{out} * I

In no-load operation, this power is zero, since no current flows through the load. In the case of a short circuit, no power is output either, since a high current flows, but the terminal voltage is zero. In this case, the current is limited solely by the internal resistance.

The maximum power is emitted by the source when the external resistance R_{out} is equal to the internal resistance R_{s} of the voltage source: R_{out} = R_{s}. This case is called power adjustment. The maximum power is thus:

The power dissipation of the internal resistance Ri is almost completely converted into thermal power (P_{i}=I^{2}⋅R_{i}). It is therefore also responsible for the fact that, for example, batteries heat up during discharging or, in the case of accumulators, also during charging. In the event of a short circuit, this thermal power can lead to a fire.

__Addendum: mathematical proof for power adjustment__