Maximum Power from a Real Voltage Source, power adjustment

Practical Voltage Source

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.

Output power of a real voltage source as a function of the resistance ratio of external resistance Rout to source resistance Rs

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=I²⋅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

Math. proof for power matching of a real voltage source