The power output is maximized when the internal resistance is equal to the external resistance, prove the reasoning process.

Let the electric potential of the power supply be E, the internal resistance be r, and the external resistance be R (r, R both > 0)

Current: I=E/(r+R)

Output power:

P=I?- R

=E?- R/(r+R)?

dP/dR=E?(r?-R?)/(r+R)^4

when R0, is an increasing function;

when R>r, dP/dR<0, is a decreasing function;

when R=r, dP/dR=0, and P obtains maximum value