# Geogebra App on Maximum Power Theorem

This simulation demonstrates the power dissipated in a variable resistor given that the battery has an internal resistance (made variable in this app as well).

Since the power dissipated by the resistor is given by

$P=I^2R$

and the current is given by

I=ER+r

,

P= E2×R(R+r)2=E2r2/R+R+2r

This power will be a maximum if the expression for the denominator

r2/R+R+2r

is a minimum.

Differentiating the expression with respect to R, we get

ddR(r2/R+R+2r)=-r2/R2+1

When the denominator is a minimum,

-r2R2+1=0

, so

r=R

.