# 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 $I=\frac{E}{R+r}$,

$P = {E^2}\times\frac{R}{(R+r)^2} = \frac{E^2}{r^2/R+R+2r}$

This power will be a maximum if the expression for the denominator ${r^2/R+R+2r}$ is a minimum.

Differentiating the expression with respect to R, we getÂ $\frac{d}{dR}({r^2/R+R+2r})={-r^2/R^2+1}$

When the denominator is a minimum, $-\frac{r^2}{R^2}+1=0$, so $r = R$.

https://physicslens.com/geogebra-app-on-maximum-power-theorem/

This site uses Akismet to reduce spam. Learn how your comment data is processed.