Physics Lens

Geogebra App on Maximum Power Theorem

GeoGebra link:

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


and the current is given by



This power will be a maximum if the expression for the denominator [latex]\dfrac{r^2}{R}+R+2r[/latex] is a minimum.

Differentiating the expression with respect to R, we get

When the denominator is a minimum,

[latex]r=R[/latex] when the power dissipated by the resistor is highest.

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