Geogebra App on Maximum Power Theorem

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 get \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.

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