Before revision: Calculus-based proof for purely resistive circuits In the simplified model of powering a load with resistance by a source with voltage and source resistance , then by Ohm's law the resulting current is simply the source voltage divided by the total circuit resistance: The power dissipated in the load is the square of the current multiplied by the resistance: The value of for which this expression is a maximum could be calculated by differentiating it, but it is easier to calculate the value of for which the denominator is a minimum.
After revision: :Calculus-based proof for purely resistive circuits In the simplified model of powering a load with resistance by a source with voltage and source resistance , then by Ohm's law the resulting current is simply the source voltage divided by the total circuit resistance: The power dissipated in the load is the square of the current multiplied by the resistance: The value of for which this expression is a maximum could be calculated by differentiating it, but it is easier to calculate the value of for which the denominator is a minimum.