Maximize Power Delivered to Circuits
Optimization Problem

The first derivative is used to maximize (optimize) the power delivered to a load in electronic circuits.


In the electronic circuit shown below, the voltage E (in Volts) and resistance r (in Ohms) are constant. R is the resistance of a load. In such a circuit, the electric current i is given by
i = E / (r + R)

and the power P delivered to the load R is given by
P = R i 2

r and R being positive, determine R so that the power P delivered to R is maximum.
maximize power problem 1

Solution to the Problem

More references on calculus problems