Question

In an electronic device, individual circuits may serve many purposes. In some cases, the flow of electricity must be controlled by reducing the power instead of amplifying it. A certain circuit has a fixed voltage of V volts and an existing resistor with resistance R ohms. If another resistor, with resistance x ohms is added, then the power absorbed (in amps) by the circuit will be

p(x) = (V^2)(x) / (R + x)^2

Find the value of x what maximizes the power absorbed.

Answer 1

Power absorbed

Differentiating with respect to x

For critical points where maxima or minima exist

(As P'(x) is changing from negative to positive so x=R is maxima point)