- #1

xAly

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- Homework Statement
- A simple circuit consists of a supply with a voltage of ##60V## as well as a variable resistor (which can be varied between ##1## and ##25 \Omega##) and resistor (##5\Omega##) connected in series. Determine the resistance of the variable resistor such that the power dissipated by it is maximised.

- Relevant Equations
- ##P = I^2 R, R = \frac{V}{I}##

Let ##R## denote resistance of standard resistor and ##R_v## the resistance of the variable resistor. I know that ##I = \frac{V}{(R_v + R)}##. Now I also know that ##P = I^2 R_v##represents the power dissipated by the variable resistor and that I need to maximise ##P##. The problem I am having is that both and ##I## and ##R_v## are dependent on each other, a decrease in ##R_v## leads to an increase in ##I## and vice versa. Therefore I don't see how to maximise ##P##, usually I would differentiate to find the critical points but I am not sure which one is the independent variable here.