Halliday, Resnick & Walker — Circuits: Problem 12

12 Figure 27-26 shows a battery connected across a uniform resistor \(R_0\). A sliding contact can move across the resistor from \(x = 0\) at the left to \(x = 10 \text{ cm}\) at the right. Moving the contact changes how much resistance is to the left of the contact and how much is to the right. Find the rate at which energy is dissipated in resistor \(R\) as a function of \(x\). Plot the function for \(\mathcal{E} = 50 \text{ V}, R = 2000 \ \Omega\), and \(R_0 = 100 \ \Omega\).