Halliday, Resnick & Walker — Circuits: Problem 5

5 In Fig. 27-20, two batteries with an emf \(\mathcal{E} = 12.0\text{ V}\) and an internal resistance \(r = 0.500\ \Omega\) are connected in parallel across a resistance \(R\). (a) For what value of \(R\) is the dissipation rate in the resistor a maximum? (b) What is that maximum? and (c) what is the total dissipation rate in the batteries? In terms of \(r\), what are (d) the effective (internal) resistance of the two-battery system and (e) the resistance \(R\) that is required to maximize the dissipation rate? This is a general result.