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title: "A battery of electromotive force \\(\\mathcal{E}\\) and internal resistance \\(r\\) is connected to an external circuit containing a load resistor of resistance \\(R\\). A switch \\(S\\) in a parallel branch containing an identical resistor of resistance \\(R\\) is initially open. With switch \\(S\\) open, the terminal voltage of the battery is \\(\\dfrac{2}{3}\\mathcal{E}\\), and the rate of energy dissipation inside the battery’s internal resistance is \\(P_0\\). In terms of \\(P_0\\), what is the rate of energy dissipation inside the battery’s internal resistance after switch \\(S\\) is closed?"
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url: "https://nerd-notes.com/ubq/124970/"
date_modified: "2026-09-28T14:12:19+00:00"
---

# A battery of electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected to an external circuit containing a load resistor of resistance \(R\). A switch \(S\) in a parallel branch containing an identical resistor of resistance \(R\) is initially open. With switch \(S\) open, the terminal voltage of the battery is \(\dfrac{2}{3}\mathcal{E}\), and the rate of energy dissipation inside the battery’s internal resistance is \(P_0\). In terms of \(P_0\), what is the rate of energy dissipation inside the battery’s internal resistance after switch \(S\) is closed?

A battery of electromotive force \(\mathcal{E}\) and internal resistance \(r\) is connected to an external circuit containing a load resistor of resistance \(R\). A switch \(S\) in a parallel branch containing an identical resistor of resistance \(R\) is initially open. With switch \(S\) open, the terminal voltage of the battery is \(\dfrac{2}{3}\mathcal{E}\), and the rate of energy dissipation inside the battery's internal resistance is \(P_0\). In terms of \(P_0\), what is the rate of energy dissipation inside the battery's internal resistance after switch \(S\) is closed?

![A rectangular circuit diagram oriented horizontally. On the left vertical branch is a non-ideal battery shown enclosed by a dashed rectangular box; inside the box is a DC voltage source labeled \(\mathcal{E}\) in series with a small resistor labeled \(r\). Two terminal dots lie on the wires just outside the dashed box. From the top and bottom of the battery branch, horizontal wires extend to the right. A first vertical branch connects the horizontal wires and contains a resistor labeled \(R\). Further to the right, a second vertical branch connects the horizontal wires and contains an open single-pole switch labeled \(S\) in series with an identical resistor labeled \(R\). No other labels, lines, text, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604739-FyXFAa.jpg)

- **A.** \(\dfrac{9}{16} P_0\)
- **B.** \(\dfrac{9}{8} P_0\)
- **C.** \(\dfrac{3}{2} P_0\)
- **D.** \(\dfrac{9}{4} P_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124970/*