---
title: "A battery with electromotive force \\(\\varepsilon\\) and internal resistance \\(r\\) is connected to two identical external resistors, each of resistance \\(R\\), connected in parallel with each other as shown in the circuit diagram.  Which of the following expressions represents the total rate of electrical energy dissipation in the two external resistors in terms of \\(\\varepsilon\\), \\(r\\), and \\(R\\)?"
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url: "https://nerd-notes.com/ubq/120436/"
date_modified: "2026-08-23T04:34:40+00:00"
---

# A battery with electromotive force \(\varepsilon\) and internal resistance \(r\) is connected to two identical external resistors, each of resistance \(R\), connected in parallel with each other as shown in the circuit diagram.

Which of the following expressions represents the total rate of electrical energy dissipation in the two external resistors in terms of \(\varepsilon\), \(r\), and \(R\)?

A battery with electromotive force \(\varepsilon\) and internal resistance \(r\) is connected to two identical external resistors, each of resistance \(R\), connected in parallel with each other as shown in the circuit diagram.

Which of the following expressions represents the total rate of electrical energy dissipation in the two external resistors in terms of \(\varepsilon\), \(r\), and \(R\)?

![A single rectangular circuit schematic rendered in grayscale. On the left vertical branch is a non-ideal battery enclosed by a dashed rectangular outline; inside the dashed box is a battery emf symbol labeled \(\varepsilon\) in series with a resistor symbol labeled \(r\). Solid conducting wires extend from the top and bottom of the battery to the right. On the right side, the circuit splits at a junction into two parallel vertical branches. The first vertical branch contains a resistor labeled \(R\), and the second vertical branch to its right contains an identical resistor labeled \(R\). The two branches recombine at a bottom junction that connects back to the negative terminal of the battery. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459679-jmp6At.jpg)

- **A.** \(\dfrac{2\varepsilon^2 R}{(r + 2R)^2}\)
- **B.** \(\dfrac{2\varepsilon^2 R}{(2r + R)^2}\)
- **C.** \(\dfrac{4\varepsilon^2 R}{(2r + R)^2}\)
- **D.** \(\dfrac{\varepsilon^2 R}{2(r + R)^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120436/*