---
title: "Two batteries with emfs \\(3\\mathcal{E}_0\\) and \\(\\mathcal{E}_0\\) are connected in a single closed loop with an external resistor, as shown. The total resistance of the circuit, including internal resistances of both batteries and the external resistor, is \\(R\\). Battery 1 (emf \\(3\\mathcal{E}_0\\)) forces current through Battery 2 (emf \\(\\mathcal{E}_0\\)) in the reverse direction, charging it.  | Row | Rate Chemical Energy Stored in Battery 2 | Total Rate Thermal Energy Dissipated | | :— | :— | :— | | A | \\(\\dfrac{\\mathcal{E}_0^2}{R}\\) | \\(\\dfrac{4\\mathcal{E}_0^2}{R}\\) | | B | \\(\\dfrac{2\\mathcal{E}_0^2}{R}\\) | \\(\\dfrac{4\\mathcal{E}_0^2}{R}\\) | | C | \\(\\dfrac{2\\mathcal{E}_0^2}{R}\\) | \\(\\dfrac{2\\mathcal{E}_0^2}{R}\\) | | D | \\(\\dfrac{6\\mathcal{E}_0^2}{R}\\) | \\(\\dfrac{4\\mathcal{E}_0^2}{R}\\) |  Which row correctly identifies the rate at which chemical energy is stored in Battery 2 and the total rate at which thermal energy is dissipated in the circuit?"
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url: "https://nerd-notes.com/ubq/118445/"
date_modified: "2026-08-04T08:10:10+00:00"
---

# Two batteries with emfs \(3\mathcal{E}_0\) and \(\mathcal{E}_0\) are connected in a single closed loop with an external resistor, as shown. The total resistance of the circuit, including internal resistances of both batteries and the external resistor, is \(R\). Battery 1 (emf \(3\mathcal{E}_0\)) forces current through Battery 2 (emf \(\mathcal{E}_0\)) in the reverse direction, charging it.

| Row | Rate Chemical Energy Stored in Battery 2 | Total Rate Thermal Energy Dissipated |
| :— | :— | :— |
| A | \(\dfrac{\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |
| B | \(\dfrac{2\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |
| C | \(\dfrac{2\mathcal{E}_0^2}{R}\) | \(\dfrac{2\mathcal{E}_0^2}{R}\) |
| D | \(\dfrac{6\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |

Which row correctly identifies the rate at which chemical energy is stored in Battery 2 and the total rate at which thermal energy is dissipated in the circuit?

Two batteries with emfs \(3\mathcal{E}_0\) and \(\mathcal{E}_0\) are connected in a single closed loop with an external resistor, as shown. The total resistance of the circuit, including internal resistances of both batteries and the external resistor, is \(R\). Battery 1 (emf \(3\mathcal{E}_0\)) forces current through Battery 2 (emf \(\mathcal{E}_0\)) in the reverse direction, charging it.

| Row | Rate Chemical Energy Stored in Battery 2 | Total Rate Thermal Energy Dissipated |
| :--- | :--- | :--- |
| A | \(\dfrac{\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |
| B | \(\dfrac{2\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |
| C | \(\dfrac{2\mathcal{E}_0^2}{R}\) | \(\dfrac{2\mathcal{E}_0^2}{R}\) |
| D | \(\dfrac{6\mathcal{E}_0^2}{R}\) | \(\dfrac{4\mathcal{E}_0^2}{R}\) |

Which row correctly identifies the rate at which chemical energy is stored in Battery 2 and the total rate at which thermal energy is dissipated in the circuit?

![A schematic of a single-loop direct-current circuit drawn in a rectangular shape with black lines on a white background. On the left vertical wire segment, a battery representing Battery 1 is oriented with its long positive terminal line on top and short negative terminal line on the bottom, labeled 3\mathcal{E}_0. On the right vertical wire segment, a second battery representing Battery 2 is oriented with its long positive terminal line on top and short negative terminal line on the bottom, labeled \mathcal{E}_0. On the bottom horizontal wire segment, a zig-zag resistor symbol is centered and labeled R. Straight connecting wires form a complete closed rectangular loop. No other labels, arrows, or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/circuit-fig-1-1785831010-13lPYA.jpg)

- **A.** Row A
- **B.** Row B
- **C.** Row C
- **D.** Row D

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118445/*