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title: "A single-loop circuit contains two ideal batteries with electromotive forces \\(\\varepsilon_1\\) and \\(\\varepsilon_2\\) and two resistors with resistances \\(R_1\\) and \\(R_2\\), as shown in the diagram. The electromotive force of the first battery is greater than that of the second battery (\\(\\varepsilon_1 > \\varepsilon_2\\)), and the batteries are arranged such that their positive terminals face one another. Which of the following expressions represents the magnitude of the electric current \\(I\\) in the circuit?"
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url: "https://nerd-notes.com/ubq/120408/"
date_modified: "2026-08-23T04:34:30+00:00"
---

# A single-loop circuit contains two ideal batteries with electromotive forces \(\varepsilon_1\) and \(\varepsilon_2\) and two resistors with resistances \(R_1\) and \(R_2\), as shown in the diagram. The electromotive force of the first battery is greater than that of the second battery (\(\varepsilon_1 > \varepsilon_2\)), and the batteries are arranged such that their positive terminals face one another. Which of the following expressions represents the magnitude of the electric current \(I\) in the circuit?

A single-loop circuit contains two ideal batteries with electromotive forces \(\varepsilon_1\) and \(\varepsilon_2\) and two resistors with resistances \(R_1\) and \(R_2\), as shown in the diagram. The electromotive force of the first battery is greater than that of the second battery (\(\varepsilon_1 > \varepsilon_2\)), and the batteries are arranged such that their positive terminals face one another. Which of the following expressions represents the magnitude of the electric current \(I\) in the circuit?

![A single rectangular circuit loop oriented horizontally. The top horizontal segment contains a battery labeled \varepsilon_1 with its longer vertical line (positive terminal) on the right and shorter thicker line (negative terminal) on the left. The right vertical segment contains a zigzag resistor labeled R_1. The bottom horizontal segment contains a battery labeled \varepsilon_2 with its longer vertical line (positive terminal) on the right and shorter thicker line (negative terminal) on the left. The left vertical segment contains a zigzag resistor labeled R_2. No other components, labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459669-6EP8aV.jpg)

- **A.** \(\dfrac{\varepsilon_1 - \varepsilon_2}{R_1 + R_2}\)
- **B.** \(\dfrac{\varepsilon_1 + \varepsilon_2}{R_1 + R_2}\)
- **C.** \(\dfrac{\varepsilon_1 - \varepsilon_2}{R_1 - R_2}\)
- **D.** \(\dfrac{(\varepsilon_1 - \varepsilon_2)(R_1 + R_2)}{R_1 R_2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120408/*