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title: "A circuit consists of an ideal battery with potential difference \\(\\varepsilon\\) connected to four resistors with resistances \\(R_1 = R\\), \\(R_2 = 2R\\), \\(R_3 = 2R\\), and \\(R_4 = R\\), as shown. Resistor \\(R_1\\) is in series with the battery, and the circuit then splits into two parallel branches: one branch contains resistors \\(R_2\\) and \\(R_3\\) in series, and the other branch contains resistor \\(R_4\\). The currents through resistors \\(R_1\\), \\(R_2\\), \\(R_3\\), and \\(R_4\\) are \\(I_1\\), \\(I_2\\), \\(I_3\\), and \\(I_4\\), respectively. Which of the following correctly ranks the magnitudes of the currents through the four resistors from greatest to least?"
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url: "https://nerd-notes.com/ubq/117446/"
date_modified: "2026-08-04T06:52:11+00:00"
---

# A circuit consists of an ideal battery with potential difference \(\varepsilon\) connected to four resistors with resistances \(R_1 = R\), \(R_2 = 2R\), \(R_3 = 2R\), and \(R_4 = R\), as shown. Resistor \(R_1\) is in series with the battery, and the circuit then splits into two parallel branches: one branch contains resistors \(R_2\) and \(R_3\) in series, and the other branch contains resistor \(R_4\). The currents through resistors \(R_1\), \(R_2\), \(R_3\), and \(R_4\) are \(I_1\), \(I_2\), \(I_3\), and \(I_4\), respectively. Which of the following correctly ranks the magnitudes of the currents through the four resistors from greatest to least?

A circuit consists of an ideal battery with potential difference \(\varepsilon\) connected to four resistors with resistances \(R_1 = R\), \(R_2 = 2R\), \(R_3 = 2R\), and \(R_4 = R\), as shown. Resistor \(R_1\) is in series with the battery, and the circuit then splits into two parallel branches: one branch contains resistors \(R_2\) and \(R_3\) in series, and the other branch contains resistor \(R_4\). The currents through resistors \(R_1\), \(R_2\), \(R_3\), and \(R_4\) are \(I_1\), \(I_2\), \(I_3\), and \(I_4\), respectively. Which of the following correctly ranks the magnitudes of the currents through the four resistors from greatest to least?

![A schematic diagram of a DC circuit drawn with clean black lines on a plain white background. At the far left, a vertical DC voltage source is labeled \varepsilon with positive terminal at top. From the top terminal, a horizontal wire extends right through resistor R_1, with an arrow labeled I_1. After R_1, the line meets a vertical junction wire that splits into two parallel horizontal branches. The upper branch contains two resistors in series, labeled R_2 and R_3, with arrows labeled I_2 and I_3 next to them. The lower branch contains a single resistor labeled R_4, with an arrow labeled I_4. To the right, both branches join a vertical wire that connects to a bottom horizontal wire returning 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-circuit-1-1785826331-kVDHoz.jpg)

- **A.** \(I_1 > I_2 = I_3 > I_4\)
- **B.** \(I_4 > I_1 > I_2 = I_3\)
- **C.** \(I_1 > I_2 > I_3 > I_4\)
- **D.** \(I_1 > I_4 > I_2 = I_3\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117446/*