---
title: "Four identical resistors, labeled \\(R_1\\), \\(R_2\\), \\(R_3\\), and \\(R_4\\), each having resistance \\(R\\), are connected to an ideal battery of potential difference \\(\\varepsilon\\) as shown in the circuit diagram. Resistor \\(R_1\\) is connected in series with the battery, followed by a junction that splits into two parallel branches: one branch contains only resistor \\(R_2\\), and the other branch contains resistors \\(R_3\\) and \\(R_4\\) in series. Which of the following correctly ranks the rate of thermal energy dissipation \\(P_1\\), \\(P_2\\), \\(P_3\\), and \\(P_4\\) in the four resistors?"
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url: "https://nerd-notes.com/ubq/120411/"
date_modified: "2026-08-23T04:34:30+00:00"
---

# Four identical resistors, labeled \(R_1\), \(R_2\), \(R_3\), and \(R_4\), each having resistance \(R\), are connected to an ideal battery of potential difference \(\varepsilon\) as shown in the circuit diagram. Resistor \(R_1\) is connected in series with the battery, followed by a junction that splits into two parallel branches: one branch contains only resistor \(R_2\), and the other branch contains resistors \(R_3\) and \(R_4\) in series. Which of the following correctly ranks the rate of thermal energy dissipation \(P_1\), \(P_2\), \(P_3\), and \(P_4\) in the four resistors?

Four identical resistors, labeled \(R_1\), \(R_2\), \(R_3\), and \(R_4\), each having resistance \(R\), are connected to an ideal battery of potential difference \(\varepsilon\) as shown in the circuit diagram. Resistor \(R_1\) is connected in series with the battery, followed by a junction that splits into two parallel branches: one branch contains only resistor \(R_2\), and the other branch contains resistors \(R_3\) and \(R_4\) in series. Which of the following correctly ranks the rate of thermal energy dissipation \(P_1\), \(P_2\), \(P_3\), and \(P_4\) in the four resistors?

![A schematic diagram of a rectangular direct-current circuit. On the left vertical segment is an ideal battery labeled with \(\varepsilon\), with the longer positive terminal on top. The wire exits the top of the battery, turns right along the top horizontal line, and contains resistor \(R_1\). To the right of \(R_1\), the top wire reaches a T-junction that splits into two parallel vertical paths. The first vertical path contains resistor \(R_2\). The second vertical path, located further to the right, contains resistor \(R_3\) positioned directly above resistor \(R_4\). Both vertical paths rejoin at a bottom horizontal wire that returns directly to the negative terminal of the battery. No other labels, text, or elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787459670-Dwmb1S.jpg)

- **A.** \(P_1 > P_2 = P_3 = P_4\)
- **B.** \(P_1 > P_2 > P_3 = P_4\)
- **C.** \(P_1 > P_3 = P_4 > P_2\)
- **D.** \(P_2 > P_1 > P_3 = P_4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120411/*