---
title: "An ideal battery of potential difference \\(\\varepsilon\\) is connected in a circuit with four identical resistors, each of resistance \\(R\\), labeled \\(R_1\\), \\(R_2\\), \\(R_3\\), and \\(R_4\\). Resistor \\(R_1\\) is located in the main branch adjacent to the battery, after which the circuit splits into two parallel branches. One parallel branch contains resistor \\(R_2\\), and the other parallel branch contains resistors \\(R_3\\) and \\(R_4\\) connected in series with each other. Which of the following correctly ranks the magnitude of the electric current \\(I\\) through each resistor?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/117355/"
date_modified: "2026-08-04T06:51:56+00:00"
---

# An ideal battery of potential difference \(\varepsilon\) is connected in a circuit with four identical resistors, each of resistance \(R\), labeled \(R_1\), \(R_2\), \(R_3\), and \(R_4\). Resistor \(R_1\) is located in the main branch adjacent to the battery, after which the circuit splits into two parallel branches. One parallel branch contains resistor \(R_2\), and the other parallel branch contains resistors \(R_3\) and \(R_4\) connected in series with each other. Which of the following correctly ranks the magnitude of the electric current \(I\) through each resistor?

An ideal battery of potential difference \(\varepsilon\) is connected in a circuit with four identical resistors, each of resistance \(R\), labeled \(R_1\), \(R_2\), \(R_3\), and \(R_4\). Resistor \(R_1\) is located in the main branch adjacent to the battery, after which the circuit splits into two parallel branches. One parallel branch contains resistor \(R_2\), and the other parallel branch contains resistors \(R_3\) and \(R_4\) connected in series with each other. Which of the following correctly ranks the magnitude of the electric current \(I\) through each resistor?

![A schematic diagram of a DC circuit. On the left side, a DC battery with potential difference \varepsilon is oriented vertically with the positive terminal on top. A wire extends from the positive terminal upward, turns right, and connects to a resistor labeled R_1 oriented horizontally. After R_1, the wire reaches a junction node that splits into two parallel vertical branches. The left parallel branch contains a single resistor labeled R_2 oriented vertically. The right parallel branch contains two resistors in series, labeled R_3 and R_4, both oriented vertically with R_3 above R_4. Below the parallel branches, the wires rejoin at a bottom junction node, and a wire returns left to the negative terminal of the battery. No other elements or labels appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785826315-9vpnr9.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117355/*