---
title: "Twelve identical resistors, each having resistance \\(R\\), are connected together to form the edges of a cube. A steady total current \\(I_0\\) enters the network at vertex \\(A\\) and exits at vertex \\(B\\), which is located at the diametrically opposite body corner of the cube. Which of the following expressions gives the equivalent resistance \\(R_{\\text{eq}}\\) of the network between vertices \\(A\\) and \\(B\\)?"
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url: "https://nerd-notes.com/ubq/121564/"
date_modified: "2026-08-23T05:24:02+00:00"
---

# Twelve identical resistors, each having resistance \(R\), are connected together to form the edges of a cube. A steady total current \(I_0\) enters the network at vertex \(A\) and exits at vertex \(B\), which is located at the diametrically opposite body corner of the cube. Which of the following expressions gives the equivalent resistance \(R_{\text{eq}}\) of the network between vertices \(A\) and \(B\)?

Twelve identical resistors, each having resistance \(R\), are connected together to form the edges of a cube. A steady total current \(I_0\) enters the network at vertex \(A\) and exits at vertex \(B\), which is located at the diametrically opposite body corner of the cube. Which of the following expressions gives the equivalent resistance \(R_{\text{eq}}\) of the network between vertices \(A\) and \(B\)?

![An oblique perspective line drawing of a wireframe cube where all twelve edges represent identical resistors labeled R. Vertex A is at the bottom-front-left corner, and an incoming arrow labeled I_0 points directly into vertex A. Vertex B is at the top-back-right corner, and an outgoing arrow labeled I_0 points directly away from vertex B. Solid black line segments form the front, top, and right faces of the cube, while dashed black line segments form the hidden back and bottom edges. The letters A and B clearly label their respective corners. No other labels, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462642-1V60ZA.jpg)

- **A.** \(\dfrac{7}{12}R\)
- **B.** \(\dfrac{2}{3}R\)
- **C.** \(\dfrac{3}{4}R\)
- **D.** \(\dfrac{5}{6}R\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121564/*