---
title: "Twelve identical resistors, each with resistance \\(R\\), are connected to form the edges of a cube. A total current \\(I\\) enters the network at vertex \\(A\\) and exits at the diagonally opposite vertex \\(B\\). Which of the following correctly pairs the equivalent resistance \\(R_{\\text{eq}}\\) between vertices \\(A\\) and \\(B\\) with the current \\(I_{\\text{central}}\\) flowing through each of the six central edge resistors located between the two intermediate sets of equipotential nodes?"
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url: "https://nerd-notes.com/ubq/118420/"
date_modified: "2026-08-04T08:09:59+00:00"
---

# Twelve identical resistors, each with resistance \(R\), are connected to form the edges of a cube. A total current \(I\) enters the network at vertex \(A\) and exits at the diagonally opposite vertex \(B\). Which of the following correctly pairs the equivalent resistance \(R_{\text{eq}}\) between vertices \(A\) and \(B\) with the current \(I_{\text{central}}\) flowing through each of the six central edge resistors located between the two intermediate sets of equipotential nodes?

Twelve identical resistors, each with resistance \(R\), are connected to form the edges of a cube. A total current \(I\) enters the network at vertex \(A\) and exits at the diagonally opposite vertex \(B\). Which of the following correctly pairs the equivalent resistance \(R_{\text{eq}}\) between vertices \(A\) and \(B\) with the current \(I_{\text{central}}\) flowing through each of the six central edge resistors located between the two intermediate sets of equipotential nodes?

![An isometric 3D wireframe outline of a cube representing an electrical resistor network. Each of the twelve edges of the cube contains a standard zig-zag resistor symbol, representing identical resistance R. Vertex A is located at the bottom-front-left corner, with a single straight input wire extending to the left labeled with an arrow pointing toward A and text I. Vertex B is located at the top-back-right corner, diagonally opposite to vertex A, with a single straight output wire extending to the right labeled with an arrow pointing away from B and text I. The six intermediate vertices at the remaining corners of the cube are shown cleanly without additional labels. No other text, arrows, or symbols appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830998-EDe98n.jpg)

- **A.** \(R_{\text{eq}} = \dfrac{3}{4}R\) ; \(I_{\text{central}} = \dfrac{1}{4}I\)
- **B.** \(R_{\text{eq}} = \dfrac{5}{6}R\) ; \(I_{\text{central}} = \dfrac{1}{6}I\)
- **C.** \(R_{\text{eq}} = \dfrac{5}{6}R\) ; \(I_{\text{central}} = \dfrac{1}{3}I\)
- **D.** \(R_{\text{eq}} = \dfrac{7}{6}R\) ; \(I_{\text{central}} = \dfrac{1}{6}I\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118420/*