---
title: "An infinite ladder network of identical resistors, each with resistance \\(R\\), is connected to terminals \\(X\\) and \\(Y\\) as shown in the schematic. The repeating T-sections extend infinitely to the right. What is the equivalent resistance \\(R_{eq}\\) between terminals \\(X\\) and \\(Y\\) in terms of \\(R\\)?"
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url: "https://nerd-notes.com/ubq/118397/"
date_modified: "2026-08-04T08:09:54+00:00"
---

# An infinite ladder network of identical resistors, each with resistance \(R\), is connected to terminals \(X\) and \(Y\) as shown in the schematic. The repeating T-sections extend infinitely to the right. What is the equivalent resistance \(R_{eq}\) between terminals \(X\) and \(Y\) in terms of \(R\)?

An infinite ladder network of identical resistors, each with resistance \(R\), is connected to terminals \(X\) and \(Y\) as shown in the schematic. The repeating T-sections extend infinitely to the right. What is the equivalent resistance \(R_{eq}\) between terminals \(X\) and \(Y\) in terms of \(R\)?

![A horizontal schematic diagram of an infinite resistor ladder network. Two terminals labeled X (top left) and Y (bottom left) connect to the network. The top wire contains a series resistor labeled R, followed by a junction node. From this node, a vertical wire with a resistor labeled R goes down to the bottom continuous horizontal wire. From the same node, the top horizontal wire continues to the right through another resistor labeled R to a second node, which connects down through a vertical resistor labeled R to the bottom wire. This pattern repeats to the right, ending with an ellipsis (three horizontal dots) indicating an infinite continuation. The bottom wire is a single straight continuous line connecting terminal Y to the bottom terminals of all vertical resistors. No other labels or components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830994-LlOFRw.jpg)

- **A.** \(\dfrac{1 + \sqrt{5}}{2} R\)
- **B.** \(\dfrac{-1 + \sqrt{5}}{2} R\)
- **C.** \(\dfrac{1 + \sqrt{3}}{2} R\)
- **D.** \((1 + \sqrt{2}) R\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118397/*