---
title: "An infinite resistor ladder network consists of repeating stages connected across input terminals \\(A\\) and \\(B\\). Each stage contains a series resistor of resistance \\(R\\) along the top conductor and a shunt resistor of resistance \\(2R\\) connected across the conductors. A finite 4-stage ladder network is created by cutting the infinite network after four identical stages, leaving the output terminals after the fourth stage as an open circuit. What is the equivalent resistance \\(R_{\\text{eq}}\\)` of the infinite network, and how does the equivalent resistance \\(R_4\\) of the 4-stage network compare to \\(R_{\\text{eq}}\\)?"
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/118458/"
date_modified: "2026-08-04T08:10:16+00:00"
---

# An infinite resistor ladder network consists of repeating stages connected across input terminals \(A\) and \(B\). Each stage contains a series resistor of resistance \(R\) along the top conductor and a shunt resistor of resistance \(2R\) connected across the conductors. A finite 4-stage ladder network is created by cutting the infinite network after four identical stages, leaving the output terminals after the fourth stage as an open circuit. What is the equivalent resistance \(R_{\text{eq}}\)` of the infinite network, and how does the equivalent resistance \(R_4\) of the 4-stage network compare to \(R_{\text{eq}}\)?

An infinite resistor ladder network consists of repeating stages connected across input terminals \(A\) and \(B\). Each stage contains a series resistor of resistance \(R\) along the top conductor and a shunt resistor of resistance \(2R\) connected across the conductors. A finite 4-stage ladder network is created by cutting the infinite network after four identical stages, leaving the output terminals after the fourth stage as an open circuit. What is the equivalent resistance \(R_{\text{eq}}\)` of the infinite network, and how does the equivalent resistance \(R_4\) of the 4-stage network compare to \(R_{\text{eq}}\)?

![A circuit diagram of a repeating ladder resistor network extending to the right from two input terminals labeled A and B on the far left. Terminal A is at the top left and terminal B is at the bottom left. A top horizontal wire extends to the right from terminal A, containing three series resistor zig-zag symbols in a row, each labeled R. A bottom horizontal wire extends straight to the right from terminal B. Between the top wire and bottom wire, three vertical branches are drawn, each containing a resistor zig-zag symbol labeled 2R. The first vertical branch is located immediately after the first top resistor R, the second after the second top resistor R, and the third after the third top resistor R. To the right of the third stage, three horizontal dots indicating continuation to infinity appear between the top and bottom wires. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785831016-XTn57k.jpg)

- **A.** \(R_{\text{eq}} = 2R\) and \(R_4 > R_{\text{eq}}\)
- **B.** \(R_{\text{eq}} = 2R\) and \(R_4 < R_{\text{eq}}\)
- **C.** \(R_{\text{eq}} = 3R\) and \(R_4 > R_{\text{eq}}\)
- **D.** \(R_{\text{eq}} = \dfrac{3}{2}R\) and \(R_4 < R_{\text{eq}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118458/*