---
title: "A set of \\(N\\) identical resistors, each with resistance \\(R\\), is connected in series to form Network 1. The same \\(N\\) resistors are then reconnected in parallel to form Network 2. In terms of \\(N\\), what is the ratio \\(\\dfrac{R_{\\text{series}}}{R_{\\text{parallel}}}\\) of the equivalent resistance of Network 1 to the equivalent resistance of Network 2?"
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url: "https://nerd-notes.com/ubq/117155/"
date_modified: "2026-08-04T06:44:49+00:00"
---

# A set of \(N\) identical resistors, each with resistance \(R\), is connected in series to form Network 1. The same \(N\) resistors are then reconnected in parallel to form Network 2. In terms of \(N\), what is the ratio \(\dfrac{R_{\text{series}}}{R_{\text{parallel}}}\) of the equivalent resistance of Network 1 to the equivalent resistance of Network 2?

A set of \(N\) identical resistors, each with resistance \(R\), is connected in series to form Network 1. The same \(N\) resistors are then reconnected in parallel to form Network 2. In terms of \(N\), what is the ratio \(\dfrac{R_{\text{series}}}{R_{\text{parallel}}}\) of the equivalent resistance of Network 1 to the equivalent resistance of Network 2?

![Two simple resistor networks drawn side by side. On the left, labeled 'Network 1', three identical resistor zig-zag symbols are connected end-to-end in series along a single horizontal wire, each labeled R. On the right, labeled 'Network 2', three identical resistor zig-zag symbols are arranged vertically in three parallel branches, each labeled R, connected at top and bottom horizontal junction wires. No batteries, ammeters, or other circuit components appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/resistor-networks-fig-1785825889-r1zgfQ.jpg)

- **A.** \(N^2\)
- **B.** \(N\)
- **C.** \(\dfrac{1}{N}\)
- **D.** \(\dfrac{1}{N^2}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/117155/*