---
title: "A copper wire consists of two cylindrical sections connected end-to-end, carrying a steady electric current \\(I\\). Section 1 has a radius \\(R\\), and Section 2 has a radius \\(2R\\). Let \\(J_1\\) and \\(J_2\\) be the current densities in Sections 1 and 2, respectively, and let \\(v_{d1}\\) and \\(v_{d2}\\) be the electron drift velocities in Sections 1 and 2, respectively. Which of the following correctly pairs the ratio \\(\\dfrac{J_1}{J_2}\\) with the ratio \\(\\dfrac{v_{d1}}{v_{d2}}\\)?"
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url: "https://nerd-notes.com/ubq/118364/"
date_modified: "2026-08-04T08:09:41+00:00"
---

# A copper wire consists of two cylindrical sections connected end-to-end, carrying a steady electric current \(I\). Section 1 has a radius \(R\), and Section 2 has a radius \(2R\). Let \(J_1\) and \(J_2\) be the current densities in Sections 1 and 2, respectively, and let \(v_{d1}\) and \(v_{d2}\) be the electron drift velocities in Sections 1 and 2, respectively. Which of the following correctly pairs the ratio \(\dfrac{J_1}{J_2}\) with the ratio \(\dfrac{v_{d1}}{v_{d2}}\)?

A copper wire consists of two cylindrical sections connected end-to-end, carrying a steady electric current \(I\). Section 1 has a radius \(R\), and Section 2 has a radius \(2R\). Let \(J_1\) and \(J_2\) be the current densities in Sections 1 and 2, respectively, and let \(v_{d1}\) and \(v_{d2}\) be the electron drift velocities in Sections 1 and 2, respectively. Which of the following correctly pairs the ratio \(\dfrac{J_1}{J_2}\) with the ratio \(\dfrac{v_{d1}}{v_{d2}}\)?

![A horizontal copper wire consisting of two coaxial cylindrical sections connected end-to-end. The left section is narrower, with a radius labeled R. The right section is wider, with a radius labeled 2R. A rightward arrow labeled I indicates a steady current flowing through both sections. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830981-yggJbZ.jpg)

- **A.** \(\dfrac{J_1}{J_2} = 4\)  and  \(\dfrac{v_{d1}}{v_{d2}} = 4\)
- **B.** \(\dfrac{J_1}{J_2} = 4\)  and  \(\dfrac{v_{d1}}{v_{d2}} = \dfrac{1}{4}\)
- **C.** \(\dfrac{J_1}{J_2} = 1\)  and  \(\dfrac{v_{d1}}{v_{d2}} = 4\)
- **D.** \(\dfrac{J_1}{J_2} = 2\)  and  \(\dfrac{v_{d1}}{v_{d2}} = 2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118364/*