---
title: "A curved resistor of uniform resistivity \\(\\rho\\) is formed from a section of a coaxial cylinder of height \\(h\\), inner radius \\(a\\), and outer radius \\(b\\), subtending an angle \\(\\theta_0\\). Two conducting flat rectangular plates are attached to the radial end faces at \\(\\theta = 0\\) and \\(\\theta = \\theta_0\\), maintaining a uniform potential difference across them such that current flows azimuthally along concentric circular arcs. Which of the following expressions represents the electrical resistance \\(R\\) between the two conducting end faces?"
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url: "https://nerd-notes.com/ubq/118366/"
date_modified: "2026-08-04T08:09:42+00:00"
---

# A curved resistor of uniform resistivity \(\rho\) is formed from a section of a coaxial cylinder of height \(h\), inner radius \(a\), and outer radius \(b\), subtending an angle \(\theta_0\). Two conducting flat rectangular plates are attached to the radial end faces at \(\theta = 0\) and \(\theta = \theta_0\), maintaining a uniform potential difference across them such that current flows azimuthally along concentric circular arcs. Which of the following expressions represents the electrical resistance \(R\) between the two conducting end faces?

A curved resistor of uniform resistivity \(\rho\) is formed from a section of a coaxial cylinder of height \(h\), inner radius \(a\), and outer radius \(b\), subtending an angle \(\theta_0\). Two conducting flat rectangular plates are attached to the radial end faces at \(\theta = 0\) and \(\theta = \theta_0\), maintaining a uniform potential difference across them such that current flows azimuthally along concentric circular arcs. Which of the following expressions represents the electrical resistance \(R\) between the two conducting end faces?

![A three-dimensional diagram showing a curved resistor segment formed from a coaxial cylinder section of height h and subtending an angle \theta_0. The inner cylindrical surface has radius a, and the outer cylindrical surface has radius b. The two flat radial end faces at \theta = 0 and \theta = \theta_0 are shaded and labeled as conducting contacts connected to potential difference V_0. Concentric dashed circular arcs indicate the direction of current flow azimuthally from one flat radial face to the other. Axis labels and radial lines mark inner radius a and outer radius b. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830982-T6BiN7.jpg)

- **A.** \(\dfrac{\rho \theta_0 (b^2 - a^2)}{2h}\)
- **B.** \(\dfrac{\rho \ln(b/a)}{\theta_0 h}\)
- **C.** \(\dfrac{\rho \theta_0}{h \ln(b/a)}\)
- **D.** \(\dfrac{\rho \theta_0 (b+a)}{2h(b-a)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118366/*