---
title: "A solid conductor of length \\(L\\) and uniform resistivity \\(\\rho\\) is shaped as a truncated circular cone. The circular end faces have radii \\(r_1\\) and \\(r_2\\), and the cross-sectional radius varies linearly with distance along the central axis. Current enters one end face and exits the other, flowing uniformly and parallel to the central axis. Which of the following expressions represents the total electrical resistance of the conductor?"
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url: "https://nerd-notes.com/ubq/121547/"
date_modified: "2026-08-23T05:23:58+00:00"
---

# A solid conductor of length \(L\) and uniform resistivity \(\rho\) is shaped as a truncated circular cone. The circular end faces have radii \(r_1\) and \(r_2\), and the cross-sectional radius varies linearly with distance along the central axis. Current enters one end face and exits the other, flowing uniformly and parallel to the central axis. Which of the following expressions represents the total electrical resistance of the conductor?

A solid conductor of length \(L\) and uniform resistivity \(\rho\) is shaped as a truncated circular cone. The circular end faces have radii \(r_1\) and \(r_2\), and the cross-sectional radius varies linearly with distance along the central axis. Current enters one end face and exits the other, flowing uniformly and parallel to the central axis. Which of the following expressions represents the total electrical resistance of the conductor?

![A horizontal truncated circular cone centered on a horizontal dashed centerline. The left circular face has radius labeled r_1, and the right circular face has larger radius labeled r_2. A horizontal dimension line below the cone indicates total length L. An arrow on the far left points rightward into the smaller face, labeled I, and an arrow on the far right points rightward out of the larger face, labeled I. A thin vertical cross-sectional slice of thickness dx is shown at position x. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787462637-OvaMm6.jpg)

- **A.** \(\dfrac{\rho L}{\pi r_1 r_2}\)
- **B.** \(\dfrac{4\rho L}{\pi (r_1 + r_2)^2}\)
- **C.** \(\dfrac{2\rho L}{\pi (r_1^2 + r_2^2)}\)
- **D.** \(\dfrac{3\rho L}{\pi (r_1^2 + r_1 r_2 + r_2^2)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121547/*