---
title: "A resistor made of a material with uniform resistivity \\(\\rho\\) is manufactured in the shape of a truncated cone of length \\(L\\). The two circular end-faces have radii \\(a\\) and \\(b\\), with \\(b > a\\). Current flows uniformly parallel to the central axis, entering one circular end and leaving through the other. Which of the following expressions represents the total resistance \\(R\\) of the resistor?"
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url: "https://nerd-notes.com/ubq/118337/"
date_modified: "2026-08-04T08:09:34+00:00"
---

# A resistor made of a material with uniform resistivity \(\rho\) is manufactured in the shape of a truncated cone of length \(L\). The two circular end-faces have radii \(a\) and \(b\), with \(b > a\). Current flows uniformly parallel to the central axis, entering one circular end and leaving through the other. Which of the following expressions represents the total resistance \(R\) of the resistor?

A resistor made of a material with uniform resistivity \(\rho\) is manufactured in the shape of a truncated cone of length \(L\). The two circular end-faces have radii \(a\) and \(b\), with \(b > a\). Current flows uniformly parallel to the central axis, entering one circular end and leaving through the other. Which of the following expressions represents the total resistance \(R\) of the resistor?

![A truncated solid cone of length L positioned horizontally along a central dashed axis x. The smaller circular left face has radius a. The larger circular right face has radius b. Current I enters horizontally through the center of the left end-face and exits horizontally from the center of the right end-face. A dimension line below the cone indicates the total length L. No other labels or lines appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/truncated-cone-resistor-1785830973-KGsVQH.jpg)

- **A.** \(R = \dfrac{4\rho L}{\pi (a+b)^2}\)
- **B.** \(R = \dfrac{2\rho L}{\pi (a^2 + b^2)}\)
- **C.** \(R = \dfrac{\rho L}{\pi a b}\)
- **D.** \(R = \dfrac{\rho L}{\pi (b-a)^2} \ln\left(\dfrac{b}{a}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118337/*