---
title: "A hollow cylindrical resistor of length \\(L\\), inner radius \\(a\\), and outer radius \\(b\\) is made of a material with uniform resistivity \\(\\rho\\).  In Configuration 1, conducting caps are attached to the inner surface at \\(r = a\\) and outer surface at \\(r = b\\), resulting in a radial current flow with resistance \\(R_{\\text{rad}}\\).  In Configuration 2, conducting caps are attached to the flat end faces at \\(z = 0\\) and \\(z = L\\), resulting in an axial current flow with resistance \\(R_{\\text{ax}}\\).  What is the ratio \\(\\dfrac{R_{\\text{rad}}}{R_{\\text{ax}}}\\)?"
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url: "https://nerd-notes.com/ubq/118334/"
date_modified: "2026-08-04T08:09:33+00:00"
---

# A hollow cylindrical resistor of length \(L\), inner radius \(a\), and outer radius \(b\) is made of a material with uniform resistivity \(\rho\).

In Configuration 1, conducting caps are attached to the inner surface at \(r = a\) and outer surface at \(r = b\), resulting in a radial current flow with resistance \(R_{\text{rad}}\).

In Configuration 2, conducting caps are attached to the flat end faces at \(z = 0\) and \(z = L\), resulting in an axial current flow with resistance \(R_{\text{ax}}\).

What is the ratio \(\dfrac{R_{\text{rad}}}{R_{\text{ax}}}\)?

A hollow cylindrical resistor of length \(L\), inner radius \(a\), and outer radius \(b\) is made of a material with uniform resistivity \(\rho\).

In Configuration 1, conducting caps are attached to the inner surface at \(r = a\) and outer surface at \(r = b\), resulting in a radial current flow with resistance \(R_{\text{rad}}\).

In Configuration 2, conducting caps are attached to the flat end faces at \(z = 0\) and \(z = L\), resulting in an axial current flow with resistance \(R_{\text{ax}}\).

What is the ratio \(\dfrac{R_{\text{rad}}}{R_{\text{ax}}}\)?

![A perspective view showing two identical hollow cylinders side by side, each of length L with inner radius a and outer radius b. The cylinder on the left shows Configuration 1, with four radial arrows extending outward from the inner surface r = a to the outer surface r = b, labeled current I. The cylinder on the right shows Configuration 2, with four parallel arrows pointing along the central axis from the left end face z = 0 to the right end face z = L, labeled current I. Dimension lines mark inner radius a, outer radius b, and length L on both cylinders. No other labels or lines appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/cylindrical-resistor-fig-1785830972-XJwKus.jpg)

- **A.** \(\dfrac{(b-a)^2}{2L^2}\)
- **B.** \(\dfrac{(b^2 - a^2)\ln\left(\dfrac{b}{a}\right)}{L^2}\)
- **C.** \(\dfrac{(b^2 - a^2)\ln\left(\dfrac{b}{a}\right)}{2L^2}\)
- **D.** \(\dfrac{2L^2}{(b^2 - a^2)\ln\left(\dfrac{b}{a}\right)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118334/*