---
title: "A non-uniform cylindrical resistor of length \\(L\\) has a uniform resistivity \\(\\rho_0\\). The cross-sectional area \\(A\\) of the resistor varies with position \\(x\\) along its central axis according to \\(A(x) = A_0 e^{x/L}\\) for \\(0 \\le x \\le L\\), where \\(A_0\\) is a constant. Which of the following expressions represents the total electrical resistance \\(R\\) of the resistor?"
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url: "https://nerd-notes.com/ubq/118388/"
date_modified: "2026-08-04T08:09:51+00:00"
---

# A non-uniform cylindrical resistor of length \(L\) has a uniform resistivity \(\rho_0\). The cross-sectional area \(A\) of the resistor varies with position \(x\) along its central axis according to \(A(x) = A_0 e^{x/L}\) for \(0 \le x \le L\), where \(A_0\) is a constant. Which of the following expressions represents the total electrical resistance \(R\) of the resistor?

A non-uniform cylindrical resistor of length \(L\) has a uniform resistivity \(\rho_0\). The cross-sectional area \(A\) of the resistor varies with position \(x\) along its central axis according to \(A(x) = A_0 e^{x/L}\) for \(0 \le x \le L\), where \(A_0\) is a constant. Which of the following expressions represents the total electrical resistance \(R\) of the resistor?

![A resistor extending horizontally along an x-axis from x = 0 to x = L. At x = 0, the resistor has a circular cross-section of area A_0. As x increases toward x = L, the circular cross-section flares smoothly outwards exponentially to a larger circular end face at x = L. The left end face is labeled x = 0 with area A_0, and the right end face is labeled x = L. A horizontal dashed line represents the central x-axis running through the middle of the shape. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830990-N9PDaw.jpg)

- **A.** \(\dfrac{\rho_0 L}{A_0} \left(1 - \dfrac{1}{e}\right)\)
- **B.** \(\dfrac{\rho_0 L}{A_0} (e - 1)\)
- **C.** \(\dfrac{\rho_0 L}{A_0 e}\)
- **D.** \(\dfrac{\rho_0 L}{A_0} \left(1 + \dfrac{1}{e}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118388/*