---
title: "A capacitor consists of two rectangular conducting plates of length \\(L\\) and width \\(W\\) tilted at a small angle \\(\\theta\\) relative to one another, such that the plate separation increases linearly from \\(d\\) at \\(x = 0\\) to \\(d + L\\theta\\) at \\(x = L\\), where \\(L\\theta \\ll d\\). Let \\(C_0 = \\dfrac{\\varepsilon_0 W L}{d}\\) be the capacitance of an ideal parallel-plate capacitor of identical dimensions with uniform separation \\(d\\). Which of the following expressions represents the best approximation for the total capacitance \\(C\\) of the tilted-plate capacitor?"
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/118244/"
date_modified: "2026-08-04T08:08:24+00:00"
---

# A capacitor consists of two rectangular conducting plates of length \(L\) and width \(W\) tilted at a small angle \(\theta\) relative to one another, such that the plate separation increases linearly from \(d\) at \(x = 0\) to \(d + L\theta\) at \(x = L\), where \(L\theta \ll d\). Let \(C_0 = \dfrac{\varepsilon_0 W L}{d}\) be the capacitance of an ideal parallel-plate capacitor of identical dimensions with uniform separation \(d\). Which of the following expressions represents the best approximation for the total capacitance \(C\) of the tilted-plate capacitor?

A capacitor consists of two rectangular conducting plates of length \(L\) and width \(W\) tilted at a small angle \(\theta\) relative to one another, such that the plate separation increases linearly from \(d\) at \(x = 0\) to \(d + L\theta\) at \(x = L\), where \(L\theta \ll d\). Let \(C_0 = \dfrac{\varepsilon_0 W L}{d}\) be the capacitance of an ideal parallel-plate capacitor of identical dimensions with uniform separation \(d\). Which of the following expressions represents the best approximation for the total capacitance \(C\) of the tilted-plate capacitor?

![A side-view diagram of a tilted parallel-plate capacitor. The bottom rectangular plate lies horizontally along the x-axis from x = 0 to x = L. The top rectangular plate is tilted upward at a small angle \theta with respect to the horizontal. At x = 0, the vertical separation between the plates is labeled d. At x = L, the vertical separation is larger, labeled d + L\theta. A differential strip of length dx at position x is indicated with a vertical dashed box of height y(x) = d + x\theta. The width W extends perpendicular to the page. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/fig-tilted-capacitor-1785830903-LglAfD.jpg)

- **A.** \(C_0 \left(1 - \dfrac{L\theta}{2d}\right)\)
- **B.** \(C_0 \left(1 + \dfrac{L\theta}{2d}\right)\)
- **C.** \(C_0 \left(1 - \dfrac{L\theta}{d}\right)\)
- **D.** \(C_0 \left(1 + \dfrac{L\theta}{d}\right)\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118244/*