---
title: "An ideal parallel-plate capacitor with plate area \\(A\\) and separation \\(d\\) has vacuum capacitance \\(C_0\\). Two configurations are constructed using a dielectric slab of dielectric constant \\(\\kappa\\):  * **Configuration 1:** The slab has thickness \\(d\\) and fills half of the plate area \\(A/2\\). * **Configuration 2:** The slab has thickness \\(d/2\\) and fills the entire plate area \\(A\\).  In terms of \\(\\kappa\\), what is the ratio \\(\\dfrac{C_1}{C_2}\\) of the equivalent capacitance of Configuration 1 to that of Configuration 2?"
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url: "https://nerd-notes.com/ubq/118280/"
date_modified: "2026-08-04T08:08:37+00:00"
---

# An ideal parallel-plate capacitor with plate area \(A\) and separation \(d\) has vacuum capacitance \(C_0\). Two configurations are constructed using a dielectric slab of dielectric constant \(\kappa\):

* **Configuration 1:** The slab has thickness \(d\) and fills half of the plate area \(A/2\).
* **Configuration 2:** The slab has thickness \(d/2\) and fills the entire plate area \(A\).

In terms of \(\kappa\), what is the ratio \(\dfrac{C_1}{C_2}\) of the equivalent capacitance of Configuration 1 to that of Configuration 2?

An ideal parallel-plate capacitor with plate area \(A\) and separation \(d\) has vacuum capacitance \(C_0\). Two configurations are constructed using a dielectric slab of dielectric constant \(\kappa\):

* **Configuration 1:** The slab has thickness \(d\) and fills half of the plate area \(A/2\).
* **Configuration 2:** The slab has thickness \(d/2\) and fills the entire plate area \(A\).

In terms of \(\kappa\), what is the ratio \(\dfrac{C_1}{C_2}\) of the equivalent capacitance of Configuration 1 to that of Configuration 2?

![Two side-by-side schematic cross-sections labeled Configuration 1 on the left and Configuration 2 on the right. Each shows two horizontal parallel conducting plates of length L separated by vertical distance d. In Configuration 1, a shaded rectangular block labeled \kappa occupies the left half from x = 0 to x = L/2 and spans the full vertical gap from 0 to d, while the right half from x = L/2 to x = L is unshaded. In Configuration 2, a shaded rectangular block labeled \kappa occupies the upper half from y = d/2 to y = d across the full length L, while the lower half from y = 0 to y = d/2 is unshaded. Vertical dashed line indicates the boundary in Configuration 1; horizontal dashed line indicates the boundary in Configuration 2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830916-JChtJm.jpg)

- **A.** \(\dfrac{4\kappa}{(\kappa + 1)^2}\)
- **B.** \(\dfrac{\kappa + 1}{2\kappa}\)
- **C.** \(\dfrac{\kappa^2 + 1}{2\kappa}\)
- **D.** \(\dfrac{(\kappa + 1)^2}{4\kappa}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118280/*