---
title: "An ideal parallel-plate capacitor has plate area \\(A\\), plate separation \\(d\\), and capacitance \\(C_0\\) when the space between the plates is filled with air. A slab of dielectric material with dielectric constant \\(\\kappa\\) and thickness \\(d/2\\) is inserted into the capacitor such that its faces are parallel to the conducting plates, leaving the remaining half of the gap filled with air. Which of the following expressions correctly gives the new equivalent capacitance \\(C\\) of the capacitor in terms of \\(C_0\\) and \\(\\kappa\\)?"
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url: "https://nerd-notes.com/ubq/118241/"
date_modified: "2026-08-04T08:08:23+00:00"
---

# An ideal parallel-plate capacitor has plate area \(A\), plate separation \(d\), and capacitance \(C_0\) when the space between the plates is filled with air. A slab of dielectric material with dielectric constant \(\kappa\) and thickness \(d/2\) is inserted into the capacitor such that its faces are parallel to the conducting plates, leaving the remaining half of the gap filled with air. Which of the following expressions correctly gives the new equivalent capacitance \(C\) of the capacitor in terms of \(C_0\) and \(\kappa\)?

An ideal parallel-plate capacitor has plate area \(A\), plate separation \(d\), and capacitance \(C_0\) when the space between the plates is filled with air. A slab of dielectric material with dielectric constant \(\kappa\) and thickness \(d/2\) is inserted into the capacitor such that its faces are parallel to the conducting plates, leaving the remaining half of the gap filled with air. Which of the following expressions correctly gives the new equivalent capacitance \(C\) of the capacitor in terms of \(C_0\) and \(\kappa\)?

![A schematic side view of a parallel-plate capacitor with two horizontal parallel rectangular plates separated vertically by distance d. A top dielectric slab with cross-hatched lines fills the top half of the gap across the full plate area, having thickness d/2 and labeled with dielectric constant \kappa. The bottom half of the gap of thickness d/2 is open air. Wire leads extend vertically outward from the top and bottom plates.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830902-PlBVfC.jpg)

- **A.** \(C = \left(\dfrac{1 + \kappa}{2}\right) C_0\)
- **B.** \(C = \left(\dfrac{\kappa}{1 + \kappa}\right) C_0\)
- **C.** \(C = \left(\dfrac{2\kappa}{1 + \kappa}\right) C_0\)
- **D.** \(C = \left(\dfrac{1 + \kappa}{2\kappa}\right) C_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118241/*