---
title: "An ideal parallel-plate capacitor with air between its plates has an initial capacitance \\(C_0\\). The capacitor is charged by a battery to a potential difference \\(V_0\\), storing an initial electrostatic energy \\(U_0\\), and is then disconnected from the battery. The surface area of each plate is subsequently doubled while the separation distance between the plates is simultaneously tripled. What are the new capacitance \\(C\\) and the new energy \\(U\\) stored in the capacitor in terms of \\(C_0\\) and \\(U_0\\)?"
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url: "https://nerd-notes.com/ubq/118273/"
date_modified: "2026-08-04T08:08:34+00:00"
---

# An ideal parallel-plate capacitor with air between its plates has an initial capacitance \(C_0\). The capacitor is charged by a battery to a potential difference \(V_0\), storing an initial electrostatic energy \(U_0\), and is then disconnected from the battery. The surface area of each plate is subsequently doubled while the separation distance between the plates is simultaneously tripled. What are the new capacitance \(C\) and the new energy \(U\) stored in the capacitor in terms of \(C_0\) and \(U_0\)?

An ideal parallel-plate capacitor with air between its plates has an initial capacitance \(C_0\). The capacitor is charged by a battery to a potential difference \(V_0\), storing an initial electrostatic energy \(U_0\), and is then disconnected from the battery. The surface area of each plate is subsequently doubled while the separation distance between the plates is simultaneously tripled. What are the new capacitance \(C\) and the new energy \(U\) stored in the capacitor in terms of \(C_0\) and \(U_0\)?

![A two-part diagram comparing two parallel-plate capacitors side by side. On the left, labeled Initial State, two horizontal rectangular plates of area A are oriented parallel to each other separated by a vertical distance d. On the right, labeled Final State, two larger horizontal rectangular plates of area 2A are oriented parallel to each other separated by a larger vertical distance 3d. Thin vertical dashed lines connect corresponding plate corners to visually emphasize the change in dimensions. Labels A and d appear on the left setup, and labels 2A and 3d appear on the right setup. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830914-x9RnZ3.jpg)

- **A.** \(C = \dfrac{2}{3}C_0\) and \(U = \dfrac{3}{2}U_0\)
- **B.** \(C = \dfrac{2}{3}C_0\) and \(U = \dfrac{2}{3}U_0\)
- **C.** \(C = \dfrac{3}{2}C_0\) and \(U = \dfrac{2}{3}U_0\)
- **D.** \(C = \dfrac{3}{2}C_0\) and \(U = \dfrac{3}{2}U_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118273/*