---
title: "Four identical parallel-plate capacitors, each with capacitance \\(C_0\\) and air between plates separated by distance \\(d_0\\), are initially connected to identical batteries that maintain a constant potential difference \\(V_0\\).  Each capacitor then undergoes a different sequence of modifications, as described in the table:  | Capacitor | Modification Procedure | |—|—| | 1 | The battery is disconnected, and then the plate separation is increased to \\(2d_0\\). | | 2 | A dielectric slab of constant \\(\\kappa = 3\\) is fully inserted while connected to the battery, and then the battery is disconnected. | | 3 | The battery is disconnected, and then a dielectric slab of constant \\(\\kappa = 3\\) is fully inserted. | | 4 | The plate separation is increased to \\(2d_0\\) while connected to the battery, and then the battery is disconnected. |  Which of the following correctly ranks the final electrostatic energy \\(U\\) stored in each capacitor from greatest to least?"
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/124868/"
date_modified: "2026-09-28T14:11:44+00:00"
---

# Four identical parallel-plate capacitors, each with capacitance \(C_0\) and air between plates separated by distance \(d_0\), are initially connected to identical batteries that maintain a constant potential difference \(V_0\).

Each capacitor then undergoes a different sequence of modifications, as described in the table:

| Capacitor | Modification Procedure |
|—|—|
| 1 | The battery is disconnected, and then the plate separation is increased to \(2d_0\). |
| 2 | A dielectric slab of constant \(\kappa = 3\) is fully inserted while connected to the battery, and then the battery is disconnected. |
| 3 | The battery is disconnected, and then a dielectric slab of constant \(\kappa = 3\) is fully inserted. |
| 4 | The plate separation is increased to \(2d_0\) while connected to the battery, and then the battery is disconnected. |

Which of the following correctly ranks the final electrostatic energy \(U\) stored in each capacitor from greatest to least?

Four identical parallel-plate capacitors, each with capacitance \(C_0\) and air between plates separated by distance \(d_0\), are initially connected to identical batteries that maintain a constant potential difference \(V_0\).

Each capacitor then undergoes a different sequence of modifications, as described in the table:

| Capacitor | Modification Procedure |
|---|---|
| 1 | The battery is disconnected, and then the plate separation is increased to \(2d_0\). |
| 2 | A dielectric slab of constant \(\kappa = 3\) is fully inserted while connected to the battery, and then the battery is disconnected. |
| 3 | The battery is disconnected, and then a dielectric slab of constant \(\kappa = 3\) is fully inserted. |
| 4 | The plate separation is increased to \(2d_0\) while connected to the battery, and then the battery is disconnected. |

Which of the following correctly ranks the final electrostatic energy \(U\) stored in each capacitor from greatest to least?

- **A.** \(U_2 > U_1 > U_4 > U_3\)
- **B.** \(U_2 > U_4 > U_1 > U_3\)
- **C.** \(U_2 > U_3 > U_1 > U_4\)
- **D.** \(U_3 > U_4 > U_1 > U_2\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124868/*