---
title: "An air-filled parallel-plate capacitor with initial capacitance \\(C_0\\) is connected to a battery that maintains a constant potential difference \\(V_0\\). The initial plate separation is \\(d\\). Two experimental procedures are conducted:  Case 1: The capacitor remains connected to the battery while an external agent slowly pulls the plates apart to a final separation of \\(2d\\).  Case 2: The capacitor is disconnected from the battery, and then an external agent slowly pulls the plates apart to a final separation of \\(2d\\).  If \\(W_1\\) and \\(W_2\\) represent the work done by the external agent in Case 1 and Case 2, respectively, what is the ratio \\(\\dfrac{W_2}{W_1}\\)?"
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url: "https://nerd-notes.com/ubq/118291/"
date_modified: "2026-08-04T08:08:44+00:00"
---

# An air-filled parallel-plate capacitor with initial capacitance \(C_0\) is connected to a battery that maintains a constant potential difference \(V_0\). The initial plate separation is \(d\). Two experimental procedures are conducted:

Case 1: The capacitor remains connected to the battery while an external agent slowly pulls the plates apart to a final separation of \(2d\).

Case 2: The capacitor is disconnected from the battery, and then an external agent slowly pulls the plates apart to a final separation of \(2d\).

If \(W_1\) and \(W_2\) represent the work done by the external agent in Case 1 and Case 2, respectively, what is the ratio \(\dfrac{W_2}{W_1}\)?

An air-filled parallel-plate capacitor with initial capacitance \(C_0\) is connected to a battery that maintains a constant potential difference \(V_0\). The initial plate separation is \(d\). Two experimental procedures are conducted:

Case 1: The capacitor remains connected to the battery while an external agent slowly pulls the plates apart to a final separation of \(2d\).

Case 2: The capacitor is disconnected from the battery, and then an external agent slowly pulls the plates apart to a final separation of \(2d\).

If \(W_1\) and \(W_2\) represent the work done by the external agent in Case 1 and Case 2, respectively, what is the ratio \(\dfrac{W_2}{W_1}\)?

![A schematic showing two flat parallel conducting plates of area A separated by a vertical distance d. The top plate has a wire extending upward and the bottom plate has a wire extending downward. Two arrows point outward from the top and bottom plates, indicating an external force expanding the separation to 2d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830924-fhrUgB.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118291/*