---
title: "A parallel-plate capacitor is completely filled with a dielectric slab of dielectric constant \\(\\kappa > 1\\) and charged by a battery of potential difference \\(V_0\\). In Scenario 1, the capacitor is disconnected from the battery, after which an external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \\(W_1\\). In Scenario 2, the capacitor remains connected to the battery while the external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \\(W_2\\). What is the ratio \\(\\dfrac{W_1}{W_2}\\)?"
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url: "https://nerd-notes.com/ubq/124833/"
date_modified: "2026-09-28T14:11:37+00:00"
---

# A parallel-plate capacitor is completely filled with a dielectric slab of dielectric constant \(\kappa > 1\) and charged by a battery of potential difference \(V_0\). In Scenario 1, the capacitor is disconnected from the battery, after which an external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \(W_1\). In Scenario 2, the capacitor remains connected to the battery while the external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \(W_2\). What is the ratio \(\dfrac{W_1}{W_2}\)?

A parallel-plate capacitor is completely filled with a dielectric slab of dielectric constant \(\kappa > 1\) and charged by a battery of potential difference \(V_0\). In Scenario 1, the capacitor is disconnected from the battery, after which an external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \(W_1\). In Scenario 2, the capacitor remains connected to the battery while the external agent slowly withdraws the slab until it is completely removed, requiring mechanical work \(W_2\). What is the ratio \(\dfrac{W_1}{W_2}\)?

![A side-view schematic showing two horizontal parallel conducting plates separated by a vertical distance d. The rectangular region between the plates is filled with a shaded slab labeled \kappa. Conducting wires run from the left edge of each plate to a DC voltage source labeled V_0. A single horizontal arrow pointing right is centered on the right edge of the slab. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604696-Qbsf33.jpg)

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

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124833/*