---
title: "An ideal parallel-plate capacitor with plate area \\(A\\) and plate separation \\(d\\) is connected to a battery that maintains a constant potential difference \\(V_0\\), establishing a capacitance \\(C_0\\) and an electric field magnitude \\(E_0\\) between the plates. The capacitor is modified by doubling the plate area to \\(2A\\) and halving the separation distance to \\(d/2\\) while remaining connected to the battery. What are the new capacitance \\(C’\\) and the new electric field magnitude \\(E’\\) between the plates?"
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url: "https://nerd-notes.com/ubq/118217/"
date_modified: "2026-08-04T08:08:14+00:00"
---

# An ideal parallel-plate capacitor with plate area \(A\) and plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\), establishing a capacitance \(C_0\) and an electric field magnitude \(E_0\) between the plates. The capacitor is modified by doubling the plate area to \(2A\) and halving the separation distance to \(d/2\) while remaining connected to the battery. What are the new capacitance \(C’\) and the new electric field magnitude \(E’\) between the plates?

An ideal parallel-plate capacitor with plate area \(A\) and plate separation \(d\) is connected to a battery that maintains a constant potential difference \(V_0\), establishing a capacitance \(C_0\) and an electric field magnitude \(E_0\) between the plates. The capacitor is modified by doubling the plate area to \(2A\) and halving the separation distance to \(d/2\) while remaining connected to the battery. What are the new capacitance \(C'\) and the new electric field magnitude \(E'\) between the plates?

![A schematic drawing showing a parallel-plate capacitor connected in a simple circuit to an ideal battery labeled V_0. The top and bottom plates each have surface area A and are separated by a vertical distance d. Downward-pointing vertical electric field lines run from the top plate to the bottom plate. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830894-3uwEaD.jpg)

- **A.** \(C' = 2C_0\) and \(E' = 2E_0\)
- **B.** \(C' = 4C_0\) and \(E' = 2E_0\)
- **C.** \(C' = 4C_0\) and \(E' = E_0\)
- **D.** \(C' = C_0\) and \(E' = \dfrac{1}{2}E_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118217/*