---
title: "An air-filled parallel-plate capacitor \\(A\\) has plate area \\(A_0\\) and plate separation \\(d_0\\). It is charged until it holds a net charge \\(Q_0\\) and is then disconnected from the charging source. Capacitor \\(A\\) is subsequently connected in parallel across an initially uncharged, air-filled parallel-plate capacitor \\(B\\), which has plate area \\(2A_0\\) and plate separation \\(d_0/2\\). After electrostatic equilibrium is reached, what is the final charge on capacitor \\(B\\)?"
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url: "https://nerd-notes.com/ubq/118300/"
date_modified: "2026-08-04T08:08:51+00:00"
---

# An air-filled parallel-plate capacitor \(A\) has plate area \(A_0\) and plate separation \(d_0\). It is charged until it holds a net charge \(Q_0\) and is then disconnected from the charging source. Capacitor \(A\) is subsequently connected in parallel across an initially uncharged, air-filled parallel-plate capacitor \(B\), which has plate area \(2A_0\) and plate separation \(d_0/2\). After electrostatic equilibrium is reached, what is the final charge on capacitor \(B\)?

An air-filled parallel-plate capacitor \(A\) has plate area \(A_0\) and plate separation \(d_0\). It is charged until it holds a net charge \(Q_0\) and is then disconnected from the charging source. Capacitor \(A\) is subsequently connected in parallel across an initially uncharged, air-filled parallel-plate capacitor \(B\), which has plate area \(2A_0\) and plate separation \(d_0/2\). After electrostatic equilibrium is reached, what is the final charge on capacitor \(B\)?

![A clean schematic diagram showing two parallel-plate capacitors connected in a simple parallel loop. On the left, capacitor A is drawn with two horizontal parallel lines labeled with plate area A_0 and plate separation d_0. On the right, capacitor B is drawn with wider parallel lines labeled with plate area 2A_0 and plate separation d_0/2. Connecting wires form a closed loop between top plates and bottom plates. No extra elements, batteries, or switches appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830931-JImruc.jpg)

- **A.** \(\dfrac{1}{5} Q_0\)
- **B.** \(\dfrac{1}{2} Q_0\)
- **C.** \(\dfrac{2}{3} Q_0\)
- **D.** \(\dfrac{4}{5} Q_0\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118300/*