---
title: "A multi-plate capacitor array consists of \\(N\\) identical, flat, parallel conducting plates, each of surface area \\(A\\). The plates are stacked vertically with a uniform gap distance \\(d\\) between adjacent plates. Alternating plates are electrically connected together to form a two-terminal device, as shown in the diagram. Which of the following best explains why this interleaved configuration increases the overall capacitance, and provides the correct expression for the total capacitance \\(C_{\\text{total}}\\)?"
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url: "https://nerd-notes.com/ubq/118208/"
date_modified: "2026-08-04T08:08:10+00:00"
---

# A multi-plate capacitor array consists of \(N\) identical, flat, parallel conducting plates, each of surface area \(A\). The plates are stacked vertically with a uniform gap distance \(d\) between adjacent plates. Alternating plates are electrically connected together to form a two-terminal device, as shown in the diagram. Which of the following best explains why this interleaved configuration increases the overall capacitance, and provides the correct expression for the total capacitance \(C_{\text{total}}\)?

A multi-plate capacitor array consists of \(N\) identical, flat, parallel conducting plates, each of surface area \(A\). The plates are stacked vertically with a uniform gap distance \(d\) between adjacent plates. Alternating plates are electrically connected together to form a two-terminal device, as shown in the diagram. Which of the following best explains why this interleaved configuration increases the overall capacitance, and provides the correct expression for the total capacitance \(C_{\text{total}}\)?

![A side view diagram of a multi-plate capacitor array with 4 horizontal parallel metal plates stacked vertically with uniform gap spacing d. The plates are numbered 1, 2, 3, 4 from top to bottom. Plates 1 and 3 are connected on the left side by a vertical wire extending to terminal A. Plates 2 and 4 are connected on the right side by a vertical wire extending to terminal B. The surface area of each plate is labeled A, and the gap between each pair of adjacent plates is labeled d. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1785830890-gx0z8A.jpg)

- **A.** The configuration creates \((N - 1)\) individual capacitors connected in series, increasing the overall capacitance to \(C_{\text{total}} = (N - 1)\dfrac{\varepsilon_0 A}{d}\).
- **B.** The configuration creates \(N\) individual capacitors connected in series, increasing the overall capacitance to \(C_{\text{total}} = N\dfrac{\varepsilon_0 A}{d}\).
- **C.** The configuration creates \(N\) individual capacitors connected in parallel, increasing the overall capacitance to \(C_{\text{total}} = N\dfrac{\varepsilon_0 A}{d}\).
- **D.** The configuration creates \((N - 1)\) individual capacitors connected in parallel, increasing the overall capacitance to \(C_{\text{total}} = (N - 1)\dfrac{\varepsilon_0 A}{d}\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118208/*