# Wiring Capacitors in Series and Parallel

Recommended for High School through College.

## Introduction

A capacitor is *defined* as any two conductors, separated by an insulator where each conductor carries a net excess charge that is equal in magnitude and opposite in sign. Its capacitance, *C*, is defined as

where *Q* is the magnitude of the excess charge on each conductor and *V* is the voltage (or potential difference) across the plates.

We can use Gauss’ Law to show that for an ideal parallel plate capacitor where the electric field lines are always perpendicular to the plates, the capacitance across the plates is related to the area, *A*, of the plates and spacing, *d*, between them as shown in Equation 2,

where κ is the dielectric constant determined by the nature of the insulator between the conducting plates and ε_{0} is the electric constant (or permittivity).

## Objectives

In this activity, you will

- Determine the effective capacitance when three different capacitors, labeled A, B, and C, are wired in series and when they are wired in parallel.
- Predict the capacitance of a network of these capacitors that has both series and parallel elements in it.
- Examine a “movie” showing what happens to the effective capacitance when these three capacitors are combined in different ways.

## Software for Experiment

This experiment uses Logger *Pro* software for video analysis. The video for analysis is included with the lab book.