Vernier Software & Technology

# Parallel Plate Capacitor: Potential Difference vs. Spacing

## 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

$C \equiv \frac{Q} {V}$

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 analyze a parallel plate capacitor if we assume that most of the electric field lines are perpendicular to the plates. According to Gauss, if air is the insulator, the capacitance, C, is related to the area of the plates, A, and the spacing between them, d, by the equation

$C = \frac{{{\varepsilon _0}A}} {d}$

ε0 is known as the electric constant (or permittivity).

## Objectives

In this activity, you will

• Explore how the voltage (a.k.a. potential difference) across the plates varies as the distance between the charged plates increases.

## Software for Experiment

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

## Physics with Video Analysis

See other experiments from the lab book.

 1 Rolling Ball 2 Big and Small: How to Scale an Image 3 Velocity Change 4 Velocity and Speed 5 Velocity and Acceleration 6 Three Movies: Determining Constant Acceleration 7 Demon Drop: A Mathematical Modeling Activity 8 Jumping on the Moon 9 2D Vectors: Pool Ball Displacement, Velocity, and Speed 10 Galileo's Projectile I: Using 17th Century Techniques 11 Galileo's Projectile II: Using Contemporary Techniques 12 Projectile Motion Vectors 13 Frictional Slowing 14 Impulsive Juggling 15 Center of Mass Motions 16 Finding a Spring Constant 17 Net Work - Kinetic Energy Theorem 18 Oscillations 19 Slinky Wave Speeds 20 Superposition of Slinky Waves 21 A Wave Pulse Equation 22 Doppler Effect: Surface Water Waves 23 Doppler Effect: Sound Waves 24 A Heat Engine: Relating Work to the P-V Cycle 25 Coulomb's Law for Two Charged Spheres 26 Discharge Rate 27 Electric Field Due to a Line of Charge 28 Resistance and Ohm's Law 29 Parallel Plate Capacitor: Potential Difference vs. Spacing 30 Wiring Capacitors in Series and Parallel 31 Using RC Decay to Determine Capacitance 32 Exploring Faraday's Law 33 Snell's Law of Refraction

### Experiment 29 from Physics with Video Analysis Lab Book

#### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.