Vernier Software & Technology

# Wiring Capacitors in Series and Parallel

## 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 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,

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

where κ is the dielectric constant determined by the nature of the insulator between the conducting plates and ε0 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.

## 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 30 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.