# 10. Capacitance and Capacitors, Energy Stored in Capacitors

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## Learning Objectives

• To be able to define what we mean by capacitance C and to explain why it is a useful concept in terms of energy storage of electric fields.
• To be able to calculate the capacitance of a parallel plate capacitor and of other capacitors with high degrees of symmetry.
• To outline why energy is stored in capacitors by describing the process by which capacitors are charged and why that process requires an amount of energy given by Q2/2C.

## Preparation

### Course Notes

Read through the course notes before watching the video.  The  course note files may also contain links to associated animations or interactive simulations.

Capacitance and Dielectrics (PDF)

## Lecture Video

### Video Excerpts

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## Learning Activities

### Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF)

### Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

### Concept Questions

Concept Questions (PDF)

Solutions (PDF)

### Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

## Problem Solving Help

Watch the Problem Solving Help videos for insights on how to approach and solve problems related to the concepts in this module.

### Problem 1: Parallel Plate Capacitor

The plates of a parallel plate capacitor are a distance d apart. The plates have an area A. Calculate the capacitance of this capacitor.

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» iTunes U (MP4 - 8MB)
» Internet Archive (MP4 - 8MB)

### Problem 2: Capacitors in Series and in Parallel

A circuit contains capacitors in series and in parallel. Find the charge on each capacitor and potential difference across each capacitor.

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» iTunes U (MP4 - 20MB)
» Internet Archive (MP4 - 20MB)

### Problem 3: Capacitance of a Spherical Capacitor

A spherical capacitor is formed from a solid metallic sphere of radius R1 surrounded by a spherical conducting shell of radius R2. Find the capacitance of this arrangement.

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» iTunes U (MP4 - 9MB)
» Internet Archive (MP4 - 9MB)

### Problem 4: Parallel Plate Capacitor with a Variable Gap

A parallel plate capacitor begins with a distance between the plates of d1. If there is no battery in the circuit, what happens to the potential between the plates when we decrease d1 to d2, with d2 < d1? What happens to the energy stored in the capacitor when this transition takes place? Now, connect the capacitor to a battery. Answer the same questions for this situation as you did for the previous case.

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» iTunes U (MP4 - 15MB)
» Internet Archive (MP4 - 15MB)

## Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

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