# Capacitors

This section contains documents created from scanned original files and other
documents that could not be made accessible to screen reader software. A "#"
symbol is used to denote such documents.

## Video Clips

#### Capacitance

RealVideo®
8:18 minutes (10:07 - 18:25)

Definition, with examples of capacitance for spheres and for parallel plate capacitors.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Energy in a Capacitor

RealVideo®
5:34 minutes (18:25 - 23:59)

How to make a small parallel plate capacitor with a large capacitance. Finding the amount of energy stored in a parallel plate capacitor.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Demonstration: Charging a Large Capacitor

RealVideo®
2:52 minutes (30:20 - 33:12)

Starting to charge a large capacitor to a potential difference of 3000 V.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### How Photo Flash Works

RealVideo®
4:48 minutes (33:12 - 38:00)

Explanation of the concepts behind a camera flash, with a demonstration using several capacitors and a light bulb.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### High Speed Photography and Strobe Lights

RealVideo®
3:19 minutes (42:08 - 45:27)

Examples of Professor Edgerton's high speed photography, including images of a bullet fired through a light bulb and a balloon being popped. Brief discussion of strobe lights and their uses.

Prior Knowledge: Capacitance (10:07 of video lecture 7) and How Photo Flash Works (33:12 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Demonstration: Discharging a Large Capacitor

RealVideo®
3:59 minutes (45:27 - 49:26)

After 15 minutes of charging, the capacitor is quickly discharged over a fuse with impressive results.

Prior Knowledge: Capacitance (10:07 of video lecture 7) and Charging a Large Capacitor (30:20 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Work to Create Electric Field

RealVideo®
10:07 minutes (0:00 - 10:07)

Exploring work required to separate two oppositely charged parallel plates, with definition of field energy density and potential energy stored in an electric field.

Prior Knowledge: Electric Field (beginning of video lecture 2) and Electric Potential (7:14 of video lecture 4)
Instructor: Prof. Walter Lewin

#### Demonstration: Parallel Plate Capacitor

RealVideo®
6:21 minutes (23:59 - 30:20)

Using an actual parallel plate capacitor to show that positive work must be done to increase the distance between the two plates.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Demonstration: Separating Plates of a Capacitor

RealVideo®
5:37 minutes (11:03 - 16:40)

The effects of increasing the separation between the plates of a capacitor.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Demonstration: Separating Plates of a Powered Capacitor

RealVideo®
7:48 minutes (18:53 - 26:41)

The effects of increasing the separation between the plates of a capacitor that is still connected to a power supply.

Prior Knowledge: Capacitance (10:07 of video lecture 7)
Instructor: Prof. Walter Lewin

#### Increasing Capacitance

RealVideo®
5:03 minutes (31:05 - 36:08)

Effects of area, separation distance, and dielectric constant on the capacitance of a parallel plate capacitor.

Prior Knowledge: Capacitance (10:07 of video lecture 7) and Dielectrics (beginning of video lecture 8)
Instructor: Prof. Walter Lewin

#### Demonstration: Leyden Jar

RealVideo®
5:33 minutes (36:08 - 41:41)

Definition and demonstration of a Leyden Jar.

Prior Knowledge: Capacitance (10:07 of video lecture 7) and Dielectrics (beginning of video lecture 8)
Instructor: Prof. Walter Lewin

#### Parallel Plate Capacitor

RealVideo®
8:44 minutes (12:37 - 21:21)

Finding the electric field, potential difference, capacitance, and electrostatic potential energy of a parallel plate capacitor.

Prior Knowledge: Capacitors (beginning of video lecture 7)
Instructor: Prof. Walter Lewin

#### Leyden Jar Revisited

RealVideo®
17:26 minutes (32:58 - 50:24)

Demonstration of the Leyden Jar, with explanation of the physics behind the unexpected result.

Prior Knowledge: Leyden Jar (36:08 of Video Lecture 8)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Capacitors and Capacitance

PDF
Page 18 to page 29

Introduction to capacitance; spherical and parallel plate capacitors.

Prior Knowledge: Electric Field (OT2.4-2.6), Electric Potential (OT3.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Energy Stored in a Capacitor

PDF
Page 32 to page 38

Work done to build up charge on a capacitor and the energy stored in a capacitor; energy density of the electric field.

Prior Knowledge: Capacitors (OT5.1-5.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Capacitors

PDF#
Page 4 to page 8

Capacitance and units; definition of capacitor; capacitance of sphere, parallel-plate, spherical, cylindrical capacitors.

Prior Knowledge: Charge distribution
Instructor: Prof. Gabriella Sciolla

#### Leyden Jars and Capacitor Energy

PDF#
Page 2 to page 3

Leyden jars and Wimshurst machine; dielectrics; energy stored by E-field in capacitor.

Prior Knowledge: Capacitors
Instructor: Prof. Gabriella Sciolla

#### Capacitor Banks

PDF#
Page 4 to page 5

Capacitance in series and in parallel; applications and problems.

Prior Knowledge: Capacitors
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### Capacitors

PDF - 1.3 MB
Page 3 to page 9

Introduction of capacitance and examples of calculating capacitance for parallel plate, cylindrical and spherical capacitors.

Prior Knowledge: Gauss's Law (OT4.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Storing Energy in the Electric Field

PDF - 1.3 MB
Page 13 to page 14

Potential energy stored in a capacitor, and the energy density of the electric field.

Prior Knowledge: Electric Field (OT2.4-2.6), Capacitors (OT5.1-5.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Equivalent Capacitance in Series and Parallel

PDF - 1.3 MB
Page 9 to page 12

Capacitors in series and parallel circuits; calculating equivalent capacitance.

Prior Knowledge: Capacitors (OT5.1-5.2), DC Circuits (OT7.1)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

## Practice Problems

#### Finding Equivalent Capacitance

PDF - 1.3 MB
Problem on page 39 to page 40

Find the equivalent capacitance for a set of capacitors connected in parallel and in series. Solution is included after problem.

Prior Knowledge: Equivalent Capacitance (OT5.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Capacitor with Two Different Dielectrics

PDF - 1.3 MB
Problem on page 40

Find the capacitance of a parallel plate capacitor filled with two different dielectrics. Solution is included after problem.

Prior Knowledge: Dielectrics (OT5.5), Equivalent Capacitance (OT5.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Spherical Capacitor with Two Different Dielectrics

PDF - 1.3 MB
Problem on page 40 to page 41

Find the capacitance of a spherical capacitor filled with two different dielectrics. Solution is included after problem.

Prior Knowledge: Dielectrics (OT5.5), Equivalent Capacitance (OT5.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Capacitor Connected to a Spring

PDF - 1.3 MB
Problem on page 42

A spring is connected to one side of a parallel plate capacitor; find the amount that the spring is stretched when the capacitor is charged. Solution is included after problem.

Prior Knowledge: Capacitors (OT5.1-5.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Force on Plates of a Capacitor

PDF - 1.3 MB
Problem on page 45 to page 46

Find the electrostatic force and pressure on the plates of a parallel plate capacitor.

Prior Knowledge: Storing Energy in the Electric Field (OT5.4)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Combination of Capacitors

PDF - 1.3 MB
Problem on page 43

Find the equivalent capacitance and the charges on each capacitor for a combination of capacitors in different switch configurations.

Prior Knowledge: Equivalent Capacitance (OT5.3)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Separating Plate Capacitors

PDF
Problem on page 2 to page 4

Identify qualitatively how the voltage, charge and stored energy of a parallel plate capacitor change when the plate separation is increased.

Prior Knowledge: Capacitors (OT5.1-5.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Conceptual Biot-Savart Law Questions

PDF
Problem on page 6 to page 7

How do potential difference and charge change when the distance between plates in a capacitor is increased, with and without a battery connected. How does the energy stored in the system change?

Prior Knowledge: Parallel Plate Capacitors
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Analysis of a Spherical Capacitor

PDF
Problem on page 24 to page 26

Find the electric field, potential difference, capacitance, and charge distribution on a spherical capacitor. Solution is included after problem.

Prior Knowledge: Capacitors (OT5.1-5.2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

#### Switching Capacitors

PDF
Problem 2

4-part capacitor problem; finding voltages across capacitors for different switch configurations.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Van de Graaff Generator

PDF
Problem 5

Calculating current, charge, capacitance delivered to Van de Graaff generator.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Parallel-Plate Capacitor

PDF
Problem 1

5-part problem; finding V, stored energy, work to move plates; inserting dielectric.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Spherical and Cylindrical Capacitors

PDF
Problem 4

Comparison of capacitors; showing that with narrow gaps, these capacitors can be approximated as parallel-plate capacitors.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

## Exam Questions

#### Charged Capacitor

PDF
Problem 1

4-part problem; finding voltage, stored energy; explaining conservation of energy in different cases.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Electron in Parallel-Plate Capacitor

PDF
Problem 9

Force on electron; balancing electric and magnetic forces.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Edge Effects of Capacitor

PDF
Problem 4

Showing that an electric field does not abruptly drop to 0 at capacitor edge.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Point Charge in a Capacitor

PDF
Problem 4

5-part problem; finding charge, potential energy, and electric potential.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Particle in Capacitor and Magnetic Field

PDF
Problem 2

4-part problem; finding E-field, trajectories for particle; computing kinetic energy.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Energy in a Capacitor

PDF
Problem 2

Determining energy stored in parallel-plate capacitor with and without dielectric.

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

## Java Applets

#### The Capacitor

Java Applet
Requires Java Virtual Machine

Applet simulating the behavior of the charges inside the plates of a parallel plate capacitor.

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans