# Capacitors in Circuits

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

#### RC Circuits: Charging a Capacitor

RealVideo®
11:42 minutes (1:24 - 13:06)

Deriving equations for voltage and current as functions of time in an RC circuit where the capacitor is being charged.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### RC Circuits: Discharging a Capacitor

RealVideo®
2:47 minutes (13:06 - 15:53)

Deriving equations for voltage and current as functions of time in an RC circuit where the capacitor is being discharged.

Prior Knowledge: Charging a Capacitor (1:24 of Video Lecture 24)
Instructor: Prof. Walter Lewin

#### Demonstration: Charging and Discharging a Capacitor

RealVideo®
5:35 minutes (15:53 - 21:28)

Graphs of the voltage and current in an RC circuit with a square wave power supply.

Prior Knowledge: RC Circuits (1:24 of Video Lecture 24)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Energy and Power in a Circuit

PDF
Page 35 to page 40

Electrical power of batteries, resistors, and capacitors; energy balance in a circuit.

Prior Knowledge: Ohm's Law (OT6.2)
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

#### RC Circuits

PDF
Page 9 to page 20

Charging and discharging capacitors; charge as a function of time; time constants and exponential decay.

Prior Knowledge: Capacitors (OT5.1-5.2), Kirchhoff's Rules (OT7.4)
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

#### RC Circuits

PDF
Page 2 to page 8

Charging and discharging capacitors; differential equation and solution; time constant; examples.

Prior Knowledge: Kirchhoff's Rules
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### RC Circuits

PDF
Page 10 to page 15

Finds charge, current and voltage during charging and discharging of a capacitor by applying Kirchhoff's loop rule; also discusses the time constant.

Prior Knowledge: Kirchhoff's Rules (OT7.4), 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 Problem

#### Charging and Discharging a Capacitor

PDF
Problem on page 28 to page 33

Find the current and charge as a function of time in a two-loop RC circuit with a switch, as a capacitor is charged and discharged. Solution is included after problem.

Prior Knowledge: RC Circuits
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

#### Charging Capacitor in a Multiloop Circuit

PDF
Problem on page 28

Find the currents in a multiloop RC circuit after the circuit is closed and determine the final charge on the capacitor.

Prior Knowledge: Kirchhoff's Rules (OT7.4), RC Circuits (OT7.6)
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

#### Multiloop Circuit with a Capacitor

PDF
Problem on page 3

A long time after a switch is closed, what is the current through a multiloop RC circuit.

Prior Knowledge: RC Circuits (OT7.6)
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

#### Two-Loop RC Circuit

PDF
Problem on page 5

Find the initial current through a resistor and capacitor in a two-loop RC circuit.

Prior Knowledge: RC Circuits
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

#### Conceptual Questions about DC and RC Circuits

PDF
Problem on page 26

Conceptual questions about equivalent resistance, charge in an RC circuit, and potential across a battery.

Prior Knowledge: Equivalent Resistance (OT7.3), RC Circuits (OT7.6), Batteries (OT7.2)
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

## Exam Questions

#### Charging a Capacitor

PDF
Problem 3

Finding charge as a function of time, as well as maximum power delivered.

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

#### Energy and Dielectrics

PDF
Problem 2

Stored energy and potential difference after inserting a dielectric.

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

#### Connecting a Circuit

PDF
Problem 3

6-part problem; potentials of capacitor plates and voltages in circuit before and after connection; doubled capacitor distance.

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

#### Field of a Charging Capacitor

PDF
Problem 5

Calculating rate of change of E-field, and B-field of charging capacitor.

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

#### Capacitor Circuit

PDF
Problem 2

4-part problem; finding charge and electric field for each capacitor in circuit.

Prior Knowledge: None
Instructor: Prof. Walter Lewin