# Steady-State Direct Current Circuits/Batteries, Resistors

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## Video Clips

#### Kirchhoff's Rules

RealVideo®
11:37 minutes (32:25 - 44:02)

Definition, with example of using the rules to solve a circuit of batteries and resistors.

Prior Knowledge: Current (beginning of video lecture 9)
Instructor: Prof. Walter Lewin

#### Ohm's Law and Kirchhoff's Rules

RealVideo®
11:27 minutes (32:47 - 44:14)

Finding currents and power in a circuit of batteries and resistors.

Prior Knowledge: Current, Resistance, Power (video lecture 9 and video lecture 10)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Batteries in Circuits

PDF
Page 14 to page 17

Describes the voltage imposed by batteries connected in series or in parallel.

Prior Knowledge: 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

#### Capacitors in Series and Parallel

PDF
Page 18 to page 24

Illustrates calculation of equivalent capacitance for capacitors connected in series or in parallel.

Prior Knowledge: Capacitors (OT5.1-5.2), Batteries
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

#### Kirchhoff's Rules

PDF
Page 5 to page 9

Kirchhoff's Second and First rules for circuits; resistors in series and parallel; finding current.

Prior Knowledge: EMF
Instructor: Prof. Gabriella Sciolla

#### More on Solving Circuits

PDF
Page 10 to page 12

Using Kirchhoff's rules to solve complex circuits; internal resistance and power dissipation.

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

## Online Textbook Chapters

#### Electrical Energy and Power

PDF
Page 7 to page 8

Work done by a battery and power dissipated by a resistor.

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

#### DC Circuits

PDF
Page 2 to page 3

Introduction to circuits, including parallel and series circuits, circuit symbols, and ground.

Prior Knowledge: Current (OT6.1)
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

#### Electromotive Force and Batteries

PDF
Page 3 to page 5

Definition of the electromotive force, comparison to voltage, and discussion of internal battery resistance.

Prior Knowledge: Current (OT6.1)
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

#### Equivalent Resistance in Series and Parallel

PDF
Page 5 to page 7

Derivations of equivalent resistance in series and in parallel.

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

#### Kirchhoff's Circuit Rules

PDF
Page 7 to page 9

Description of Kirchhoff's loop rule and Kirchhoff's junction rule; illustrates how to use them to solve 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

#### Measuring Voltage and Current

PDF
Page 9

Discussion of how ammeters and voltmeters are designed to minimize disturbance of the circuit being measured.

Prior Knowledge: DC Circuits (OT7.1), Equivalent Resistance (OT7.3)
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

#### Resistor Color Value Codes

PDF
Page 9 to page 10

Description of how to read the color bars on a resistor indicating its value and tolerance.

Prior Knowledge: None
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

#### Problem Solving: Applying Kirchhoff's Rules

PDF
Page 16 to page 19

Illustrates circuit analysis strategy by using Kirchhoff's circuit rules to write down simultaneous equations.

Prior Knowledge: 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

## Practice Problems

#### Tuning Equivalent Resistance

PDF
Problem on page 19 to page 20

For a network of four resistors, find the resistor value that gives the desired equivalent resistance. Solution is included after problem.

Prior Knowledge: Equivalent Resistance (OT7.3)
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

#### Maximizing Power Delivery

PDF
Problem on page 20 to page 21

At what load resistance does a battery deliver the most power? Solution is included after problem.

Prior Knowledge: Batteries (OT 7.2), Equivalent Resistance (OT 7.3), Electrical Power (OT6.3)
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

#### Resistors in Parallel vs. Series

PDF
Problem on page 22 to page 25

Compare the total power used by two resistors when they are connected to a battery in series vs. in parallel. Solution is included after problem.

Prior Knowledge: Equivalent Resistance (OT7.3), Electrical Power (OT6.3)
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

#### Cube Network of Resistors

PDF
Problem on page 25 to page 26

Determine the equivalent resistance of twelve identical resistors connected in a cube. Solution is included after problem.

Prior Knowledge: Equivalent Resistance (OT7.3)
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

#### Batteries in Parallel vs. Series

PDF
Problem on page 26 to page 27

Compare the load current when two batteries with internal resistance are connected in series vs. in parallel.

Prior Knowledge: Batteries (OT7.2), 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

#### Current in a Multiloop Circuit

PDF
Problem on page 27

Find the current through each of three resistors in a multiloop circuit with three batteries.

Prior Knowledge: 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

#### Power in a Multiloop Circuit

PDF
Problem on page 27

Find the power dissipated in each of three resistors in a multiloop circuit.

Prior Knowledge: 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

#### Infinite Resistor Network

PDF
Problem on page 27

Show the equivalent resistance of an infinite network of resistors.

Prior Knowledge: Equivalent Resistance (OT7.3)
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

#### Five Resistor Network

PDF
Problem on page 28

Find the potential difference across one resistor in a network of five resistors.

Prior Knowledge: 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

#### Bulbs and Batteries

PDF
Problem on page 2 to page 5

Identify how the current and power in a battery-bulb circuit change when a second bulb is added in series or in parallel.

Prior Knowledge: 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

#### Charges on Connected Capacitors

PDF
Problem on page 5

Capacitors in a circuit are charged with a battery, but then the battery is removed. How does the charge on the capacitors change?

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

#### Resistor Network

PDF
Problem 7

Finding potential differences and currents in a network of resistors.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Voltage and Resistance

PDF
Problem 2

Explaining connection between V and R across capacitor.

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

## Exam Questions

#### 3-Resistor Circuit

PDF
Problem 1

5-part problem; determining which bulbs in a circuit are lit when various switches are closed and which are brightest.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Wheatstone Bridge

PDF
Problem 3

Finding unknown resistance in Wheatstone Bridge.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Changing Magnetic Field in Resistor Circuit

PDF
Problem 13

Finding voltmeter readings and current in a circuit enclosing a changing magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### 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