Current, Resistance, Power

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Video Clips

Current

RealVideo®
6:52 minutes (0:00 - 6:52)

Definition, with example of calculating the drift velocity current for a copper wire.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

Ohm's Law

RealVideo®
6:22 minutes (6:52 - 13:14)

Statement of Ohm's Law with definitions of conductivity, resistance, and resistivity.

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

Ohm's Law for Insulators and Conductors

RealVideo®
3:59 minutes (13:14 - 17:13)

Comparison of the properties of good conductors and good insulators.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Ohm's Law and Temperature

RealVideo®
5:56 minutes (17:13 - 23:09)

Explanation that temperature can cause Ohm's Law to break down. Includes a demonstration of Ohm's Law holding for one resistor and not for another.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Demonstration: Breakdown of Ohm's Law

RealVideo®
4:01 minutes (23:09 - 27:10)

Ohm's Law failing to hold for a light bulb with a resistance that varies with temperature.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Resistors in Series and in Parallel

RealVideo®
5:28 minutes (27:10 - 32:38)

Definition and comparison of values for resistance, current, and voltage.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Demonstration: Increasing the Conductivity of Air

RealVideo®
4:15 minutes (32:38 - 36:53)

Using a candle to increase the conductivity of air near an electroscope.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Demonstration: Increasing the Conductivity of Water

RealVideo®
6:15 minutes (36:53 - 43:08)

Using salt to increase the conductivity of water and light a bulb.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

RealVideo®
6:08 minutes (43:08 - 49:16)

Calculation of resistance between body and Earth through a pair of shoes, including a demonstration that this resistance is not high enough to keep charge from flowing.

Prior Knowledge: Ohm's Law (6:52 of video lecture 9)
Instructor: Prof. Walter Lewin

Power Supply

RealVideo®
7:16 minutes (0:00 - 7:16)

Definition and explanation of how a battery works, with examples.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

Batteries in Circuits

RealVideo®
3:34 minutes (7:16 - 10:50)

Symbol for a battery in a circuit diagram, definition of electromotive force and internal resistance.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

Demonstration: Batteries in Series

RealVideo®
4:30 minutes (10:50 - 15:20)

Connecting two batteries in series to demonstrate that the electromotive force doubles.

Prior Knowledge: Power Supplies (beginning of video lecture 10)
Instructor: Prof. Walter Lewin

Power

RealVideo®
2:54 minutes (15:20 - 18:14)

Derivation of the equation for power P=IV, including definition of Watts as unit of power.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

Power in a Resistor

RealVideo®
5:43 minutes (18:14 - 23:57)

Finding the power consumed by a resistor, with examples including light bulbs, heaters, and the human body.

Prior Knowledge: Power (15:20 of video lecture 10)
Instructor: Prof. Walter Lewin

Power in a Battery

RealVideo®
4:33 minutes (23:57 - 28:30)

Finding the power supplied by a battery, with a demonstration of a 9 V battery being shorted out.

Prior Knowledge: Power (15:20 of video lecture 10)
Instructor: Prof. Walter Lewin

Demonstration: Shorting a Car Battery

RealVideo®
2:48 minutes (28:30 - 31:18)

Showing the large current and power supplied by a car battery when it is shorted out.

Prior Knowledge: Power (15:20 of video lecture 10)
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

High Voltage Power Lines

RealVideo®
12:19 minutes (20:39 - 32:58)

Discussion of the advantages of transporting electric energy at high voltages to minimize power loss. Calculation of the maximum voltage possible without causing corona discharge, including a slide of corona discharge on a power line during a storm.

Prior Knowledge: Electric Breakdown (32:02 of video lecture 6)
Instructor: Prof. Walter Lewin

Lecture Notes

Current in DC Circuits

PDF
Page 6 to page 17

Definition of current and current density; microscopic and macroscopic Ohm's Law.

Prior Knowledge: Charge (OT2.1)
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

Circuit Conventions

PDF
Page 18 to page 22

Circuit element symbols; sign conventions; drawing resistors and capacitors.

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

Equivalent Resistance

PDF
Page 23 to page 26

Rules governing resistors in series and parallel; how to calculate equivalent resistance in each.

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

Kirchoff's Circuit Rules

PDF
Page 27 to page 34

Illustration of Kirchoff's Circuit Rules and method for solving a circuit; includes discussion of internal resistance in batteries.

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 4 to page 7

How to measure voltage, current, and resistance in a circuit.

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

Electromotive Force

PDF
Page 3 to page 5

Definition from E-field; car batteries; direction of current flow.

Prior Knowledge: Current
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

Current and Current Density

PDF
Page 2 to page 4

Definition of macroscopic current and microscopic current density.

Prior Knowledge: Electric Charge (2.1)
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

Ohm's Law, Resistance, and Resitivity

PDF
Page 4 to page 7

Derivation of macroscopic Ohm's Law (V = IR) from microscopic; introduction of resistance, resistivity and conductivity, including temperature effect on resistivity.

Prior Knowledge: Current Density (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

Typical Values of Resistivity

PDF
Page 7

A table of values for resistivity and conductivity of several materials.

Prior Knowledge: Resistivity (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

Practice Problems

Resistance of a Cable

PDF
Problem on page 9 to page 10

Given the dimensions and resistivity of a wire, determine its resistance. Solution is included after problem.

Prior Knowledge: Resistivity (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

Drift Velocity in Sea Water

PDF
Problem on page 11 to page 12

Find the average drift velocity for ions in a tube of sea water when a voltage is applied across its length. Solution is included after problem.

Prior Knowledge: Current Density (OT6.1), Microscopic 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

Resistance of a Hollow Cylinder

PDF
Problem on page 13 to page 14

Determine the resistance of a hollow cylinder between the ends and between the inside and outside. Solution is included after problem.

Prior Knowledge: Resistivity (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

Conceptual Questions on Resistance and Power

PDF
Problem on page 14

Discuss the dependence of resistance on dimensions and temperature, and the dependence of power dissipation on resistance.

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

Current of a Whirling Charge

PDF
Problem on page 14

A conceptual question about current density of a charged sphere spun in a circle.

Prior Knowledge: Current Density (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

Ohm's Law for a Radiant Heater

PDF
Problem on page 14 to page 15

Given the power and operating voltage of a radiant heater, find the current, resistance and output of the heater.

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

Drift Speed of Electrons in Copper Wire

PDF
Problem on page 15 to page 16

How long does it take for an individual electron to travel from a car battery to the starter motor?

Prior Knowledge: Current Density and Drift Velocity (OT6.1), 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

Current Sheets

PDF
Problem on page 16

Describes the concept of a current sheet and explores the calculation of current density per unit length using a Van de Graaff belt example.

Prior Knowledge: Current Density (OT6.1), Charge Density (OT2.9)
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

Resistance of a Drawn Out Wire

PDF
Problem on page 16 to page 17

How does the resistance of a wire change if it is drawn out so that its length is increased?

Prior Knowledge: Resistivity (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

Ohm's Law for a Lightbulb

PDF
Problem on page 17

Given the power and operating voltage of a lightbulb, find the current, resistance and electricity consumption of the bulb.

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

Resistivity and Resistance

PDF
Problem on page 1

Identify how the resistance of a conductor depends on its length and area.

Prior Knowledge: Resistivity (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

Voltage in Power Lines

PDF
Problem 1

5-part power problem; finding resistance, power, voltage conditions, and Lorentz force in power lines.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

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