Home » Physics » AP Physics 1 & 2 » Electric Potential Difference

Dan Fullerton

Dan Fullerton

Electric Potential Difference

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Table of Contents

Section 1: Introduction
What is Physics?

7m 38s

Intro
0:00
Objectives
0:12
What is Physics?
0:31
What is Matter, Energy, and How to They Interact
0:55
Why?
0:58
Physics Answers the 'Why' Questions.
1:05
Matter
1:23
Matter
1:29
Mass
1:33
Inertial Mass
1:53
Gravitational Mass
2:12
A Spacecraft's Mass
2:58
Energy
3:37
Energy: The Ability or Capacity to Do Work
3:39
Work: The Process of Moving an Object
3:45
The Ability or Capacity to Move an Object
3:54
Mass-Energy Equivalence
4:51
Relationship Between Mass and Energy E=mc2
5:01
The Mass of An Object is Really a Measure of Its Energy
5:05
The Study of Everything
5:42
Introductory Course
6:19
Next Steps
7:15
Math Review

24m 12s

Intro
0:00
Outline
0:10
Objectives
0:28
Why Do We Need Units?
0:52
Need to Set Specific Standards for Our Measurements
1:01
Physicists Have Agreed to Use the Systeme International
1:24
The Systeme International
1:50
Based on Powers of 10
1:52
7 Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Kelvin, Mole
2:02
The Meter
2:18
Meter is a Measure of Length
2:20
Measurements Smaller than a Meter, Use: Centimeter, Millimeter, Micrometer, Nanometer
2:25
Measurements Larger Than a Meter, Use Kilometer
2:38
The Kilogram
2:46
Roughly Equivalent to 2.2 English Pounds
2:49
Grams, Milligrams
2:53
Megagram
2:59
Seconds
3:10
Base Unit of Time
3:12
Minute, Hour, Day
3:20
Milliseconds, Microseconds
3:33
Derived Units
3:41
Velocity
3:45
Acceleration
3:57
Force
4:04
Prefixes for Powers of 10
4:21
Converting Fundamental Units, Example 1
4:53
Converting Fundamental Units, Example 2
7:18
Two-Step Conversions, Example 1
8:24
Two-Step Conversions, Example 2
10:06
Derived Unit Conversions
11:29
Multi-Step Conversions
13:25
Metric Estimations
15:04
What are Significant Figures?
16:01
Represent a Manner of Showing Which Digits In a Number Are Known to Some Level of Certainty
16:03
Example
16:09
Measuring with Sig Figs
16:36
Rule 1
16:40
Rule 2
16:44
Rule 3
16:52
Reading Significant Figures
16:57
All Non-Zero Digits Are Significant
17:04
All Digits Between Non-Zero Digits Are Significant
17:07
Zeros to the Left of the Significant Digits
17:11
Zeros to the Right of the Significant Digits
17:16
Non-Zero Digits
17:21
Digits Between Non-Zeros Are Significant
17:45
Zeroes to the Right of the Sig Figs Are Significant
18:17
Why Scientific Notation?
18:36
Physical Measurements Vary Tremendously in Magnitude
18:38
Example
18:47
Scientific Notation in Practice
19:23
Example 1
19:28
Example 2
19:44
Using Scientific Notation
20:02
Show Your Value Using Correct Number of Significant Figures
20:05
Move the Decimal Point
20:09
Show Your Number Being Multiplied by 10 Raised to the Appropriate Power
20:14
Accuracy and Precision
20:23
Accuracy
20:36
Precision
20:41
Example 1: Scientific Notation w/ Sig Figs
21:48
Example 2: Scientific Notation - Compress
22:25
Example 3: Scientific Notation - Compress
23:07
Example 4: Scientific Notation - Expand
23:31
Vectors & Scalars

25m 5s

Intro
0:00
Objectives
0:05
Scalars
0:29
Definition of Scalar
0:39
Temperature, Mass, Time
0:45
Vectors
1:12
Vectors are Quantities That Have Magnitude and Direction
1:13
Represented by Arrows
1:31
Vector Representations
1:47
Graphical Vector Addition
2:42
Graphical Vector Subtraction
4:58
Vector Components
6:08
Angle of a Vector
8:22
Vector Notation
9:52
Example 1: Vector Components
14:30
Example 2: Vector Components
16:05
Example 3: Vector Magnitude
17:26
Example 4: Vector Addition
19:38
Example 5: Angle of a Vector
24:06
Section 2: Mechanics
Defining & Graphing Motion

30m 11s

Intro
0:00
Objectives
0:07
Position
0:40
An Object's Position Cab Be Assigned to a Variable on a Number Scale
0:43
Symbol for Position
1:07
Distance
1:13
When Position Changes, An Object Has Traveled Some Distance
1:14
Distance is Scalar and Measured in Meters
1:21
Example 1: Distance
1:34
Displacement
2:17
Displacement is a Vector Which Describes the Straight Line From Start to End Point
2:18
Measured in Meters
2:27
Example 2: Displacement
2:39
Average Speed
3:32
The Distance Traveled Divided by the Time Interval
3:33
Speed is a Scalar
3:47
Example 3: Average Speed
3:57
Average Velocity
4:37
The Displacement Divided by the Time Interval
4:38
Velocity is a Vector
4:53
Example 4: Average Velocity
5:06
Example 5: Chuck the Hungry Squirrel
5:55
Acceleration
8:02
Rate At Which Velocity Changes
8:13
Acceleration is a Vector
8:26
Example 6: Acceleration Problem
8:52
Average vs. Instantaneous
9:44
Average Values Take Into Account an Entire Time Interval
9:50
Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time
9:54
Example 7: Average Velocity
10:06
Particle Diagrams
11:57
Similar to the Effect of Oil Leak from a Car on the Pavement
11:59
Accelerating
13:03
Position-Time Graphs
14:17
Shows Position as a Function of Time
14:24
Slope of x-t Graph
15:08
Slope Gives You the Velocity
15:09
Negative Indicates Direction
16:27
Velocity-Time Graphs
16:45
Shows Velocity as a Function of Time
16:49
Area Under v-t Graphs
17:47
Area Under the V-T Graph Gives You Change in Displacement
17:48
Example 8: Slope of a v-t Graph
19:45
Acceleration-Time Graphs
21:44
Slope of the v-t Graph Gives You Acceleration
21:45
Area Under the a-t Graph Gives You an Object's Change in Velocity
22:24
Example 10: Motion Graphing
24:03
Example 11: v-t Graph
27:14
Example 12: Displacement From v-t Graph
28:14
Kinematic Equations

36m 13s

Intro
0:00
Objectives
0:07
Problem-Solving Toolbox
0:42
Graphs Are Not Always the Most Effective
0:47
Kinematic Equations Helps us Solve for Five Key Variables
0:56
Deriving the Kinematic Equations
1:29
Kinematic Equations
7:40
Problem Solving Steps
8:13
Label Your Horizontal or Vertical Motion
8:20
Choose a Direction as Positive
8:24
Create a Motion Analysis Table
8:33
Fill in Your Givens
8:42
Solve for Unknowns
8:45
Example 1: Horizontal Kinematics
8:51
Example 2: Vertical Kinematics
11:13
Example 3: 2 Step Problem
13:25
Example 4: Acceleration Problem
16:44
Example 5: Particle Diagrams
17:56
Example 6: Quadratic Solution
20:13
Free Fall
24:24
When the Only Force Acting on an Object is the Force of Gravity, the Motion is Free Fall
24:27
Air Resistance
24:51
Drop a Ball
24:56
Remove the Air from the Room
25:02
Analyze the Motion of Objects by Neglecting Air Resistance
25:06
Acceleration Due to Gravity
25:22
g = 9.8 m/s2
25:25
Approximate g as 10 m/s2 on the AP Exam
25:37
G is Referred to as the Gravitational Field Strength
25:48
Objects Falling From Rest
26:15
Objects Starting from Rest Have an Initial velocity of 0
26:19
Acceleration is +g
26:34
Example 7: Falling Objects
26:47
Objects Launched Upward
27:59
Acceleration is -g
28:04
At Highest Point, the Object has a Velocity of 0
28:19
Symmetry of Motion
28:27
Example 8: Ball Thrown Upward
28:47
Example 9: Height of a Jump
29:23
Example 10: Ball Thrown Downward
33:08
Example 11: Maximum Height
34:16
Projectiles

20m 32s

Intro
0:00
Objectives
0:06
What is a Projectile?
0:26
An Object That is Acted Upon Only By Gravity
0:29
Typically Launched at an Angle
0:43
Path of a Projectile
1:03
Projectiles Launched at an Angle Move in Parabolic Arcs
1:06
Symmetric and Parabolic
1:32
Horizontal Range and Max Height
1:49
Independence of Motion
2:17
Vertical
2:49
Horizontal
2:52
Example 1: Horizontal Launch
3:49
Example 2: Parabolic Path
7:41
Angled Projectiles
8:30
Must First Break Up the Object's Initial Velocity Into x- and y- Components of Initial Velocity
8:32
An Object Will Travel the Maximum Horizontal Distance with a Launch Angle of 45 Degrees
8:43
Example 3: Human Cannonball
8:55
Example 4: Motion Graphs
12:55
Example 5: Launch From a Height
15:33
Example 6: Acceleration of a Projectile
19:56
Relative Motion

10m 52s

Intro
0:00
Objectives
0:06
Reference Frames
0:18
Motion of an Observer
0:21
No Way to Distinguish Between Motion at Rest and Motion at a Constant Velocity
0:44
Motion is Relative
1:35
Example 1
1:39
Example 2
2:09
Calculating Relative Velocities
2:31
Example 1
2:43
Example 2
2:48
Example 3
2:52
Example 1
4:58
Example 2: Airspeed
6:19
Example 3: 2-D Relative Motion
7:39
Example 4: Relative Velocity with Direction
9:40
Newton's 1st Law of Motion

10m 16s

Intro
0:00
Objective
0:05
Newton's 1st Law of Motion
0:16
An Object At Rest Will Remain At Rest
0:21
An Object In Motion Will Remain in Motion
0:26
Net Force
0:39
Also Known As the Law of Inertia
0:46
Force
1:02
Push or Pull
1:04
Newtons
1:08
Contact and Field Forces
1:31
Contact Forces
1:50
Field Forces
2:11
What is a Net Force?
2:30
Vector Sum of All the Forces Acting on an Object
2:33
Translational Equilibrium
2:37
Unbalanced Force Is a Net Force
2:46
What Does It Mean?
3:49
An Object Will Continue in Its Current State of Motion Unless an Unbalanced Force Acts Upon It
3:50
Example of Newton's First Law
4:20
Objects in Motion
5:05
Will Remain in Motion At Constant Velocity
5:06
Hard to Find a Frictionless Environment on Earth
5:10
Static Equilibrium
5:40
Net Force on an Object is 0
5:44
Inertia
6:21
Tendency of an Object to Resist a Change in Velocity
6:23
Inertial Mass
6:35
Gravitational Mass
6:40
Example 1: Inertia
7:10
Example 2: Inertia
7:37
Example 3: Translational Equilibrium
8:03
Example 4: Net Force
8:40
Newton's 2nd Law of Motion

34m 55s

Intro
0:00
Objective
0:07
Free Body Diagrams
0:37
Tools Used to Analyze Physical Situations
0:40
Show All the Forces Acting on a Single Object
0:45
Drawing FBDs
0:58
Draw Object of Interest as a Dot
1:00
Sketch a Coordinate System
1:10
Example 1: Falling Elephant
1:18
Example 2: Falling Elephant with Air Resistance
2:07
Example 3: Soda on Table
3:00
Example 4: Box in Equilibrium
4:25
Example 5: Block on a Ramp
5:01
Pseudo-FBDs
5:53
Draw When Forces Don't Line Up with Axes
5:56
Break Forces That Don’t Line Up with Axes into Components That Do
6:00
Example 6: Objects on a Ramp
6:32
Example 7: Car on a Banked Turn
10:23
Newton's 2nd Law of Motion
12:56
The Acceleration of an Object is in the Direction of the Directly Proportional to the Net Force Applied
13:06
Newton's 1st Two Laws Compared
13:45
Newton's 1st Law
13:51
Newton's 2nd Law
14:10
Applying Newton's 2nd Law
14:50
Example 8: Applying Newton's 2nd Law
15:23
Example 9: Stopping a Baseball
16:52
Example 10: Block on a Surface
19:51
Example 11: Concurrent Forces
21:16
Mass vs. Weight
22:28
Mass
22:29
Weight
22:47
Example 12: Mass vs. Weight
23:16
Translational Equilibrium
24:47
Occurs When There Is No Net Force on an Object
24:49
Equilibrant
24:57
Example 13: Translational Equilibrium
25:29
Example 14: Translational Equilibrium
26:56
Example 15: Determining Acceleration
28:05
Example 16: Suspended Mass
31:03
Newton's 3rd Law of Motion

5m 58s

Intro
0:00
Objectives
0:06
Newton's 3rd Law of Motion
0:20
All Forces Come in Pairs
0:24
Examples
1:22
Action-Reaction Pairs
2:07
Girl Kicking Soccer Ball
2:11
Rocket Ship in Space
2:29
Gravity on You
2:53
Example 1: Force of Gravity
3:34
Example 2: Sailboat
4:00
Example 3: Hammer and Nail
4:49
Example 4: Net Force
5:06
Friction

17m 49s

Intro
0:00
Objectives
0:06
Examples
0:23
Friction Opposes Motion
0:24
Kinetic Friction
0:27
Static Friction
0:36
Magnitude of Frictional Force Is Determined By Two Things
0:41
Coefficient Friction
2:27
Ratio of the Frictional Force and the Normal Force
2:28
Chart of Different Values of Friction
2:48
Kinetic or Static?
3:31
Example 1: Car Sliding
4:18
Example 2: Block on Incline
5:03
Calculating the Force of Friction
5:48
Depends Only Upon the Nature of the Surfaces in Contact and the Magnitude of the Force
5:50
Terminal Velocity
6:14
Air Resistance
6:18
Terminal Velocity of the Falling Object
6:33
Example 3: Finding the Frictional Force
7:36
Example 4: Box on Wood Surface
9:13
Example 5: Static vs. Kinetic Friction
11:49
Example 6: Drag Force on Airplane
12:15
Example 7: Pulling a Sled
13:21
Dynamics Applications

35m 27s

Intro
0:00
Objectives
0:08
Free Body Diagrams
0:49
Drawing FBDs
1:09
Draw Object of Interest as a Dot
1:12
Sketch a Coordinate System
1:18
Example 1: FBD of Block on Ramp
1:39
Pseudo-FBDs
1:59
Draw Object of Interest as a Dot
2:00
Break Up the Forces
2:07
Box on a Ramp
2:12
Example 2: Box at Rest
4:28
Example 3: Box Held by Force
5:00
What is an Atwood Machine?
6:46
Two Objects are Connected by a Light String Over a Mass-less Pulley
6:49
Properties of Atwood Machines
7:13
Ideal Pulleys are Frictionless and Mass-less
7:16
Tension is Constant in a Light String Passing Over an Ideal Pulley
7:23
Solving Atwood Machine Problems
8:02
Alternate Solution
12:07
Analyze the System as a Whole
12:12
Elevators
14:24
Scales Read the Force They Exert on an Object Placed Upon Them
14:42
Can be Used to Analyze Using Newton's 2nd Law and Free body Diagrams
15:23
Example 4: Elevator Accelerates Upward
15:36
Example 5: Truck on a Hill
18:30
Example 6: Force Up a Ramp
19:28
Example 7: Acceleration Down a Ramp
21:56
Example 8: Basic Atwood Machine
24:05
Example 9: Masses and Pulley on a Table
26:47
Example 10: Mass and Pulley on a Ramp
29:15
Example 11: Elevator Accelerating Downward
33:00
Impulse & Momentum

26m 6s

Intro
0:00
Objectives
0:06
Momentum
0:31
Example
0:35
Momentum measures How Hard It Is to Stop a Moving Object
0:47
Vector Quantity
0:58
Example 1: Comparing Momenta
1:48
Example 2: Calculating Momentum
3:08
Example 3: Changing Momentum
3:50
Impulse
5:02
Change In Momentum
5:05
Example 4: Impulse
5:26
Example 5: Impulse-Momentum
6:41
Deriving the Impulse-Momentum Theorem
9:04
Impulse-Momentum Theorem
12:02
Example 6: Impulse-Momentum Theorem
12:15
Non-Constant Forces
13:55
Impulse or Change in Momentum
13:56
Determine the Impulse by Calculating the Area of the Triangle Under the Curve
14:07
Center of Mass
14:56
Real Objects Are More Complex Than Theoretical Particles
14:59
Treat Entire Object as if Its Entire Mass Were Contained at the Object's Center of Mass
15:09
To Calculate the Center of Mass
15:17
Example 7: Force on a Moving Object
15:49
Example 8: Motorcycle Accident
17:49
Example 9: Auto Collision
19:32
Example 10: Center of Mass (1D)
21:29
Example 11: Center of Mass (2D)
23:28
Collisions

21m 59s

Intro
0:00
Objectives
0:09
Conservation of Momentum
0:18
Linear Momentum is Conserved in an Isolated System
0:21
Useful for Analyzing Collisions and Explosions
0:27
Momentum Tables
0:58
Identify Objects in the System
1:05
Determine the Momenta of the Objects Before and After the Event
1:10
Add All the Momenta From Before the Event and Set Them Equal to Momenta After the Event
1:15
Solve Your Resulting Equation for Unknowns
1:20
Types of Collisions
1:31
Elastic Collision
1:36
Inelastic Collision
1:56
Example 1: Conservation of Momentum (1D)
2:02
Example 2: Inelastic Collision
5:12
Example 3: Recoil Velocity
7:16
Example 4: Conservation of Momentum (2D)
9:29
Example 5: Atomic Collision
16:02
Describing Circular Motion

7m 18s

Intro
0:00
Objectives
0:07
Uniform Circular Motion
0:20
Circumference
0:32
Average Speed Formula Still Applies
0:46
Frequency
1:03
Number of Revolutions or Cycles Which Occur Each Second
1:04
Hertz
1:24
Formula for Frequency
1:28
Period
1:36
Time It Takes for One Complete Revolution or Cycle
1:37
Frequency and Period
1:54
Example 1: Car on a Track
2:08
Example 2: Race Car
3:55
Example 3: Toy Train
4:45
Example 4: Round-A-Bout
5:39
Centripetal Acceleration & Force

26m 37s

Intro
0:00
Objectives
0:08
Uniform Circular Motion
0:38
Direction of ac
1:41
Magnitude of ac
3:50
Centripetal Force
4:08
For an Object to Accelerate, There Must Be a Net Force
4:18
Centripetal Force
4:26
Calculating Centripetal Force
6:14
Example 1: Acceleration
7:31
Example 2: Direction of ac
8:53
Example 3: Loss of Centripetal Force
9:19
Example 4: Velocity and Centripetal Force
10:08
Example 5: Demon Drop
10:55
Example 6: Centripetal Acceleration vs. Speed
14:11
Example 7: Calculating ac
15:03
Example 8: Running Back
15:45
Example 9: Car at an Intersection
17:15
Example 10: Bucket in Horizontal Circle
18:40
Example 11: Bucket in Vertical Circle
19:20
Example 12: Frictionless Banked Curve
21:55
Gravitation

32m 56s

Intro
0:00
Objectives
0:08
Universal Gravitation
0:29
The Bigger the Mass the Closer the Attraction
0:48
Formula for Gravitational Force
1:16
Calculating g
2:43
Mass of Earth
2:51
Radius of Earth
2:55
Inverse Square Relationship
4:32
Problem Solving Hints
7:21
Substitute Values in For Variables at the End of the Problem Only
7:26
Estimate the Order of Magnitude of the Answer Before Using Your Calculator
7:38
Make Sure Your Answer Makes Sense
7:55
Example 1: Asteroids
8:20
Example 2: Meteor and the Earth
10:17
Example 3: Satellite
13:13
Gravitational Fields
13:50
Gravity is a Non-Contact Force
13:54
Closer Objects
14:14
Denser Force Vectors
14:19
Gravitational Field Strength
15:09
Example 4: Astronaut
16:19
Gravitational Potential Energy
18:07
Two Masses Separated by Distance Exhibit an Attractive Force
18:11
Formula for Gravitational Field
19:21
How Do Orbits Work?
19:36
Example5: Gravitational Field Strength for Space Shuttle in Orbit
21:35
Example 6: Earth's Orbit
25:13
Example 7: Bowling Balls
27:25
Example 8: Freely Falling Object
28:07
Example 9: Finding g
28:40
Example 10: Space Vehicle on Mars
29:10
Example 11: Fg vs. Mass Graph
30:24
Example 12: Mass on Mars
31:14
Example 13: Two Satellites
31:51
Rotational Kinematics

15m 33s

Intro
0:00
Objectives
0:07
Radians and Degrees
0:26
In Degrees, Once Around a Circle is 360 Degrees
0:29
In Radians, Once Around a Circle is 2π
0:34
Example 1: Degrees to Radians
0:57
Example 2: Radians to Degrees
1:31
Linear vs. Angular Displacement
2:00
Linear Position
2:05
Angular Position
2:10
Linear vs. Angular Velocity
2:35
Linear Speed
2:39
Angular Speed
2:42
Direction of Angular Velocity
3:05
Converting Linear to Angular Velocity
4:22
Example 3: Angular Velocity Example
4:41
Linear vs. Angular Acceleration
5:36
Example 4: Angular Acceleration
6:15
Kinematic Variable Parallels
7:47
Displacement
7:52
Velocity
8:10
Acceleration
8:16
Time
8:22
Kinematic Variable Translations
8:30
Displacement
8:34
Velocity
8:42
Acceleration
8:50
Time
8:58
Kinematic Equation Parallels
9:09
Kinematic Equations
9:12
Delta
9:33
Final Velocity Squared and Angular Velocity Squared
9:54
Example 5: Medieval Flail
10:24
Example 6: CD Player
10:57
Example 7: Carousel
12:13
Example 8: Circular Saw
13:35
Torque

11m 21s

Intro
0:00
Objectives
0:05
Torque
0:18
Force That Causes an Object to Turn
0:22
Must be Perpendicular to the Displacement to Cause a Rotation
0:27
Lever Arm: The Stronger the Force, The More Torque
0:45
Direction of the Torque Vector
1:53
Perpendicular to the Position Vector and the Force Vector
1:54
Right-Hand Rule
2:08
Newton's 2nd Law: Translational vs. Rotational
2:46
Equilibrium
3:58
Static Equilibrium
4:01
Dynamic Equilibrium
4:09
Rotational Equilibrium
4:22
Example 1: Pirate Captain
4:32
Example 2: Auto Mechanic
5:25
Example 3: Sign Post
6:44
Example 4: See-Saw
9:01
Rotational Dynamics

36m 6s

Intro
0:00
Objectives
0:08
Types of Inertia
0:39
Inertial Mass (Translational Inertia)
0:42
Moment of Inertia (Rotational Inertia)
0:53
Moment of Inertia for Common Objects
1:48
Example 1: Calculating Moment of Inertia
2:53
Newton's 2nd Law - Revisited
5:09
Acceleration of an Object
5:15
Angular Acceleration of an Object
5:24
Example 2: Rotating Top
5:47
Example 3: Spinning Disc
7:54
Angular Momentum
9:41
Linear Momentum
9:43
Angular Momentum
10:00
Calculating Angular Momentum
10:51
Direction of the Angular Momentum Vector
11:26
Total Angular Momentum
12:29
Example 4: Angular Momentum of Particles
14:15
Example 5: Rotating Pedestal
16:51
Example 6: Rotating Discs
18:39
Angular Momentum and Heavenly Bodies
20:13
Types of Kinetic Energy
23:41
Objects Traveling with a Translational Velocity
23:45
Objects Traveling with Angular Velocity
24:00
Translational vs. Rotational Variables
24:33
Example 7: Kinetic Energy of a Basketball
25:45
Example 8: Playground Round-A-Bout
28:17
Example 9: The Ice Skater
30:54
Example 10: The Bowler
33:15
Work & Power

31m 20s

Intro
0:00
Objectives
0:09
What Is Work?
0:31
Power Output
0:35
Transfer Energy
0:39
Work is the Process of Moving an Object by Applying a Force
0:46
Examples of Work
0:56
Calculating Work
2:16
Only the Force in the Direction of the Displacement Counts
2:33
Formula for Work
2:48
Example 1: Moving a Refrigerator
3:16
Example 2: Liberating a Car
3:59
Example 3: Crate on a Ramp
5:20
Example 4: Lifting a Box
7:11
Example 5: Pulling a Wagon
8:38
Force vs. Displacement Graphs
9:33
The Area Under a Force vs. Displacement Graph is the Work Done by the Force
9:37
Find the Work Done
9:49
Example 6: Work From a Varying Force
11:00
Hooke's Law
12:42
The More You Stretch or Compress a Spring, The Greater the Force of the Spring
12:46
The Spring's Force is Opposite the Direction of Its Displacement from Equilibrium
13:00
Determining the Spring Constant
14:21
Work Done in Compressing the Spring
15:27
Example 7: Finding Spring Constant
16:21
Example 8: Calculating Spring Constant
17:58
Power
18:43
Work
18:46
Power
18:50
Example 9: Moving a Sofa
19:26
Calculating Power
20:41
Example 10: Motors Delivering Power
21:27
Example 11: Force on a Cyclist
22:40
Example 12: Work on a Spinning Mass
23:52
Example 13: Work Done by Friction
25:05
Example 14: Units of Power
28:38
Example 15: Frictional Force on a Sled
29:43
Energy

20m 15s

Intro
0:00
Objectives
0:07
What is Energy?
0:24
The Ability or Capacity to do Work
0:26
The Ability or Capacity to Move an Object
0:34
Types of Energy
0:39
Energy Transformations
2:07
Transfer Energy by Doing Work
2:12
Work-Energy Theorem
2:20
Units of Energy
2:51
Kinetic Energy
3:08
Energy of Motion
3:13
Ability or Capacity of a Moving Object to Move Another Object
3:17
A Single Object Can Only Have Kinetic Energy
3:46
Example 1: Kinetic Energy of a Motorcycle
5:08
Potential Energy
5:59
Energy An Object Possesses
6:10
Gravitational Potential Energy
7:21
Elastic Potential Energy
9:58
Internal Energy
10:16
Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration
10:20
Calculating Gravitational Potential Energy in a Constant Gravitational Field
10:57
Sources of Energy on Earth
12:41
Example 2: Potential Energy
13:41
Example 3: Energy of a System
14:40
Example 4: Kinetic and Potential Energy
15:36
Example 5: Pendulum
16:55
Conservation of Energy

23m 20s

Intro
0:00
Objectives
0:08
Law of Conservation of Energy
0:22
Energy Cannot Be Created or Destroyed.. It Can Only Be Changed
0:27
Mechanical Energy
0:34
Conservation Laws
0:40
Examples
0:49
Kinematics vs. Energy
4:34
Energy Approach
4:56
Kinematics Approach
6:04
The Pendulum
8:07
Example 1: Cart Compressing a Spring
13:09
Example 2
14:23
Example 3: Car Skidding to a Stop
16:15
Example 4: Accelerating an Object
17:27
Example 5: Block on Ramp
18:06
Example 6: Energy Transfers
19:21
Simple Harmonic Motion

58m 30s

Intro
0:00
Objectives
0:08
What Is Simple Harmonic Motion?
0:57
Nature's Typical Reaction to a Disturbance
1:00
A Displacement Which Results in a Linear Restoring Force Results in SHM
1:25
Review of Springs
1:43
When a Force is Applied to a Spring, the Spring Applies a Restoring Force
1:46
When the Spring is in Equilibrium, It Is 'Unstrained'
1:54
Factors Affecting the Force of A Spring
2:00
Oscillations
3:42
Repeated Motions
3:45
Cycle 1
3:52
Period
3:58
Frequency
4:07
Spring-Block Oscillator
4:47
Mass of the Block
4:59
Spring Constant
5:05
Example 1: Spring-Block Oscillator
6:30
Diagrams
8:07
Displacement
8:42
Velocity
8:57
Force
9:36
Acceleration
10:09
U
10:24
K
10:47
Example 2: Harmonic Oscillator Analysis
16:22
Circular Motion vs. SHM
23:26
Graphing SHM
25:52
Example 3: Position of an Oscillator
28:31
Vertical Spring-Block Oscillator
31:13
Example 4: Vertical Spring-Block Oscillator
34:26
Example 5: Bungee
36:39
The Pendulum
43:55
Mass Is Attached to a Light String That Swings Without Friction About the Vertical Equilibrium
44:04
Energy and the Simple Pendulum
44:58
Frequency and Period of a Pendulum
48:25
Period of an Ideal Pendulum
48:31
Assume Theta is Small
48:54
Example 6: The Pendulum
50:15
Example 7: Pendulum Clock
53:38
Example 8: Pendulum on the Moon
55:14
Example 9: Mass on a Spring
56:01
Section 3: Fluids
Density & Buoyancy

19m 48s

Intro
0:00
Objectives
0:09
Fluids
0:27
Fluid is Matter That Flows Under Pressure
0:31
Fluid Mechanics is the Study of Fluids
0:44
Density
0:57
Density is the Ratio of an Object's Mass to the Volume It Occupies
0:58
Less Dense Fluids
1:06
Less Dense Solids
1:09
Example 1: Density of Water
1:27
Example 2: Volume of Gold
2:19
Example 3: Floating
3:06
Buoyancy
3:54
Force Exerted by a Fluid on an Object, Opposing the Object's Weight
3:56
Buoyant Force Determined Using Archimedes Principle
4:03
Example 4: Buoyant Force
5:12
Example 5: Shark Tank
5:56
Example 6: Concrete Boat
7:47
Example 7: Apparent Mass
10:08
Example 8: Volume of a Submerged Cube
13:21
Example 9: Determining Density
15:37
Pressure & Pascal's Principle

18m 7s

Intro
0:00
Objectives
0:09
Pressure
0:25
Pressure is the Effect of a Force Acting Upon a Surface
0:27
Formula for Pressure
0:41
Force is Always Perpendicular to the Surface
0:50
Exerting Pressure
1:03
Fluids Exert Outward Pressure in All Directions on the Sides of Any Container Holding the Fluid
1:36
Earth's Atmosphere Exerts Pressure
1:42
Example 1: Pressure on Keyboard
2:17
Example 2: Sleepy Fisherman
3:03
Example 3: Scale on Planet Physica
4:12
Example 4: Ranking Pressures
5:00
Pressure on a Submerged Object
6:45
Pressure a Fluid Exerts on an Object Submerged in That Fluid
6:46
If There Is Atmosphere Above the Fluid
7:03
Example 5: Gauge Pressure Scuba Diving
7:27
Example 6: Absolute Pressure Scuba Diving
8:13
Pascal's Principle
8:51
Force Multiplication Using Pascal's Principle
9:24
Example 7: Barber's Chair
11:38
Example 8: Hydraulic Auto Lift
13:26
Example 9: Pressure on a Penny
14:41
Example 10: Depth in Fresh Water
16:39
Example 11: Absolute vs. Gauge Pressure
17:23
Continuity Equation for Fluids

7m

Intro
0:00
Objectives
0:08
Conservation of Mass for Fluid Flow
0:18
Law of Conservation of Mass for Fluids
0:21
Volume Flow Rate Remains Constant Throughout the Pipe
0:35
Volume Flow Rate
0:59
Quantified In Terms Of Volume Flow Rate
1:01
Area of Pipe x Velocity of Fluid
1:05
Must Be Constant Throughout Pipe
1:10
Example 1: Tapered Pipe
1:44
Example 2: Garden Hose
2:37
Example 3: Oil Pipeline
4:49
Example 4: Roots of Continuity Equation
6:16
Bernoulli's Principle

20m

Intro
0:00
Objectives
0:08
Bernoulli's Principle
0:21
Airplane Wings
0:35
Venturi Pump
1:56
Bernoulli's Equation
3:32
Example 1: Torricelli's Theorem
4:38
Example 2: Gauge Pressure
7:26
Example 3: Shower Pressure
8:16
Example 4: Water Fountain
12:29
Example 5: Elevated Cistern
15:26
Section 4: Thermal Physics
Temperature, Heat, & Thermal Expansion

24m 17s

Intro
0:00
Objectives
0:12
Thermal Physics
0:42
Explores the Internal Energy of Objects Due to the Motion of the Atoms and Molecules Comprising the Objects
0:46
Explores the Transfer of This Energy From Object to Object
0:53
Temperature
1:00
Thermal Energy Is Related to the Kinetic Energy of All the Particles Comprising the Object
1:03
The More Kinetic Energy of the Constituent Particles Have, The Greater the Object's Thermal Energy
1:12
Temperature and Phases of Matter
1:44
Solids
1:48
Liquids
1:56
Gases
2:02
Average Kinetic Energy and Temperature
2:16
Average Kinetic Energy
2:24
Boltzmann's Constant
2:29
Temperature Scales
3:06
Converting Temperatures
4:37
Heat
5:03
Transfer of Thermal Energy
5:06
Accomplished Through Collisions Which is Conduction
5:13
Methods of Heat Transfer
5:52
Conduction
5:59
Convection
6:19
Radiation
6:31
Quantifying Heat Transfer in Conduction
6:37
Rate of Heat Transfer is Measured in Watts
6:42
Thermal Conductivity
7:12
Example 1: Average Kinetic Energy
7:35
Example 2: Body Temperature
8:22
Example 3: Temperature of Space
9:30
Example 4: Temperature of the Sun
10:44
Example 5: Heat Transfer Through Window
11:38
Example 6: Heat Transfer Across a Rod
12:40
Thermal Expansion
14:18
When Objects Are Heated, They Tend to Expand
14:19
At Higher Temperatures, Objects Have Higher Average Kinetic Energies
14:24
At Higher Levels of Vibration, The Particles Are Not Bound As Tightly to Each Other
14:30
Linear Expansion
15:11
Amount a Material Expands is Characterized by the Material's Coefficient of Expansion
15:14
One-Dimensional Expansion -> Linear Coefficient of Expansion
15:20
Volumetric Expansion
15:38
Three-Dimensional Expansion -> Volumetric Coefficient of Expansion
15:45
Volumetric Coefficient of Expansion is Roughly Three Times the Linear Coefficient of Expansion
16:03
Coefficients of Thermal Expansion
16:24
Example 7: Contracting Railroad Tie
16:59
Example 8: Expansion of an Aluminum Rod
18:37
Example 9: Water Spilling Out of a Glass
20:18
Example 10: Average Kinetic Energy vs. Temperature
22:18
Example 11: Expansion of a Ring
23:07
Ideal Gases

24m 15s

Intro
0:00
Objectives
0:10
Ideal Gases
0:25
Gas Is Comprised of Many Particles Moving Randomly in a Container
0:34
Particles Are Far Apart From One Another
0:46
Particles Do Not Exert Forces Upon One Another Unless They Come In Contact in an Elastic Collision
0:53
Ideal Gas Law
1:18
Atoms, Molecules, and Moles
2:56
Protons
2:59
Neutrons
3:15
Electrons
3:18
Examples
3:25
Example 1: Counting Moles
4:58
Example 2: Moles of CO2 in a Bottle
6:00
Example 3: Pressurized CO2
6:54
Example 4: Helium Balloon
8:53
Internal Energy of an Ideal Gas
10:17
The Average Kinetic Energy of the Particles of an Ideal Gas
10:21
Total Internal Energy of the Ideal Gas Can Be Found by Multiplying the Average Kinetic Energy of the Gas's Particles by the Numbers of Particles in the Gas
10:32
Example 5: Internal Energy of Oxygen
12:00
Example 6: Temperature of Argon
12:41
Root-Mean-Square Velocity
13:40
This is the Square Root of the Average Velocity Squared For All the Molecules in the System
13:43
Derived from the Maxwell-Boltzmann Distribution Function
13:56
Calculating vrms
14:56
Example 7: Average Velocity of a Gas
18:32
Example 8: Average Velocity of a Gas
19:44
Example 9: vrms of Molecules in Equilibrium
20:59
Example 10: Moles to Molecules
22:25
Example 11: Relating Temperature and Internal Energy
23:22
Thermodynamics

22m 29s

Intro
0:00
Objectives
0:06
Zeroth Law of Thermodynamics
0:26
First Law of Thermodynamics
1:00
The Change in the Internal Energy of a Closed System is Equal to the Heat Added to the System Plus the Work Done on the System
1:04
It is a Restatement of the Law of Conservation of Energy
1:19
Sign Conventions Are Important
1:25
Work Done on a Gas
1:44
Example 1: Adding Heat to a System
3:25
Example 2: Expanding a Gas
4:07
P-V Diagrams
5:11
Pressure-Volume Diagrams are Useful Tools for Visualizing Thermodynamic Processes of Gases
5:13
Use Ideal Gas Law to Determine Temperature of Gas
5:25
P-V Diagrams II
5:55
Volume Increases, Pressure Decreases
6:00
As Volume Expands, Gas Does Work
6:19
Temperature Rises as You Travel Up and Right on a PV Diagram
6:29
Example 3: PV Diagram Analysis
6:40
Types of PV Processes
7:52
Adiabatic
8:03
Isobaric
8:19
Isochoric
8:28
Isothermal
8:35
Adiabatic Processes
8:47
Heat Is not Transferred Into or Out of The System
8:50
Heat = 0
8:55
Isobaric Processes
9:19
Pressure Remains Constant
9:21
PV Diagram Shows a Horizontal Line
9:27
Isochoric Processes
9:51
Volume Remains Constant
9:52
PV Diagram Shows a Vertical Line
9:58
Work Done on the Gas is Zero
10:01
Isothermal Processes
10:27
Temperature Remains Constant
10:29
Lines on a PV Diagram Are Isotherms
10:31
PV Remains Constant
10:38
Internal Energy of Gas Remains Constant
10:40
Example 4: Adiabatic Expansion
10:46
Example 5: Removing Heat
11:25
Example 6: Ranking Processes
13:08
Second Law of Thermodynamics
13:59
Heat Flows Naturally From a Warmer Object to a Colder Object
14:02
Heat Energy Cannot be Completely Transformed Into Mechanical Work
14:11
All Natural Systems Tend Toward a Higher Level of Disorder
14:19
Heat Engines
14:52
Heat Engines Convert Heat Into Mechanical Work
14:56
Efficiency of a Heat Engine is the Ratio of the Engine You Get Out to the Energy You Put In
14:59
Power in Heat Engines
16:09
Heat Engines and PV Diagrams
17:38
Carnot Engine
17:54
It Is a Theoretical Heat Engine That Operates at Maximum Possible Efficiency
18:02
It Uses Only Isothermal and Adiabatic Processes
18:08
Carnot's Theorem
18:11
Example 7: Carnot Engine
18:49
Example 8: Maximum Efficiency
21:02
Example 9: PV Processes
21:51
Section 5: Electricity & Magnetism
Electric Fields & Forces

38m 24s

Intro
0:00
Objectives
0:10
Electric Charges
0:34
Matter is Made Up of Atoms
0:37
Protons Have a Charge of +1
0:45
Electrons Have a Charge of -1
1:00
Most Atoms Are Neutral
1:04
Ions
1:15
Fundamental Unit of Charge is the Coulomb
1:29
Like Charges Repel, While Opposites Attract
1:50
Example 1: Charge on an Object
2:22
Example 2: Charge of an Alpha Particle
3:36
Conductors and Insulators
4:27
Conductors Allow Electric Charges to Move Freely
4:30
Insulators Do Not Allow Electric Charges to Move Freely
4:39
Resistivity is a Material Property
4:45
Charging by Conduction
5:05
Materials May Be Charged by Contact, Known as Conduction
5:07
Conductors May Be Charged by Contact
5:24
Example 3: Charging by Conduction
5:38
The Electroscope
6:44
Charging by Induction
8:00
Example 4: Electrostatic Attraction
9:23
Coulomb's Law
11:46
Charged Objects Apply a Force Upon Each Other = Coulombic Force
11:52
Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges
12:04
Example 5: Determine Electrostatic Force
13:09
Example 6: Deflecting an Electron Beam
15:35
Electric Fields
16:28
The Property of Space That Allows a Charged Object to Feel a Force
16:44
Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge
17:01
The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force
17:24
Example 7: Field Between Metal Plates
17:58
Visualizing the Electric Field
19:27
Electric Field Lines Point Away from Positive Charges and Toward Negative Charges
19:40
Electric Field Lines Intersect Conductors at Right Angles to the Surface
19:50
Field Strength and Line Density Decreases as You Move Away From the Charges
19:58
Electric Field Lines
20:09
E Field Due to a Point Charge
22:32
Electric Fields Are Caused by Charges
22:35
Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law
22:38
To Find the Electric Field Due to Multiple Charges
23:09
Comparing Electricity to Gravity
23:56
Force
24:02
Field Strength
24:16
Constant
24:37
Charge/ Mass Units
25:01
Example 8: E Field From 3 Point Charges
25:07
Example 9: Where is the E Field Zero?
31:43
Example 10: Gravity and Electricity
36:38
Example 11: Field Due to Point Charge
37:34
Electric Potential Difference

35m 58s

Intro
0:00
Objectives
0:09
Electric Potential Energy
0:32
When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done
0:35
When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done
0:43
Electric Potential Difference
1:30
Example 1: Charge From Work
2:06
Example 2: Electric Energy
3:09
The Electron-Volt
4:02
Electronvolt (eV)
4:15
1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:28
Example 3: Energy in eV
5:33
Equipotential Lines
6:32
Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential
6:36
Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines
6:57
Drawing Equipotential Lines
8:15
Potential Due to a Point Charge
10:46
Calculate the Electric Field Vector Due to a Point Charge
10:52
Calculate the Potential Difference Due to a Point Charge
11:05
To Find the Potential Difference Due to Multiple Point Charges
11:16
Example 4: Potential Due to a Point Charge
11:52
Example 5: Potential Due to Point Charges
13:04
Parallel Plates
16:34
Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other
16:37
These Can Create a Capacitor
16:45
E Field Due to Parallel Plates
17:14
Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant
17:15
Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation
17:47
Capacitors
18:09
Electric Device Used to Store Charge
18:11
Once the Plates Are Charged, They Are Disconnected
18:30
Device's Capacitance
18:46
Capacitors Store Energy
19:28
Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other
19:31
Example 6: Capacitance
20:28
Example 7: Charge on a Capacitor
22:03
Designing Capacitors
24:00
Area of the Plates
24:05
Separation of the Plates
24:09
Insulating Material
24:13
Example 8: Designing a Capacitor
25:35
Example 9: Calculating Capacitance
27:39
Example 10: Electron in Space
29:47
Example 11: Proton Energy Transfer
30:35
Example 12: Two Conducting Spheres
32:50
Example 13: Equipotential Lines for a Capacitor
34:48
Current & Resistance

21m 14s

Intro
0:00
Objectives
0:06
Electric Current
0:19
Path Through Current Flows
0:21
Current is the Amount of Charge Passing a Point Per Unit Time
0:25
Conventional Current is the Direction of Positive Charge Flow
0:43
Example 1: Current Through a Resistor
1:19
Example 2: Current Due to Elementary Charges
1:47
Example 3: Charge in a Light Bulb
2:35
Example 4: Flashlights
3:03
Conductivity and Resistivity
4:41
Conductivity is a Material's Ability to Conduct Electric Charge
4:53
Resistivity is a Material's Ability to Resist the Movement of Electric Charge
5:11
Resistance vs. Resistivity vs. Resistors
5:35
Resistivity Is a Material Property
5:40
Resistance Is a Functional Property of an Element in an Electric Circuit
5:57
A Resistor is a Circuit Element
7:23
Resistors
7:45
Example 5: Calculating Resistance
8:17
Example 6: Resistance Dependencies
10:09
Configuration of Resistors
10:50
When Placed in a Circuit, Resistors Can be Organized in Both Serial and Parallel Arrangements
10:53
May Be Useful to Determine an Equivalent Resistance Which Could Be Used to Replace a System or Resistors with a Single Equivalent Resistor
10:58
Resistors in Series
11:15
Resistors in Parallel
12:35
Example 7: Finding Equivalent Resistance
15:01
Example 8: Length and Resistance
17:43
Example 9: Comparing Resistors
18:21
Example 10: Comparing Wires
19:12
Ohm's Law & Power

10m 35s

Intro
0:00
Objectives
0:06
Ohm's Law
0:21
Relates Resistance, Potential Difference, and Current Flow
0:23
Example 1: Resistance of a Wire
1:22
Example 2: Circuit Current
1:58
Example 3: Variable Resistor
2:30
Ohm's 'Law'?
3:22
Very Useful Empirical Relationship
3:31
Test if a Material is 'Ohmic'
3:40
Example 4: Ohmic Material
3:58
Electrical Power
4:24
Current Flowing Through a Circuit Causes a Transfer of Energy Into Different Types
4:26
Example: Light Bulb
4:36
Example: Television
4:58
Calculating Power
5:09
Electrical Energy
5:14
Charge Per Unit Time Is Current
5:29
Expand Using Ohm's Law
5:48
Example 5: Toaster
7:43
Example 6: Electric Iron
8:19
Example 7: Power of a Resistor
9:19
Example 8: Information Required to Determine Power in a Resistor
9:55
Circuits & Electrical Meters

8m 44s

Intro
0:00
Objectives
0:08
Electrical Circuits
0:21
A Closed-Loop Path Through Which Current Can Flow
0:22
Can Be Made Up of Most Any Materials, But Typically Comprised of Electrical Devices
0:27
Circuit Schematics
1:09
Symbols Represent Circuit Elements
1:30
Lines Represent Wires
1:33
Sources for Potential Difference: Voltaic Cells, Batteries, Power Supplies
1:36
Complete Conducting Paths
2:43
Voltmeters
3:20
Measure the Potential Difference Between Two Points in a Circuit
3:21
Connected in Parallel with the Element to be Measured
3:25
Have Very High Resistance
3:59
Ammeters
4:19
Measure the Current Flowing Through an Element of a Circuit
4:20
Connected in Series with the Circuit
4:25
Have Very Low Resistance
4:45
Example 1: Ammeter and Voltmeter Placement
4:56
Example 2: Analyzing R
6:27
Example 3: Voltmeter Placement
7:12
Example 4: Behavior or Electrical Meters
7:31
Circuit Analysis

48m 58s

Intro
0:00
Objectives
0:07
Series Circuits
0:27
Series Circuits Have Only a Single Current Path
0:29
Removal of any Circuit Element Causes an Open Circuit
0:31
Kirchhoff's Laws
1:36
Tools Utilized in Analyzing Circuits
1:42
Kirchhoff's Current Law States
1:47
Junction Rule
2:00
Kirchhoff's Voltage Law States
2:05
Loop Rule
2:18
Example 1: Voltage Across a Resistor
2:23
Example 2: Current at a Node
3:45
Basic Series Circuit Analysis
4:53
Example 3: Current in a Series Circuit
9:21
Example 4: Energy Expenditure in a Series Circuit
10:14
Example 5: Analysis of a Series Circuit
12:07
Example 6: Voltmeter In a Series Circuit
14:57
Parallel Circuits
17:11
Parallel Circuits Have Multiple Current Paths
17:13
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
17:15
Basic Parallel Circuit Analysis
18:19
Example 7: Parallel Circuit Analysis
21:05
Example 8: Equivalent Resistance
22:39
Example 9: Four Parallel Resistors
23:16
Example 10: Ammeter in a Parallel Circuit
26:27
Combination Series-Parallel Circuits
28:50
Look For Portions of the Circuit With Parallel Elements
28:56
Work Back to Original Circuit
29:09
Analysis of a Combination Circuit
29:20
Internal Resistance
34:11
In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'
34:16
Terminal Voltage of the Voltage Source is Reduced Slightly
34:25
Example 11: Two Voltage Sources
35:16
Example 12: Internal Resistance
42:46
Example 13: Complex Circuit with Meters
45:22
Example 14: Parallel Equivalent Resistance
48:24
RC Circuits

24m 47s

Intro
0:00
Objectives
0:08
Capacitors in Parallel
0:34
Capacitors Store Charge on Their Plates
0:37
Capacitors In Parallel Can Be Replaced with an Equivalent Capacitor
0:46
Capacitors in Series
2:42
Charge on Capacitors Must Be the Same
2:44
Capacitor In Series Can Be Replaced With an Equivalent Capacitor
2:47
RC Circuits
5:40
Comprised of a Source of Potential Difference, a Resistor Network, and One or More Capacitors
5:42
Uncharged Capacitors Act Like Wires
6:04
Charged Capacitors Act Like Opens
6:12
Charging an RC Circuit
6:23
Discharging an RC Circuit
11:36
Example 1: RC Analysis
14:50
Example 2: More RC Analysis
18:26
Example 3: Equivalent Capacitance
21:19
Example 4: More Equivalent Capacitance
22:48
Magnetic Fields & Properties

19m 48s

Intro
0:00
Objectives
0:07
Magnetism
0:32
A Force Caused by Moving Charges
0:34
Magnetic Domains Are Clusters of Atoms with Electrons Spinning in the Same Direction
0:51
Example 1: Types of Fields
1:23
Magnetic Field Lines
2:25
Make Closed Loops and Run From North to South Outside the Magnet
2:26
Magnetic Flux
2:42
Show the Direction the North Pole of a Magnet Would Tend to Point If Placed in the Field
2:54
Example 2: Lines of Magnetic Force
3:49
Example 3: Forces Between Bar Magnets
4:39
The Compass
5:28
The Earth is a Giant Magnet
5:31
The Earth's Magnetic North pole is Located Near the Geographic South Pole, and Vice Versa
5:33
A Compass Lines Up with the Net Magnetic Field
6:07
Example 3: Compass in Magnetic Field
6:41
Example 4: Compass Near a Bar Magnet
7:14
Magnetic Permeability
7:59
The Ratio of the Magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
8:02
Free Space
8:13
Highly Magnetic Materials Have Higher Values of Magnetic Permeability
8:34
Magnetic Dipole Moment
8:41
The Force That a Magnet Can Exert on Moving Charges
8:46
Relative Strength of a Magnet
8:54
Forces on Moving Charges
9:10
Moving Charges Create Magnetic Fields
9:11
Magnetic Fields Exert Forces on Moving Charges
9:17
Direction of the Magnetic Force
9:57
Direction is Given by the Right-Hand Rule
10:05
Right-Hand Rule
10:09
Mass Spectrometer
10:52
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
10:58
Used to Determine the Mass of an Unknown Particle
11:04
Velocity Selector
12:44
Mass Spectrometer with an Electric Field Added
12:47
Example 5: Force on an Electron
14:13
Example 6: Velocity of a Charged Particle
15:25
Example 7: Direction of the Magnetic Force
16:52
Example 8: Direction of Magnetic Force on Moving Charges
17:43
Example 9: Electron Released From Rest in Magnetic Field
18:53
Current-Carrying Wires

21m 29s

Intro
0:00
Objectives
0:09
Force on a Current-Carrying Wire
0:30
A Current-Carrying Wire in a Magnetic Field May Experience a Magnetic Force
0:33
Direction Given by the Right-Hand Rule
1:11
Example 1: Force on a Current-Carrying Wire
1:38
Example 2: Equilibrium on a Submerged Wire
2:33
Example 3: Torque on a Loop of Wire
5:55
Magnetic Field Due to a Current-Carrying Wire
8:49
Moving Charges Create Magnetic Fields
8:53
Wires Carry Moving Charges
8:56
Direction Given by the Right-Hand Rule
9:21
Example 4: Magnetic Field Due to a Wire
10:56
Magnetic Field Due to a Solenoid
12:12
Solenoid is a Coil of Wire
12:19
Direction Given by the Right-Hand Rule
12:47
Forces on 2 Parallel Wires
13:34
Current Flowing in the Same Direction
14:52
Current Flowing in Opposite Directions
14:57
Example 5: Magnetic Field Due to Wires
15:19
Example 6: Strength of an Electromagnet
18:35
Example 7: Force on a Wire
19:30
Example 8: Force Between Parallel Wires
20:47
Intro to Electromagnetic Induction

17m 26s

Intro
0:00
Objectives
0:09
Induced EMF
0:42
Charges Flowing Through a Wire Create Magnetic Fields
0:45
Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
0:49
Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
0:57
Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
1:17
Finding the Magnetic Flux
1:36
Magnetic Field Strength
1:39
Angle Between the Magnetic Field Strength and the Normal to the Area
1:51
Calculating Induced EMF
3:01
The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux
3:04
Induced EMF in a Rectangular Loop of Wire
4:03
Lenz's Law
5:17
Electric Generators and Motors
9:28
Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field
9:31
Generators Use Mechanical Energy to Turn the Coil of Wire
9:39
Electric Motor Operates Using Same Principle
10:30
Example 1: Finding Magnetic Flux
10:43
Example 2: Finding Induced EMF
11:54
Example 3: Changing Magnetic Field
13:52
Example 4: Current Induced in a Rectangular Loop of Wire
15:23
Section 6: Waves & Optics
Wave Characteristics

26m 41s

Intro
0:00
Objectives
0:09
Waves
0:32
Pulse
1:00
A Pulse is a Single Disturbance Which Carries Energy Through a Medium or Space
1:05
A Wave is a Series of Pulses
1:18
When a Pulse Reaches a Hard Boundary
1:37
When a Pulse Reaches a Soft or Flexible Boundary
2:04
Types of Waves
2:44
Mechanical Waves
2:56
Electromagnetic Waves
3:14
Types of Wave Motion
3:38
Longitudinal Waves
3:39
Transverse Waves
4:18
Anatomy of a Transverse Wave
5:18
Example 1: Waves Requiring a Medium
6:59
Example 2: Direction of Displacement
7:36
Example 3: Bell in a Vacuum Jar
8:47
Anatomy of a Longitudinal Wave
9:22
Example 4: Tuning Fork
9:57
Example 5: Amplitude of a Sound Wave
10:24
Frequency and Period
10:47
Example 6: Period of an EM Wave
11:23
Example 7: Frequency and Period
12:01
The Wave Equation
12:32
Velocity of a Wave is a Function of the Type of Wave and the Medium It Travels Through
12:36
Speed of a Wave is Related to Its Frequency and Wavelength
12:41
Example 8: Wavelength Using the Wave Equation
13:54
Example 9: Period of an EM Wave
14:35
Example 10: Blue Whale Waves
16:03
Sound Waves
17:29
Sound is a Mechanical Wave Observed by Detecting Vibrations in the Inner Ear
17:33
Particles of Sound Wave Vibrate Parallel With the Direction of the Wave's Velocity
17:56
Example 11: Distance from Speakers
18:24
Resonance
19:45
An Object with the Same 'Natural Frequency' May Begin to Vibrate at This Frequency
19:55
Classic Example
20:01
Example 12: Vibrating Car
20:32
Example 13: Sonar Signal
21:28
Example 14: Waves Across Media
24:06
Example 15: Wavelength of Middle C
25:24
Wave Interference

20m 45s

Intro
0:00
Objectives
0:09
Superposition
0:30
When More Than One Wave Travels Through the Same Location in the Same Medium
0:32
The Total Displacement is the Sum of All the Individual Displacements of the Waves
0:46
Example 1: Superposition of Pulses
1:01
Types of Interference
2:02
Constructive Interference
2:05
Destructive Interference
2:18
Example 2: Interference
2:47
Example 3: Shallow Water Waves
3:27
Standing Waves
4:23
When Waves of the Same Frequency and Amplitude Traveling in Opposite Directions Meet in the Same Medium
4:26
A Wave in Which Nodes Appear to be Standing Still and Antinodes Vibrate with Maximum Amplitude Above and Below the Axis
4:35
Standing Waves in String Instruments
5:36
Standing Waves in Open Tubes
8:49
Standing Waves in Closed Tubes
9:57
Interference From Multiple Sources
11:43
Constructive
11:55
Destructive
12:14
Beats
12:49
Two Sound Waves with Almost the Same Frequency Interfere to Create a Beat Pattern
12:52
A Frequency Difference of 1 to 4 Hz is Best for Human Detection of Beat Phenomena
13:05
Example 4
14:13
Example 5
18:03
Example 6
19:14
Example 7: Superposition
20:08
Wave Phenomena

19m 2s

Intro
0:00
Objective
0:08
Doppler Effect
0:36
The Shift In A Wave's Observed Frequency Due to Relative Motion Between the Source of the Wave and Observer
0:39
When Source and/or Observer Move Toward Each Other
0:45
When Source and/or Observer Move Away From Each Other
0:52
Practical Doppler Effect
1:01
Vehicle Traveling Past You
1:05
Applications Are Numerous and Widespread
1:56
Doppler Effect - Astronomy
2:43
Observed Frequencies Are Slightly Lower Than Scientists Would Predict
2:50
More Distant Celestial Objects Are Moving Away from the Earth Faster Than Nearer Objects
3:22
Example 1: Car Horn
3:36
Example 2: Moving Speaker
4:13
Diffraction
5:35
The Bending of Waves Around Obstacles
5:37
Most Apparent When Wavelength Is Same Order of Magnitude as the Obstacle/ Opening
6:10
Single-Slit Diffraction
6:16
Double-Slit Diffraction
8:13
Diffraction Grating
11:07
Sharper and Brighter Maxima
11:46
Useful for Determining Wavelengths Accurately
12:07
Example 3: Double Slit Pattern
12:30
Example 4: Determining Wavelength
16:05
Example 5: Radar Gun
18:04
Example 6: Red Shift
18:29
Light As a Wave

11m 35s

Intro
0:00
Objectives
0:14
Electromagnetic (EM) Waves
0:31
Light is an EM Wave
0:43
EM Waves Are Transverse Due to the Modulation of the Electric and Magnetic Fields Perpendicular to the Wave Velocity
1:00
Electromagnetic Wave Characteristics
1:37
The Product of an EM Wave's Frequency and Wavelength Must be Constant in a Vacuum
1:43
Polarization
3:36
Unpoloarized EM Waves Exhibit Modulation in All Directions
3:47
Polarized Light Consists of Light Vibrating in a Single Direction
4:07
Polarizers
4:29
Materials Which Act Like Filters to Only Allow Specific Polarizations of Light to Pass
4:33
Polarizers Typically Are Sheets of Material in Which Long Molecules Are Lined Up Like a Picket Fence
5:10
Polarizing Sunglasses
5:22
Reduce Reflections
5:26
Polarizing Sunglasses Have Vertical Polarizing Filters
5:48
Liquid Crystal Displays
6:08
LCDs Use Liquid Crystals in a Suspension That Align Themselves in a Specific Orientation When a Voltage is Applied
6:13
Cross-Orienting a Polarizer and a Matrix of Liquid Crystals so Light Can Be Modulated Pixel-by-Pixel
6:26
Example 1: Color of Light
7:30
Example 2: Analyzing an EM Wave
8:49
Example 3: Remote Control
9:45
Example 4: Comparing EM Waves
10:32
Reflection & Mirrors

24m 32s

Intro
0:00
Objectives
0:10
Waves at Boundaries
0:37
Reflected
0:43
Transmitted
0:45
Absorbed
0:48
Law of Reflection
0:58
The Angle of Incidence is Equal to the Angle of Reflection
1:00
They Are Both Measured From a Line Perpendicular, or Normal, to the Reflecting Surface
1:22
Types of Reflection
1:54
Diffuse Reflection
1:57
Specular Reflection
2:08
Example 1: Specular Reflection
2:24
Mirrors
3:20
Light Rays From the Object Reach the Plane Mirror and Are Reflected to the Observer
3:27
Virtual Image
3:33
Magnitude of Image Distance
4:05
Plane Mirror Ray Tracing
4:15
Object Distance
4:26
Image Distance
4:43
Magnification of Image
7:03
Example 2: Plane Mirror Images
7:28
Example 3: Image in a Plane Mirror
7:51
Spherical Mirrors
8:10
Inner Surface of a Spherical Mirror
8:19
Outer Surface of a Spherical Mirror
8:30
Focal Point of a Spherical Mirror
8:40
Converging
8:51
Diverging
9:00
Concave (Converging) Spherical Mirrors
9:09
Light Rays Coming Into a Mirror Parallel to the Principal Axis
9:14
Light Rays Passing Through the Center of Curvature
10:17
Light Rays From the Object Passing Directly Through the Focal Point
10:52
Mirror Equation (Lens Equation)
12:06
Object and Image Distances Are Positive on the Reflecting Side of the Mirror
12:13
Formula
12:19
Concave Mirror with Object Inside f
12:39
Example 4: Concave Spherical Mirror
14:21
Example 5: Image From a Concave Mirror
14:51
Convex (Diverging) Spherical Mirrors
16:29
Light Rays Coming Into a Mirror Parallel to the Principal Axis
16:37
Light Rays Striking the Center of the Mirror
16:50
Light Rays Never Converge on the Reflective Side of a Convex Mirror
16:54
Convex Mirror Ray Tracing
17:07
Example 6: Diverging Rays
19:12
Example 7: Focal Length
19:28
Example 8: Reflected Sonar Wave
19:53
Example 9: Plane Mirror Image Distance
20:20
Example 10: Image From a Concave Mirror
21:23
Example 11: Converging Mirror Image Distance
23:09
Refraction & Lenses

39m 42s

Intro
0:00
Objectives
0:09
Refraction
0:42
When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium
0:43
Wavelength Must Change If the Wave's Speed Changes
0:57
Refraction is When This Causes The Wave to Bend as It Enters the New Medium
1:12
Marching Band Analogy
1:22
Index of Refraction
2:37
Measure of How Much Light Slows Down in a Material
2:40
Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction
3:03
Indices of Refraction
3:21
Dispersion
4:01
White Light is Refracted Twice in Prism
4:23
Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency
4:41
Example 1: Determining n
5:14
Example 2: Light in Diamond and Crown Glass
5:55
Snell's Law
6:24
The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction
6:32
Light Bends Toward the Normal as it Enters a Material With a Higher n
7:08
Light Bends Toward the Normal as it Enters a Material With a Lower n
7:14
Example 3: Angle of Refraction
7:42
Example 4: Changes with Refraction
9:31
Total Internal Reflection
10:10
When the Angle of Refraction Reaches 90 Degrees
10:23
Critical Angle
10:34
Total Internal Reflection
10:51
Applications of TIR
12:13
Example 5: Critical Angle of Water
13:17
Thin Lenses
14:15
Convex Lenses
14:22
Concave Lenses
14:31
Convex Lenses
15:24
Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens
15:28
A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent
15:53
Example 6: Converging Lens Image
16:46
Example 7: Image Distance of Convex Lens
17:18
Concave Lenses
18:21
Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens
18:25
Concave Lenses Produce Upright, Virtual, Reduced Images
20:30
Example 8: Light Ray Thought a Lens
20:36
Systems of Optical Elements
21:05
Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element
21:16
Example 9: Lens and Mirrors
21:35
Thin Film Interference
27:22
When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film
27:25
If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere
27:31
Phase Change for Every Reflection from Low-Index to High-Index
28:09
Example 10: Thin Film Interference
28:41
Example 11: Wavelength in Diamond
32:07
Example 12: Light Incident on Crown Glass
33:57
Example 13: Real Image from Convex Lens
34:44
Example 14: Diverging Lens
35:45
Example 15: Creating Enlarged, Real Images
36:22
Example 16: Image from a Converging Lens
36:48
Example 17: Converging Lens System
37:50
Wave-Particle Duality

23m 47s

Intro
0:00
Objectives
0:11
Duality of Light
0:37
Photons
0:47
Dual Nature
0:53
Wave Evidence
1:00
Particle Evidence
1:10
Blackbody Radiation & the UV Catastrophe
1:20
Very Hot Objects Emitted Radiation in a Specific Spectrum of Frequencies and Intensities
1:25
Color Objects Emitted More Intensity at Higher Wavelengths
1:45
Quantization of Emitted Radiation
1:56
Photoelectric Effect
2:38
EM Radiation Striking a Piece of Metal May Emit Electrons
2:41
Not All EM Radiation Created Photoelectrons
2:49
Photons of Light
3:23
Photon Has Zero Mass, Zero Charge
3:32
Energy of a Photon is Quantized
3:36
Energy of a Photon is Related to its Frequency
3:41
Creation of Photoelectrons
4:17
Electrons in Metals Were Held in 'Energy Walls'
4:20
Work Function
4:32
Cutoff Frequency
4:54
Kinetic Energy of Photoelectrons
5:14
Electron in a Metal Absorbs a Photon with Energy Greater Than the Metal's Work Function
5:16
Electron is Emitted as a Photoelectron
5:24
Any Absorbed Energy Beyond That Required to Free the Electron is the KE of the Photoelectron
5:28
Photoelectric Effect in a Circuit
6:37
Compton Effect
8:28
Less of Energy and Momentum
8:49
Lost by X-Ray Equals Energy and Gained by Photoelectron
8:52
Compton Wavelength
9:09
Major Conclusions
9:36
De Broglie Wavelength
10:44
Smaller the Particle, the More Apparent the Wave Properties
11:03
Wavelength of a Moving Particle is Known as Its de Broglie Wavelength
11:07
Davisson-Germer Experiment
11:29
Verifies Wave Nature of Moving Particles
11:30
Shoot Electrons at Double Slit
11:34
Example 1
11:46
Example 2
13:07
Example 3
13:48
Example 4A
15:33
Example 4B
18:47
Example 5: Wave Nature of Light
19:54
Example 6: Moving Electrons
20:43
Example 7: Wavelength of an Electron
21:11
Example 8: Wrecking Ball
22:50
Section 7: Modern Physics
Atomic Energy Levels

14m 21s

Intro
0:00
Objectives
0:09
Rutherford's Gold Foil Experiment
0:35
Most of the Particles Go Through Undeflected
1:12
Some Alpha Particles Are Deflected Large Amounts
1:15
Atoms Have a Small, Massive, Positive Nucleus
1:20
Electrons Orbit the Nucleus
1:23
Most of the Atom is Empty Space
1:26
Problems with Rutherford's Model
1:31
Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons
1:39
Lose Energy When They Release Photons
1:46
Orbits Should Decay and They Should Be Unstable
1:50
Bohr Model of the Atom
2:09
Electrons Don't Lose Energy as They Accelerate
2:20
Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level
2:35
Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels
2:40
Energy Level Diagrams
3:29
n=1 is the Lowest Energy State
3:34
Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom
4:03
When Electron Reaches 0 eV It Is No Longer Bound
4:20
Electron Cloud Model (Probability Model)
4:46
Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus
4:53
Electron Orbitals Are Probability Regions
4:58
Atomic Spectra
5:16
Atoms Can Only Emit Certain Frequencies of Photons
5:19
Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels
5:34
This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element
5:37
Incandescence Emits a Continuous Energy
5:43
If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels
6:16
Continuous Spectrum
6:42
Absorption Spectrum
6:50
Emission Spectrum
7:08
X-Rays
7:36
The Photoelectric Effect in Reverse
7:38
Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate
7:53
Example 1: Electron in Hydrogen Atom
8:24
Example 2: EM Emission in Hydrogen
10:05
Example 3: Photon Frequencies
11:30
Example 4: Bright-Line Spectrum
12:24
Example 5: Gas Analysis
13:08
Nuclear Physics

15m 47s

Intro
0:00
Objectives
0:08
The Nucleus
0:33
Protons Have a Charge or +1 e
0:39
Neutrons Are Neutral (0 Charge)
0:42
Held Together by the Strong Nuclear Force
0:43
Example 1: Deconstructing an Atom
1:20
Mass-Energy Equivalence
2:06
Mass is a Measure of How Much Energy an Object Contains
2:16
Universal Conservation of Laws
2:31
Nuclear Binding Energy
2:53
A Strong Nuclear Force Holds Nucleons Together
3:04
Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus
3:19
Binding Energy of the Nucleus
3:32
Mass Defect
3:37
Nuclear Decay
4:30
Alpha Decay
4:42
Beta Decay
5:09
Gamma Decay
5:46
Fission
6:40
The Splitting of a Nucleus Into Two or More Nuclei
6:42
For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split
6:47
Fusion
8:14
The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus
8:15
This Fuels Our Sun and Stars
8:28
Basis of Hydrogen Bomb
8:31
Forces in the Universe
9:00
Strong Nuclear Force
9:06
Electromagnetic Force
9:13
Weak Nuclear Force
9:22
Gravitational Force
9:27
Example 2: Deuterium Nucleus
9:39
Example 3: Particle Accelerator
10:24
Example 4: Tritium Formation
12:03
Example 5: Beta Decay
13:02
Example 6: Gamma Decay
14:15
Example 7: Annihilation
14:39
Section 8: Sample AP Exams
AP Practice Exam: Multiple Choice, Part 1

38m 1s

Intro
0:00
Problem 1
1:33
Problem 2
1:57
Problem 3
2:50
Problem 4
3:46
Problem 5
4:13
Problem 6
4:41
Problem 7
6:12
Problem 8
6:49
Problem 9
7:49
Problem 10
9:31
Problem 11
10:08
Problem 12
11:03
Problem 13
11:30
Problem 14
12:28
Problem 15
14:04
Problem 16
15:05
Problem 17
15:55
Problem 18
17:06
Problem 19
18:43
Problem 20
19:58
Problem 21
22:03
Problem 22
22:49
Problem 23
23:28
Problem 24
24:04
Problem 25
25:07
Problem 26
26:46
Problem 27
28:03
Problem 28
28:49
Problem 29
30:20
Problem 30
31:10
Problem 31
33:03
Problem 32
33:46
Problem 33
34:47
Problem 34
36:07
Problem 35
36:44
AP Practice Exam: Multiple Choice, Part 2

37m 49s

Intro
0:00
Problem 36
0:18
Problem 37
0:42
Problem 38
2:13
Problem 39
4:10
Problem 40
4:47
Problem 41
5:52
Problem 42
7:22
Problem 43
8:16
Problem 44
9:11
Problem 45
9:42
Problem 46
10:56
Problem 47
12:03
Problem 48
13:58
Problem 49
14:49
Problem 50
15:36
Problem 51
15:51
Problem 52
17:18
Problem 53
17:59
Problem 54
19:10
Problem 55
21:27
Problem 56
22:40
Problem 57
23:19
Problem 58
23:50
Problem 59
25:35
Problem 60
26:45
Problem 61
27:57
Problem 62
28:32
Problem 63
29:52
Problem 64
30:27
Problem 65
31:27
Problem 66
32:22
Problem 67
33:18
Problem 68
35:21
Problem 69
36:27
Problem 70
36:46
AP Practice Exam: Free Response, Part 1

16m 53s

Intro
0:00
Question 1
0:23
Question 2
8:55
AP Practice Exam: Free Response, Part 2

9m 20s

Intro
0:00
Question 3
0:14
Question 4
4:34
AP Practice Exam: Free Response, Part 3

18m 12s

Intro
0:00
Question 5
0:15
Question 6
3:29
Question 7
6:18
Question 8
12:53
Section 9: Additional Examples
Metric Estimation

3m 53s

Intro
0:00
Question 1
0:38
Question 2
0:51
Question 3
1:09
Question 4
1:24
Question 5
1:49
Question 6
2:11
Question 7
2:27
Question 8
2:49
Question 9
3:03
Question 10
3:23
Defining Motion

7m 6s

Intro
0:00
Question 1
0:13
Question 2
0:50
Question 3
1:56
Question 4
2:24
Question 5
3:32
Question 6
4:01
Question 7
5:36
Question 8
6:36
Motion Graphs

6m 48s

Intro
0:00
Question 1
0:13
Question 2
2:01
Question 3
3:06
Question 4
3:41
Question 5
4:30
Question 6
5:52
Horizontal Kinematics

8m 16s

Intro
0:00
Question 1
0:19
Question 2
2:19
Question 3
3:16
Question 4
4:36
Question 5
6:43
Free Fall

7m 56s

Intro
0:00
Question 1-4
0:12
Question 5
2:36
Question 6
3:11
Question 7
4:44
Question 8
6:16
Projectile Motion

4m 17s

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2:32
Question 6
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Newton's 1st Law

4m 34s

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Newton's 2nd Law

5m 40s

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Newton's 3rd Law

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Friction

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Ramps and Inclines

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5:08
Circular Motion

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Gravity

6m 33s

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Momentum & Impulse

9m 29s

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Conservation of Momentum

9m 33s

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Work & Power

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Springs

7m 59s

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Energy & Energy Conservation

8m 47s

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1:27
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Question 10
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Question 11
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Electric Charge

7m 6s

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6:26
Coulomb's Law

4m 13s

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Electric Fields & Forces

4m 11s

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0:51
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1:30
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3:12
Electric Potential

5m 12s

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0:42
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Electrical Current

6m 54s

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Resistance

5m 15s

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Ohm's Law

4m 27s

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0:33
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Circuit Analysis

6m 36s

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2:16
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Magnetism

3m 43s

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1:35
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2:36
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3:03
Wave Basics

4m 21s

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0:36
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1:27
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2:51
Question 10
3:32
Wave Characteristics

5m 33s

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1:04
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2:50
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3:12
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3:57
Question 7
4:16
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4:42
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4:56
Wave Behaviors

3m 52s

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0:40
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1:17
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1:39
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2:07
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2:41
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3:09
Reflection

3m 48s

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0:50
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1:29
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1:46
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3:08
Refraction

2m 49s

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1:03
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1:24
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Diffraction

2m 34s

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Question 6
2:04
Electromagnetic Spectrum

7m 6s

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0:39
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1:51
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Question 7
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4:30
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5:04
Question 11
6:01
Question 12
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Wave-Particle Duality

5m 30s

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0:34
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2:16
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3:45
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4:13
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4:33
Energy Levels

8m 13s

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0:25
Question 2
1:18
Question 3
1:43
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2:08
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3:17
Question 6
3:54
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5:54
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6:41
Question 11
7:14
Mass-Energy Equivalence

8m 15s

Intro
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0:19
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1:02
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1:37
Question 4
2:17
Question 5
2:55
Question 6
3:32
Question 7
4:13
Question 8
5:04
Question 9
5:29
Question 10
5:58
Question 11
6:48
Question 12
7:39
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Lecture Comments (21)

1 answer

Last reply by: Professor Dan Fullerton
Sat Apr 22, 2017 6:49 AM

Post by sania sarwar on April 22, 2017

hello professor
in example 5, how can the potential at zero and 2 be the same?

1 answer

Last reply by: Professor Dan Fullerton
Thu Mar 31, 2016 3:43 PM

Post by Nikhar Kawediya on March 26, 2016

Hello Professor Dan Fullerton. In example 7, when the voltage is 3 volts, and if we use the formula (1/2)qV, why do we get an energy of 1.8 * 10^-6 J while different in the formula (1/2)CV^2 where the energy is 9*10^-7 J ?

1 answer

Last reply by: Professor Dan Fullerton
Tue Mar 22, 2016 6:55 AM

Post by john lee on March 21, 2016

Why the capacitance is bigger when the d is smaller?

1 answer

Last reply by: Professor Dan Fullerton
Mon Apr 20, 2015 7:59 PM

Post by Vibha Pandurangi on April 20, 2015

In example 12, why do the charges flow from 1 to 2?

1 answer

Last reply by: Professor Dan Fullerton
Tue Dec 9, 2014 3:11 PM

Post by Siyan He on December 9, 2014

when calculating the energy, when are we using the formula Ue=Vq and when do we use U=1/2CV^2

1 answer

Last reply by: Professor Dan Fullerton
Tue Nov 4, 2014 6:30 AM

Post by Jungle Jones on November 3, 2014

In ex. 11, it asks for the speed of the electron, was that a type? Was it meant to be proton?

1 answer

Last reply by: Professor Dan Fullerton
Sun Oct 19, 2014 7:06 AM

Post by Sally Acebo on October 18, 2014

For Ex 11, how did you get this setup again... Ui=Uf + K.E? How do you
know to add K.E. to the right side?

1 answer

Last reply by: Professor Dan Fullerton
Fri Jun 27, 2014 8:46 PM

Post by Madina Abdullah on June 6, 2014

Thank you

1 answer

Last reply by: Professor Dan Fullerton
Tue May 7, 2013 12:50 PM

Post by Nawaphan Jedjomnongkit on May 7, 2013

From Ex 7 about energy stored in capacitance U=1/2 CV^2 and U=1/2 QV .... but if the voltage is reduced from 6 to 3 why we can't get the same amount of energy store when we use U=1/2 QV? Or the condition have to be for fully charged capacitor?

2 answers

Last reply by: help me
Tue May 7, 2013 9:15 PM

Post by help me on May 6, 2013

For Example 9, why did you keep the same capacitance to answer the second part of the question? Thus leaving the original permittivity, multiplied by the new permittivity constant. I would think you would have to substitute the original constant of 8.85*10^-12 with the new one of 3.9. But you multiplied it. Could you explain? Let me know if you would like me to elaborate more, I don't think I was descriptive enough. Thanks in advance!

Electric Potential Difference

  • The work done per unit charge in moving a charge between two points in an electric field is a scalar quantity known as the electric potential difference, or voltage.
  • The work done in move this charge is equal to the change in the object's electric potential energy (U=qV)
  • Equipotential lines show lines of equal electrical potential. They always cross electric field lines at right angles.
  • The electric potential due to a point charge is given by kq/r. To find the potential difference due to multiple point charges, add up the potentials due to each individual charge.
  • Parallel conducting plates separated by an insulator can be used to create a capacitor, an electrical device used to store charge. The capacitance is equal to the charge stored on one plate divided by the potential difference between the plates (C=Q/V).
  • The energy stored in a capacitor is given by 0.5*C*V^2.
  • Between two even but oppositely charged parallel plates at points far from the edges, the electric field is perpendicular to the plates and constant in magnitude (E=V/d)
  • Equipotential lines show points of equal electric potential (similar to how topographic maps show points of equal altitude, or gravitational potential).
  • As the distance between equipotential lines decreases, the steepness of the surface (or the gradient of the potential) increases.
  • Electric permittivity is a material property describing a material's ability to store energy in an electric field.

Electric Potential Difference

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  1. Intro
    • Objectives
      • Electric Potential Energy
      • Example 1: Charge From Work
        • Example 2: Electric Energy
          • The Electron-Volt
          • Example 3: Energy in eV
            • Equipotential Lines
            • Drawing Equipotential Lines
              • Potential Due to a Point Charge
              • Example 4: Potential Due to a Point Charge
                • Example 5: Potential Due to Point Charges
                  • Parallel Plates
                  • E Field Due to Parallel Plates
                  • Capacitors
                  • Capacitors Store Energy
                  • Example 6: Capacitance
                    • Example 7: Charge on a Capacitor
                      • Designing Capacitors
                      • Example 8: Designing a Capacitor
                        • Example 9: Calculating Capacitance
                          • Example 10: Electron in Space
                            • Example 11: Proton Energy Transfer
                              • Example 12: Two Conducting Spheres
                                • Example 13: Equipotential Lines for a Capacitor
                                  • Intro 0:00
                                  • Objectives 0:09
                                  • Electric Potential Energy 0:32
                                    • When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done
                                    • When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done
                                    • Electric Potential Difference
                                  • Example 1: Charge From Work 2:06
                                  • Example 2: Electric Energy 3:09
                                  • The Electron-Volt 4:02
                                    • Electronvolt (eV)
                                    • 1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
                                  • Example 3: Energy in eV 5:33
                                  • Equipotential Lines 6:32
                                    • Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential
                                    • Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines
                                  • Drawing Equipotential Lines 8:15
                                  • Potential Due to a Point Charge 10:46
                                    • Calculate the Electric Field Vector Due to a Point Charge
                                    • Calculate the Potential Difference Due to a Point Charge
                                    • To Find the Potential Difference Due to Multiple Point Charges
                                  • Example 4: Potential Due to a Point Charge 11:52
                                  • Example 5: Potential Due to Point Charges 13:04
                                  • Parallel Plates 16:34
                                    • Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other
                                    • These Can Create a Capacitor
                                  • E Field Due to Parallel Plates 17:14
                                    • Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant
                                    • Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation
                                  • Capacitors 18:09
                                    • Electric Device Used to Store Charge
                                    • Once the Plates Are Charged, They Are Disconnected
                                    • Device's Capacitance
                                  • Capacitors Store Energy 19:28
                                    • Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other
                                  • Example 6: Capacitance 20:28
                                  • Example 7: Charge on a Capacitor 22:03
                                  • Designing Capacitors 24:00
                                    • Area of the Plates
                                    • Separation of the Plates
                                    • Insulating Material
                                  • Example 8: Designing a Capacitor 25:35
                                  • Example 9: Calculating Capacitance 27:39
                                  • Example 10: Electron in Space 29:47
                                  • Example 11: Proton Energy Transfer 30:35
                                  • Example 12: Two Conducting Spheres 32:50
                                  • Example 13: Equipotential Lines for a Capacitor 34:48

                                  Transcription: Electric Potential Difference

                                  Hi everyone and welcome back to Educator.com.0000

                                  This lesson is on electric potential difference, oftentimes called just electric potential or voltage.0003

                                  Our objectives are going to be to find and calculate electric potential energy and electric potential difference, to determine the potential difference due to a series of point charges...0009

                                  ...finding the electric field strength between two charged parallel plates, finding the energy stored in a parallel plate capacitor and finally, calculating the capacitance of the parallel plate capacitor.0019

                                  Let us start by talking about electric potential energy.0032

                                  When we lifted an object against gravity by applying a force for some distance, work was done to give that object gravitational potential energy.0035

                                  At the same token, when you take a charged object and it is moved against an electric field by applying a force for some distance, you have to do work to give that object electric potential energy.0043

                                  Imagine we have a positive charge here; it is stuck in space and a long ways away, infinitely far away, I have a little point charge.0053

                                  If I want to bring that point charge -- its positive -- close to this big positive charge, I have to do work -- I have to push harder and harder, and harder, and harder, and harder to get it closer and closer.0060

                                  Once it is in this position it has a lot of potential energy -- electric potential energy.0070

                                  It wants to be repelled because if I let go of it, it is going to flinging off that way; it is going to convert that electric potential energy into kinetic energy.0075

                                  So we had to do work in bringing it from a long ways away until it was at this position.0083

                                  If we do work on an object, we have given it energy and in this case, we gave electric potential energy.0089

                                  Now the work done per unit charge, and moving that charge through that electric field, is a scalar and that is known as the electric potential or electric potential difference if you are talking about the potential between two different areas.0093

                                  The units are volts which is equal to a joule per coulomb (J/C) and the work done is equal to the change in the object's electric potential energy.0109

                                  So electric potential energy is charge times electric potential difference.0117

                                  Let us start off with a problem.0127

                                  If we have a potential difference of 10 volts between two points (A) and (B) in an electric field, what is the magnitude of charge that requires 2 × 10-2 J of work to move it from (A) to (B)?0129

                                  Well let us start off with our givens -- electric potential difference (V) is 10 volts; our electric potential energy is going to be 2 × 10-2 J because that is the amount of work we had to do, and we are looking for charge.0142

                                  If electric potential energy is Q × V, then that means (Q) must be electric potential energy divided by (V) or 2 × 10-2 J/10 volts, which gives us a charge of 2 × 10-3 C.0162

                                  It is pretty straightforward.0187

                                  Let us take a look at electric energy.0189

                                  How much electric energy is required to move a 4 microcoulomb (MC) charge through a potential difference of 36 volts?0191

                                  Well our charge now is 4 MC and MC is 4 × 10-6 C; our potential difference is V = 36 volts, and we are looking for electrical energy.0199

                                  Electrical energy is charge times voltage, which is going to be 4 × 10-6 C × 36 volts (voltage)...0216

                                  ...which implies that our electric potential energy will be 0.00014 J.0227

                                  Oftentimes, when we are dealing with very small charges -- something like a joule -- is not a very convenient form of energy.0242

                                  We are talking about things × 10-15, -16, -17, -18 J -- it is just not very convenient.0249

                                  So there is another non-standard unit of energy that is very commonly used, it is called the electron-volt and it is given the symbol (eV) and it is a very small portion of a joule.0255

                                  It is the amount of work done in moving an elementary charge through a potential difference of 1 volt.0268

                                  So if you were to think about it, if electric potential energy is charge times voltage and your charge is 1 elementary charge and you move it through 1 volt, the electric potential energy is 1 eV.0273

                                  If we were to do that in standard units, we would have said that this is the charge of 1e, which is 1.6 × 10-19 C × 1 volt and that would have given us 1.6 × 10-19 J.0290

                                  These have to be the same, therefore, 1 eV = 1.6 × 10-19 J.0306

                                  It is just another unit of energy that you oftentimes use when you are dealing with very small charges.0313

                                  Keep in mind though, if you are going to use these values for energy in other formulas, the SI unit, the standard unit that is going to make all your units work out, is still going to be joules. That is the standard.0319

                                  A proton is moved through a potential difference of 10 V in an electric field. How much work in electron-volts was required to move this charge?0334

                                  Let us look at how easy this can be if we use electron-volts.0342

                                  If our charge of a proton is +1 elementary charge, our potential difference is 10 volts, then the electric potential energy is charge times potential difference or 1e × 10 volts, which is 10 eV -- very straightforward.0346

                                  If we wanted to do that in joules, we could have done 1.6 × 10-19 C × 10 volts = 1.6 × 10-18 J if we went through all that, or we could have converted electron-volts to joules and we are all done, knowing that 1 eV = 1.6 × 10-19 J.0364

                                  Thankfully, this problem made it nice and easy though in telling us that the answer was going to be in electron-volts.0384

                                  All right. Let us talk about equipotential lines for a minute.0392

                                  When you talk about topographic maps, if you have gone hiking or you were in some sort of surveying an organization, you have probably seen a topographic map where you have lines that show you areas of equal altitude.0397

                                  Those are lines of equal gravitational potential energy.0411

                                  We have the same sort of thing in the electrical world -- we have lines of equal electrical potential which we call equipotential lines.0415

                                  Now equipotential lines always cross electric field lines at right angles and if you move a charged particle in space, as long as you stay on an equipotential line, you do not do any work.0423

                                  As equipotential lines get closer together, the gradient of the potential increases.0435

                                  You have a steeper slope of potentials -- kind of like if you have a topographic map and your equal altitude lines get closer together, you are looking at a steeper cliff, a steeper gradient.0440

                                  So what I am showing here on the right is a positive charge -- we have the electric field lines which we have done before -- the black lines radiating away from the positive charge -- our equipotential lines must cross them at right angles.0451

                                  Everywhere that an electric field line intersects an equipotential line, we have a 90 degree or a right angle, and equipotential lines show lines of constant potential.0464

                                  If I were to take a charge -- let us put a charge right here -- and I want to move it over to here, somewhere else on the same equipotential line.0476

                                  The net work done is going to be 0 because you end up at the same potential energy, the same potential because you have the same charge.0486

                                  Let us take a look at how we could draw some equipotential lines.0496

                                  Around positive point charges, they are pretty easy because it always intersects at a right angle, so these must look like circles.0499

                                  I will do my best to draw a circle here -- that would be 1 equipotential line, and we could probably draw another equipotential line here -- pretty close -- and in a perfect world, all of those would intersect at 90 degrees.0508

                                  Around a negative point charge, we would have the same idea -- crossing all the electric field lines at right angles, so we will get a circular pattern for our equipotential lines.0523

                                  Over here on the bottom left where we have our dipole again of a positive and negative charge -- well now our equipotential lines get a little bit more complicated.0536

                                  The one right here is pretty easy, if we draw an equipotential line right through the middle -- that is pretty straightforward -- it crosses all of those at 90 degrees.0544

                                  But in order to cross all of these at 90 degrees as we move in here, we are going to have to adjust that a little bit and we are going to start to see some curve to it.0554

                                  So there is an equipotential line on that side and on the other side, we are going to have the same sort of thing by symmetry.0565

                                  I am trying to cross all these as best as I can at 90 degrees and we will get an equipotential line that looks something like that.0574

                                  And over here on the right, now again we have two positive charges, so let us see what we get here.0584

                                  Again, right down the middle, we are going to have that point where we do not have anything.0591

                                  But as we go just a little bit off here, we are going to have to cross this at 90 degrees; we are going to have to get really, really steep here to cross at 90 degrees, and as we do that, it looks like we are going to come back around.0598

                                  I am doing my best to draw that at 90 degree intersecting angles, let us try that again over here.0617

                                  We will start from this side this time, crossing all of these at about 90 degrees and that must curve pretty steeply to come back there to give us our equipotential lines.0622

                                  So the key point is: equipotential lines always cross electric field lines at right angles.0636

                                  Let us talk about the potential due to a point charge just like we talked about the electric field due to a point charge.0646

                                  To calculate the potential difference due to a point charge, the electric potential -- well if force is KQ1Q2/R2 and we found electric field was going to be KQ/R2, well potential is just going to be KQ/R.0652

                                  The nice thing about potential is that it is a scalar.0668

                                  We do not have to worry about direction, we can add them up in scalar form and save us a lot of work.0671

                                  And to find the potential difference due to multiple point charges, we just take the sum of the electric potentials due to each individual point charge -- again not worrying about any vector nature.0676

                                  Electric potential energy then can be found by multiplying the electric potential by the charge.0686

                                  So the electric potential energy due to a point charge is (QV) or Q × KQ/R, therefore electric potential energy is going to be (K) times the product of your two charges divided by the distance between them.0691

                                  Let us take a look at a sample problem here.0712

                                  Find the electric potential at point (P) which is located 3 m away from a -2 C charge.0715

                                  What is the electric potential energy of a half-coulomb charge situated at point (P)?0721

                                  Let us start by finding the electric potential at point (P).0726

                                  (V) at point (P) is going to be KQ/R where K = 9 × 109 N-m2/C2, our Q = -2 C, and our distance = 3 m, so that is going to give us about -6 × 109 V.0729

                                  What is the electric potential energy of a half-coulomb charge situated at that point?0751

                                  Well the electric potential energy is charge times voltage -- our potential -- which is going to be 0.5 C × -6 × 109 V or -3 × 109 J.0756

                                  A nice, straightforward applications of those formulas.0779

                                  Let us try one that is a little more involved, kind of mirroring what we did with the electric field.0783

                                  Let us find the electric potential at the origin due to the three charges shown in the diagram and at the end it says if we place an electron at the origin, what electric potential energy does it possess?0787

                                  Now this is awfully similar to what we did when we were finding the net electric field at the origin, but now we are looking for potential.0797

                                  So we are going to do it with the same basic strategy -- let us find the potential at the origin due to each of the three individual charges and then we will add them up.0803

                                  So the potential due to the green charge, that is going to be KQ/R = 9 × 109N-m2/C2, our charge is 2 C and our distance from the origin is 8.0812

                                  That is going to be just 2.25 × 109 V.0828

                                  Now let us do the red charge -- V = KQ/R, which is going to be 9 × 109 × -2 C/8, which is going to be -2.25 × 109 volts.0836

                                  And finally, let us find the potential due to our 1 C charge -- V = KQ/R or 9 × 109 × 1/R.0857

                                  We said last time that if we make a right triangle here, that side is 2, that side is 2, therefore the hypotenuse must be the square root of 22 + 22...0871

                                  ...so (R) is going to be square root of 22 + 22 or square root of 8, which is 3.18 × 109 volts.0881

                                  Now to find the total -- the potential here at the origin -- we have to sum up the potentials to each of those three charges.0894

                                  The total is just going to be: 2.25 × 109 + -2.25 × 109, so we are going to cancel this out, that is going to be 0, and all we are left with is this 3.18 × 109 volts.0902

                                  That is the potential due to those three point charges when you are here at the origin.0917

                                  Finally, we are asked to find what happens to the electric potential energy if we place an electron at the origin; what is its electric potential energy?0922

                                  Well, let us do that.0931

                                  The electric potential energy due to that electron is just going to be charge times voltage and our charge is -1.6 × 10-19 C, because it is an electron; it is a negative...0934

                                  Our voltage is 3.18 × 109 volts, which is going to give us a potential energy of about -5.1 × 10-10 J.0947

                                  Let us point out one other item here.0961

                                  If instead we did this in electron-volts, this would have been -1e × 3.18 × 109 volts, which would have given us -3.18 × 109 eV.0963

                                  So you can see where using electron-volts could be a lot more convenient, but since it does not specify which units it wants for our answer, we will circle both of them -- they will both be correct.0979

                                  All right. Let us talk a little bit about parallel plate configurations.0994

                                  Configurations in which we have two parallel plates of opposite charge that are situated a fixed distance from each other are very common in physics because this is how we make a capacitor, an electrical device used to store charge.0997

                                  And the general look of these is, we will take one plate, put another one just a little bit of distance from it, they have some cross-sectional area (A), and we will situate them at some distance from each other (D), and then typically we are going to put some charge like (+Q) up here and (-Q) there -- there is the basics of a capacitor.1009

                                  Now the electric field due to two parallel plates -- as long as you are away from the edges of those plates -- is constant.1034

                                  And the electric field, as we know, runs from positive to negative, so anywhere between these parallel plates -- as long as we stay a little bit away from the edges -- is constant throughout this entire region; it is given by the voltage, the potential difference across the plates divided by their distance.1040

                                  A nice and easy way to calculate a uniform electric field, and that is true -- equals V/D here, here, here, here, here -- anywhere between those plates, it is constant.1056

                                  The magnitude of that electric field strength is given by the potential difference divided by the plate separation and the units are going to be Newton's per coulomb (N/C) again for an electric field or volts over distance (V/m).1066

                                  So we are proving that we have the same units (N/C) as equivalent to a (V/m)1082

                                  All right. A capacitor is an electrical device used to store charge.1090

                                  It consists of two conducting plates separated by some sort of insulator.1094

                                  That insulator could be air, it could be vacuum, it could be paper, it could be Jell-O; anything that is an insulator you could put in between the plates and you would still have a capacitor.1100

                                  Now once the plates are charged, they are disconnected.1111

                                  The charges then stuck on the plates until the plates are reconnected.1113

                                  So if you put a charge on each plate, you create an electric field between the plates.1116

                                  If you disconnect them, then the charge is stuck there, and you have all that energy that is stored in the electric field.1120

                                  The amount of charge a capacitor can store for some given amount of potential difference across it is known as the device's capacitance (C).1126

                                  Now notice (C) is capacitance, but it is also used as a unit of charge, coulombs, so we have to be careful with our (C)'s.1134

                                  The units of capacitance are coulombs per volt also known as a farad (F), and a farad is a very large amount of capacitance.1142

                                  So much more often we will be talking about millifarads, microfarads, nanofarads, even picofarads.1151

                                  Our key formula for capacitance -- capacitance is equal to the charge divided by the potential difference between the plates or C = Q/V.1158

                                  Capacitors store energy -- because the charges are on opposite plates of the capacitor, they exert forces on each other; it becomes an energy storage device where that energy is stored in the electric field.1170

                                  You can find the energy stored in a capacitor by the formula: potential energy in a capacitor is 1/2 times the capacitance times the square of the potential difference.1180

                                  If we write this as 1/2 CV2 -- well we also just learned that C = Q/V, so I could write this as 1/2 and I am going to replace (C) with Q/V and I still have a V2.1190

                                  I can do a little bit of simplification here -- (V) -- and the squared goes away and we will come up with 1/2 QV, which is also equal to (V), potential energy stored in a charged capacitor.1208

                                  Let us do an example with capacitance.1228

                                  A capacitor stores 3 microcoulombs of charge -- Q = 3 × 10-6 C -- with a potential difference of 1.5 volts across the plates, V = 1.5.1231

                                  What is its capacitance and how much energy is stored in it?1244

                                  Well its capacitance is C = Q/V or 3 × 10-6 C/1.5volts = 2 × 10-6 F which is 2 microfarads.1248

                                  How much energy is stored in the capacitor?1270

                                  We could do this a couple of different ways, but let us start off with 1/2 CV2 -- that is going to be 1/2 times...1273

                                  ...we just found our capacitance, 2 microfarads or 2 × 10-6 F, and our potential difference, 1.5 volts 2, gives us 2.25 × 10-6 J).1280

                                  Or we could have used u = 1/2 QV, which will be 1/2 × 3 × 10-6 C (charge) × 1.5 volts (potential difference), which amazingly is 2.25 × 10-6 J.1296

                                  And of course those have to be the same; we said the formulas were equivalent.1315

                                  All right. Looking at the charge on a capacitor -- How much charge sits on the top plate of a 200 nanofarad capacitor when charged to a potential difference of 6 volts?1323

                                  Well let us start there.1334

                                  Capacitance is C = 200 nanofarads or 200 × 10-9 F and potential difference is V = 6 volts.1337

                                  So if C = Q/V, then that means our charge (Q) must be (CV) or 200 × 10-9 F × 6 volts (potential difference), which is going to be about 1.2 × 10-6 C.1347

                                  How much energy is stored in the capacitor when it is fully charged?1369

                                  Well when it is fully charged, u = 1/2 CV2 which is 1/2 our capacitance, 200 × 10-9 or 200 nanofarads × 6 volts2, which is going to give us about 3.6 × 10-6 J.1373

                                  How much energy is stored in the capacitor when the voltage across its plate is 3 volts?1398

                                  Well when we get to 3 volts, u = 1/2 CV2 again -- that is going to be 1/2 × 200 × 10-9 × 3 volts2 = 9 × 10-7 J.1404

                                  That will be 1/4 of that value, so if we cut the voltage in half, we have 1/4 the value, and that is because of that V2 relationship -- so pretty good at calculating charge on a capacitor and the energy stored in a charged capacitor.1422

                                  Let us talk about the design of capacitors.1437

                                  What determines how much charge a capacitor can store?1440

                                  Well the area of the plates -- as you have bigger plates you can store more charge, the separation of the plates plays a role in the capacitance and the insulating material between them.1444

                                  In short, the capacitance is given by this value, ε -- that is called the permittivity and that is a constant that has to do with the material between the plates -- cross-sectional area in square meters and the separation of the plates (D).1462

                                  Now if you have an air gap capacitor or a vacuum capacitor, our baseline ε, our baseline permittivity is 8.85 × 10-12 C2/N-m2.1481

                                  If you put something other than air or vacuum between the plates, then you have to go from the permittivity of free space and multiply it by what is known as the dielectric constant, where your permittivity is going to be your dielectric constant (K) × ε0 and materials have larger (K)'s.1495

                                  For air or vacuum, that is going to be 1, so ε is equal to that.1517

                                  If you have something that is a little bit more resistive, a better insulator for example, that is going to be a bigger number for (K), so that will increase your capacitance as you put a different insulator in there.1521

                                  Let us see how that works.1535

                                  How far apart should the plates of an air gap capacitor be if the area of the top plate is 5 × 10-4 m2 and the capacitor must store 50 mJ of charge and an operating potential difference of 100 volts.1537

                                  It should say it must store 50 mJ of energy -- that makes more sense.1554

                                  Well if our area is 5 × 10-4 m2 and our potential energy is 0.05 J, we would have a potential of 100 volts.1559

                                  Let us see what we can determine here -- u = 1/2 CV2, but we also know that C = ε0 A/D and because it is an air gap capacitor, I can leave that ε0, because I do not have any dielectric constant that I have to put in front of it there.1571

                                  So that means that u = 1/2 × ε0 A/D × V2.1591

                                  If I rearrange this a little bit to find how far apart or the distance between them, I would say that the distance then solving for (D) is going to be...1605

                                  ...ε0 × (A) × V2 divided by 2 × 8.85 × 10-12 (potential energy) × 5 × 10-4 m2 (area)...1613

                                  ...× 100 volts2 (potential)/2 × 0.05 J.1631

                                  When I do all that, I come up with a separation distance of about 4.43 × 10-10 m, so just combining our formulas in order to solve for the unknown.1642

                                  Let us do some more capacitance calculations.1658

                                  Find the capacitance of two parallel plates of length 1 mm and with 2 mm if they are separated by 3 micrometers of air.1662

                                  All right. To begin with, capacitance is ε0 A/D; it is an air gap capacitor so I do not have to worry about a dielectric constant there.1673

                                  That will be 8.85 × 10-12 × our area, which is length × width, or 0.001 m × 0.002 m/3 micrometers or 3 × 10-6 m (the separation of the plates).1682

                                  If I put that in my calculator, and I come up with about 5.9 × 10-12 F which is also 5.9 picofarads.1703

                                  Now what would the device's capacitance be if we replace that air with glass which has a dielectric constant of 3.9?1719

                                  Well the only thing we have to do there is, if before, (C) was ε0 A/D -- because we are no longer using air or vacuum because we have a dielectric constant of 3.9 -- 3.9 ε0 becomes my permittivity.1727

                                  So now, all I have to do -- all of this is the same -- is multiply my answer by 3.9.1747

                                  That is going to be 3.9 × 5.9 × 10-12 F or 2.3 × 10-11 F which is 23 picofarads.1752

                                  By inserting a dielectric material with a higher dielectric constant, I increased my capacitance because the dielectric constant was 3.9 times larger than the original, so my capacitance is 3.9 times larger than the original.1768

                                  All right. Let us go through a couple more problems to make sure we have everything down.1787

                                  An electron sits on a equipotential line of 5 volts.1790

                                  How much work is required to move the electron to an equipotential line of -25 volts?1794

                                  Let us make this one easy, let us do it in electron-volts.1799

                                  As we do this, the potential energy is equal to charge times potential difference.1803

                                  The charge on our electron is -1 elementary charge, and our potential difference, if we go from 5 to -25 volts -- well δV is final minus initial, so that is going to be -25 - 5 = -30 volts or 30 eV -- nice and straightforward.1809

                                  Let us take a look at conservation of energy as we talk about these problems.1835

                                  A proton is held at a fixed point in space where the electric potential is 500 kilovolts or 500,000 volts; the proton is then released.1840

                                  Assuming no energy is lost to non-conservative forces, what is the speed of the electron at a point in space where the electric potential is 100,000 volts?1849

                                  This is a conservation of energy problem.1859

                                  It starts out initially with electric potential energy and that must be equal to its final electric potential energy.1861

                                  Where did any excess energy go? That must be the final kinetic energy of our proton.1869

                                  Well we know the initial is going to be (Q) times our initial voltage, so that must be equal to (Q) times our final voltage and our kinetic energy is going to be 1/2 mv2.1875

                                  So as I start solving to get v2 all by itself, I could say then that v2 = Q(Vi - Vf).1889

                                  I will have the 2 in there, so 2 will factor out the Q (Vi - Vf) divided by (m), must be equal to V2.1902

                                  Therefore, v2 = 2 × 1.6 × 10-19 C (charge on our proton); Vi - Vf = 500,000 volts - 100,000 volts all divided by the mass.1912

                                  If you have to look up the mass of a proton, you will find that it is about 1.67 × 10-27 kg.1933

                                  Plug all that into my calculator and I come up with something around 7.66 × 1013 m2/s2.1941

                                  So if I want just velocity, I take the square root of both sides and get that V = 8.75 × 106 m/s -- converting electric potential energy into kinetic energy.1951

                                  All right. Let us take a look at a problem with two conducting spheres.1970

                                  These two conducting spheres, each with charge (Q) are connected by a wire as shown.1973

                                  Do any charges flow between the spheres and how do their potentials compare?1979

                                  Well the first thing we have to realize is when we connect them by a wire, all of a sudden they must be at equipotential -- anything that is connected by a conductor is going to be at equipotential.1984

                                  So once we do that, these have to be at the same voltage.1993

                                  That means that if we look over here at Q1, V1 = KQ1/R1.1997

                                  Over here on the right-hand side, V2 = KQ2/R2, and because the potentials must be equal then, we could say that KQ1/R1 = KQ2/R2.2006

                                  We have a nice simplification we can make there -- divide (K) out of both sides, therefore Q1/R1 = Q2/R2.2024

                                  And since we know that R2 is going to be twice R1 -- measuring those lines, we could figure that out -- then Q1/R1 must equal Q2/2R,1...2036

                                  ...or with a little bit more rearrangement to say that Q2 = R1Q1/R1 or that is going to be just 2Q1.2054

                                  If Q2 is equal to twice Q1, then we must have charge flowing from 1 to 2.2067

                                  So our charge must be flowing that way -- we will have charge flowing from Q1 to Q2.2073

                                  How did their potentials compare? They have to be equal.2082

                                  Equipotential lines for a capacitor -- Draw the equipotential lines for the parallel plate capacitor below.2089

                                  The first thing that I am going to do is it is probably easier to draw the electric field first, going from positive to negative.2095

                                  So I will put in some electric field lines first, in green here -- electric field is constant between those.2101

                                  And then we know that equipotential's are always crossing electric field lines perpendicularly, at right angles, so I could draw my equipotential's that way.2108

                                  And if this is 0 volts, that will be maybe 1, 2, 3 volts, 4 volts, 5 volts.2127

                                  We have a constant electric field between these but we do not have a constant potential.2136

                                  Potential is going to have a linear gradient from 5 volts down to 0 volts.2140

                                  Hopefully that gets you a good start on electric potential and electric potential difference.2146

                                  We talked about electric potential energy and even some capacitors in there.2151

                                  Thanks so much for your time, and make it a great day everyone!2155

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