  Dan Fullerton

Circuit Analysis

Slide Duration:

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
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
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
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
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
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
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
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
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
0:26
In Degrees, Once Around a Circle is 360 Degrees
0:29
In Radians, Once Around a Circle is 2π
0:34
0:57
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
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
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
8:03
Isobaric
8:19
Isochoric
8:28
Isothermal
8:35
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
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
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
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
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
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

Intro
0:00
Question 1
0:13
Question 2
0:45
Question 3
1:25
Question 4
2:00
Question 5
2:32
Question 6
3:38
Newton's 1st Law

4m 34s

Intro
0:00
Question 1
0:15
Question 2
1:02
Question 3
1:50
Question 4
2:04
Question 5
2:26
Question 6
2:54
Question 7
3:11
Question 8
3:29
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3:47
Question 10
4:02
Newton's 2nd Law

5m 40s

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0:16
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0:55
Question 3
1:50
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2:40
Question 5
3:33
Question 6
3:56
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4:29
Newton's 3rd Law

3m 44s

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0:17
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0:44
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2:11
Question 6
2:29
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2:53
Friction

6m 37s

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0:13
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0:47
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1:25
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3:43
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4:41
Question 7
5:13
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5:50
Ramps and Inclines

6m 13s

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0:18
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1:01
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2:50
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3:11
Question 5
5:08
Circular Motion

5m 17s

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0:21
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1:01
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1:50
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2:33
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3:10
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3:31
Question 7
3:56
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4:33
Gravity

6m 33s

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0:19
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1:05
Question 3
2:09
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2:53
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3:17
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4:00
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4:41
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5:20
Momentum & Impulse

9m 29s

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2:17
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3:25
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4:28
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6:18
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6:57
Question 9
7:47
Conservation of Momentum

9m 33s

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2:08
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4:10
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6:08
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6:55
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8:26
Work & Power

6m 2s

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0:29
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3:22
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4:01
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4:18
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4:49
Springs

7m 59s

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0:13
Question 4
2:26
Question 5
3:37
Question 6
4:39
Question 7
5:28
Question 8
5:51
Energy & Energy Conservation

8m 47s

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0:18
Question 2
1:27
Question 3
1:44
Question 4
2:33
Question 5
2:44
Question 6
3:33
Question 7
4:41
Question 8
5:19
Question 9
5:37
Question 10
7:12
Question 11
7:40
Electric Charge

7m 6s

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0:10
Question 2
1:03
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1:32
Question 4
2:12
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3:01
Question 6
3:49
Question 7
4:24
Question 8
4:50
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5:32
Question 10
5:55
Question 11
6:26
Coulomb's Law

4m 13s

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0:14
Question 2
0:47
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1:25
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2:25
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3:01
Electric Fields & Forces

4m 11s

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0:19
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0:51
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1:30
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2:19
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3:12
Electric Potential

5m 12s

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0:14
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0:42
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1:08
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1:43
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2:22
Question 6
2:49
Question 7
3:14
Question 8
4:02
Electrical Current

6m 54s

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0:42
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2:01
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3:52
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4:15
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4:37
Question 8
4:59
Question 9
5:50
Resistance

5m 15s

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0:12
Question 2
0:53
Question 3
1:44
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2:31
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3:21
Question 6
4:06
Ohm's Law

4m 27s

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0:33
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0:59
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1:32
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1:56
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2:50
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3:19
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3:50
Circuit Analysis

6m 36s

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2:16
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2:33
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2:42
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3:18
Question 6
5:51
Question 7
6:00
Magnetism

3m 43s

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0:31
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0:56
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1:19
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1:35
Question 6
2:36
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3:03
Wave Basics

4m 21s

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0:13
Question 2
0:36
Question 3
0:47
Question 4
1:13
Question 5
1:27
Question 6
1:39
Question 7
1:54
Question 8
2:22
Question 9
2:51
Question 10
3:32
Wave Characteristics

5m 33s

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0:23
Question 2
1:04
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2:01
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2:50
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3:12
Question 6
3:57
Question 7
4:16
Question 8
4:42
Question 9
4:56
Wave Behaviors

3m 52s

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0:13
Question 2
0:40
Question 3
1:04
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1:17
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1:39
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2:07
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2:41
Question 8
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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Question 1
0:29
Question 5
1:03
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1:24
Question 7
2:01
Diffraction

2m 34s

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0:31
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0:50
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1:05
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1:37
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2:04
Electromagnetic Spectrum

7m 6s

Intro
0:00
Question 1
0:24
Question 2
0:39
Question 3
1:05
Question 4
1:51
Question 5
2:03
Question 6
2:58
Question 7
3:14
Question 8
3:52
Question 9
4:30
Question 10
5:04
Question 11
6:01
Question 12
6:16
Wave-Particle Duality

5m 30s

Intro
0:00
Question 1
0:15
Question 2
0:34
Question 3
0:53
Question 4
1:54
Question 5
2:16
Question 6
2:27
Question 7
2:42
Question 8
2:59
Question 9
3:45
Question 10
4:13
Question 11
4:33
Energy Levels

8m 13s

Intro
0:00
Question 1
0:25
Question 2
1:18
Question 3
1:43
Question 4
2:08
Question 5
3:17
Question 6
3:54
Question 7
4:40
Question 8
5:15
Question 9
5:54
Question 10
6:41
Question 11
7:14
Mass-Energy Equivalence

8m 15s

Intro
0:00
Question 1
0:19
Question 2
1:02
Question 3
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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• ## Related Books 3 answers Last reply by: Professor Dan FullertonMon Apr 15, 2019 6:03 AMPost by James Glass on February 11, 2018Hello,  In example 11 when analyizing the 2 voltage source circuit, why doesn't the current from the 12V source also have to go through R2? Similar question for the other source, why doesn't the current form the 16V source also have to go through R1?  It seems like both the 12V and the 16V current would have to travel around the smaller loop and the larger outside loop.  Thanks. 1 answer Last reply by: Professor Dan FullertonSat Jan 14, 2017 3:16 PMPost by Vivian Ni on January 13, 2017At 33:02, I understand how you got 3.2 V, but how is V the same for both R2 and R3? The resistance is different for both, so I'm confused as to how the voltage is the same. Thanks! 1 answer Last reply by: Professor Dan FullertonThu Aug 20, 2015 8:05 AMPost by Anh Dang on August 19, 2015Sorry about this question, but can you remind me what exactly a potential drop is? 2 answers Last reply by: Professor Dan FullertonThu Jun 25, 2015 3:45 PMPost by Derek Boutin on June 25, 2015Professor Fullerton, the lecture was extremely helpful. However, I do have two questions. In Example 11, why do you use -12 and -16? Also, in Example 13, why do you start with 30 Volts and end with 0 Volts? Thanks! 1 answer Last reply by: Professor Dan FullertonMon Feb 23, 2015 9:03 PMPost by Yahaira Leon on February 23, 2015Why did you divide 50*30 by 80 1 answer Last reply by: Professor Dan FullertonSat Mar 29, 2014 7:39 AMPost by Hoa Huynh on March 29, 2014Dear Professor,At 46:11, I do not understand why the voltage right below the emf 5V is 0. If we use the loop, the current should flow from the + side to -side. Please, explain me how can we know the current flow on what way. Thank you 1 answer Last reply by: Professor Dan FullertonWed Mar 5, 2014 5:42 AMPost by ibrahim shawi on March 5, 2014is it possible to use VIRP for this problem? 1 answer Last reply by: Professor Dan FullertonWed Mar 5, 2014 5:44 AMPost by ibrahim shawi on March 4, 2014for example 13 complex circuit with meters, You labeled the first resistor R1 and then the second one also as R1 is it because they are in series? also in the beginning of the equation you made the 30 negative.... is that because of equation..... kirchhoff's law? 1 answerLast reply by: ibrahim shawiTue Mar 4, 2014 9:52 PMPost by ibrahim shawi on March 4, 2014for the basic parallel circuit analysis lecture at 20:53 you said that total R is equal to 667 and i see how you got it but when i solve for the answer using 1/R=1/R+1/R+1/R I get 1.5x10^-3.... 1 answer Last reply by: Professor Dan FullertonThu Jan 30, 2014 7:38 AMPost by Karpis Sanosyan on January 29, 2014You really help me understand, but i don't understand how you get the voltage by putting one side 0? 1 answer Last reply by: Professor Dan FullertonSun Oct 27, 2013 10:01 AMPost by Yadira Perez on October 26, 2013Excellent explanations, I was so lost in class but you have made a difference thank you!! 1 answer Last reply by: Professor Dan FullertonWed May 8, 2013 6:12 AMPost by Nawaphan Jedjomnongkit on May 8, 2013Thank you so much for great lecture and I like your teaching style that give a lot of example questions after theory part. Yet I still not so confident about circuit analysis with 2 voltage sources. Is it possible that the voltage from one sauce cancel the other like when I put batteries in wrong side will have no power? Take care , don't catch a cold ^_^

### Circuit Analysis

• The values of currents and electric potential difference in an electric circuit are determined by the properties and arrangement of the individual circuit elements.
• Kirchhoff's Current Law (KCL) states that the sum of the current entering any point in a circuit is equal to the current leaving that point. This is also known as the junction rule, and is a restatement of the law of conservation of charge.
• Kirchhoff's Voltage Law (KVL) states that the sum of the potential drops in any closed loop of a circuit has to equal zero. This is also known as the loop rule, and is a restatement of the law of conservation of energy.
• Real batteries and voltage sources have some finite amount of internal resistance. The terminal voltage of a real battery is equal to the battery's emf - the voltage drop across the internal resistance.

### Circuit Analysis

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.

• Intro 0:00
• Objectives 0:07
• Series Circuits 0:27
• Series Circuits Have Only a Single Current Path
• Removal of any Circuit Element Causes an Open Circuit
• Kirchhoff's Laws 1:36
• Tools Utilized in Analyzing Circuits
• Kirchhoff's Current Law States
• Junction Rule
• Kirchhoff's Voltage Law States
• Loop Rule
• 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
• Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
• 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
• Work Back to Original Circuit
• Analysis of a Combination Circuit 29:20
• Internal Resistance 34:11
• In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'
• Terminal Voltage of the Voltage Source is Reduced Slightly
• 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

### Transcription: Circuit Analysis

Hi folks. Welcome back to Educator.com0000

I am Dan Fullerton and today we are going to talk about circuit analysis.0002

Our goals are going to be to draw and interpret schematic diagrams of circuits, to solve both series and parallel circuit problems using VIRP tables, to calculate equivalent resistances for resistors in both series and parallel configurations, and finally to calculate power and energy used in electric circuits.0007

Let us start by talking about series circuits.0025

Series circuits have only a single current path. If you remove any circuit element you cause an open circuit.0029

For example, think of a Christmas light.0035

If you have one go bad, you have seen the whole strand go out -- that is a series circuit.0037

The way we would draw a series circuit is we must have a source of potential difference, so we will put a battery here, where the long side is positive and the short side is negative.0043

And then we will draw some resistors.0051

That could be (R1), another resistor, a couple of more resistors, and then we complete the circuit.0054

Current wants to flow from positive high potential to negative potential, meaning electrons would go the other way.0070

Now, it is a series circuit, which means if any one of these elements breaks, the entire circuit stops working.0077

For example, if this resistor burnt out and became an open, all of a sudden nothing lights up anymore.0082

You will no longer have current flow and your circuit no longer functions, so that is a series circuit.0089

One of the tools we are going to use to analyze circuits is known as Kirchhoff's Laws.0096

Kirchhoff's Laws are tools utilized in analyzing these circuits.0101

We are going to focus on two laws: Kirchhoff's Current Law, or KCL, states that the sum of all current entering any point in a circuit equals the sum of all current leaving that point in a circuit.0105

It is really just a restatement of conservation of charge -- What goes in, must come out.0115

It is also known as the Junction Rule.0121

The other law we are going to look at is Kirchhoff's Voltage Law, or KVL, and that says that the sum of all the potential drops in any closed loop in a circuit must sum to zero.0125

That is really a restatement of the conservation of energy and it is also known as the Loop Rule -- KVL, Kirchhoff's Voltage Law.0135

Let us take a look at our first example here.0145

A 3-ohm resistor and a 6-ohm resistor are connected in series in an operating electric circuit.0147

At some point in the circuit we must have a 3-ohm resistor and a 6-ohm resistor, and there has to be more to the circuit, but we will just draw that piece for now.0153

If the current through the 3-ohm resistor is 4 A -- so we have 4 A going through the 3-ohm resistor.0164

What is the potential difference across the 6-ohm resistor?0170

To answer this I have to figure out the current going through the 6-ohm resistor, and if I have 4 A going through the 3-ohm resistor, Kirchhoff's Current Law says I must have that same current here and same current here. -- what goes in, must come out.0173

So I must have 4 A going through the 6-ohm resistor; current does not get used up in a circuit.0186

Now that I know the resistance and the current flow, I can find the voltage drop.0193

The potential difference from one side to the other is going to be I × R, which is 4 A × 6-ohms or 24 volts.0198

So if the current is going this way, we must drop 24 volts from the positive to the negative side as the current goes in that direction.0209

What is the potential difference across the 6-ohm resistor? 24 volts.0218

Let us take another look here.0226

The diagram below represents currents in a segment of an electric circuit. What is the reading of ammeter A?0227

We have an ammeter here, and here we have a junction where all of these come together.0233

This is going to be a great place for us to apply Kirchhoff's Current Law, or the Junction Rule.0237

The current coming into that junction must equal the current leaving that junction, so coming in we have 2 A, we have 3 A -- so in, we have 2 + 3 and let us just assume for now that we will call that current coming in...0242

...so +A -- and if we get a negative we know it is going the opposite direction -- must equal the current leaving and the current leaving -- well, here we have our 4 A, we have 1 A, and we have 2 A.0260

When I put this all together, I have 5 + A = 7, therefore, A must equal 2 A, and yes, it is going in, so our ammeter would read: 2 A.0277

As we talk about basic series circuit analysis, we can use Kirchhoff's Current Law and Kirchhoff's Voltage Law along with Ohm's Law to find a bunch of unknowns.0294

But one of the most helpful tools, especially when you are starting out with simple circuits is what I call a VIRP Table.0303

What we are going to do is we are going to analyze the voltage, (V), the current, (I), the resistance, (R), and the power dissipated, (P), for every element in the circuit as well as for the total circuit.0308

Here is what I am talking about.0320

We have here a power supply and 3 resistors; I will call this R1, that one R2, and that one R3.0322

Now I am going to make a table. I will make a row for every circuit element: R1, R2, R3, and one for the total.0331

What I am going to analyze for each of these is the potential difference (V), the current flow (I), the resistance (R), and the power dissipated, (P).0344

I am just going to make this look like a nice pretty table -- to help us organize our thoughts.0355

Then we will fill in what we know about the circuit already.0372

Well, I know R1, R2, and R3, each of those is 2 kilo-ohms or 2,000-ohms so I will fill those in.0375

I know the total voltage must be 12 volts because that is the extent of my power supply, so that is 12.0386

I could also figure out the equivalent resistance.0393

Because it is a series circuit, so I just add up my resistors: 2,000 + 2,000 + 2,000, which will give me a total of 6,000.0395

Now what is really neat here is anytime you know any two things in a row, using Ohm's Law or your power definitions, you can figure out the other two.0404

Once you know two items in any row, you can find the other two, so current -- right here -- I is going to be V/R --Ohm's Law, so total current, I = V/R, is 12 volts/6,000 ohms, which is going to be .002 A, so I will fill that in right here.0414

That means I have .002 A flowing through my circuit this way, and since it is a series circuit, I must have the same current everywhere in the circuit.0436

That means that I have .002 A flowing through R1; I have .002 A flowing through R2, and of course, .002 A flowing through R3.0445

Now I know two things in all of these rows.0457

If I want the voltage here, through R1, the voltage drop across R1 -- that I can find by Ohm's Law V = RI, so that is 0.002 × 2,000, which is going to give me voltage of 4 volts -- potential difference of 4 volts from one side to the other is 4.0460

It is pretty easy to see R2 and R3 are going to have the same values.0479

The sum of the potential drops here all add up, so the potential drops 4 volts here, 4 volts there, 4 volts there, and that brings us back to 12 volts, which is what we would expect.0483

For the power, I could get that a bunch of different ways.0497

I could use power equals IV, I could use power equals I2R, or I could use power equals V2/R, since I know all of those things.0501

We will take the easy one right now -- power equals V × I, that will be 0.008 watts dissipated in R1 or 8 milliwatts.0510

We will have the same for R2, the same for R3, and the total power dissipated is just going to be the sum of those or I could find it by multiplying V times I down here, but either way 0.008 + 0.008 + 0.008 or 12 × 0.002 -- regardless, I am going to get the same answer of 0.024.0519

I am dissipating 0.024 W in my entire circuit.0539

That is basically how we are going to use these VIRP tables to help us organize our information.0544

As I write these down you will notice that I am skipping putting units anywhere.0548

I am assuming that V potential difference is in volts, current is in amps, (R) is in ohms, and power is in watts.0552

Let us take a look at another problem -- current in a series circuit.0562

A 2-ohm resistor and a 4-ohm resistor are connected in series with a 12-volt battery.0565

Let us draw that first. We have a 12-volt battery and we have in there a 2-ohm resistor, and a 4-ohm resistor.0570

If the current through the 2-ohm resistor is 2 amperes, so we must have 2 A flowing through the 2-ohm resistor, what is the current through the 4-ohm resistor?0586

I do not even have to do a VIRP table because this is just Kirchhoff's Current Law.0595

I must have 2 A flowing through there as well due to KCL, Kirchhoff's Current Law -- I = 2 A -- very straightforward there.0599

Let us talk about energy expenditure in a series circuit.0614

In the circuit diagram below, we have two 4-ohm resistors connected to a 16-volt battery as shown.0617

Fill in a VIRP Table for the circuit and determine the rate at which electrical energy is expended in the circuit.0623

Let us call this R1 and this is R2, so that when we do that now and make our VIRP table, we have R1, R2, and a row for the total, and we have V, I, R, and P.0629

We will start with what we know. Our total voltage must be 16 volts, R1 is 4, and R2 is 4.0656

And if we have two resistors in series then that means our total resistance is the sum of those, and that is going to be 8-ohms.0665

We know two things in the row: I = v/r or 16/8 and that is going to give us a current of 2 A.0673

If we have a current of 2 A here, we must have a current of 2 A through R1 and a current of 2 A through R2, so we can fill those in.0680

Now, it is just an exercise in math. V = I × R, 2 × 4, and that will be 8 volts, and 8 volts there, and the sum of (R), individual potential drops, gives us our total potential drop.0689

For power, we will just go right to power equals V × I or 8 × 2 = 16 W and 8 × 2 = 16 W, and I could add those together or 16 × 2 = 32 W.0704

What is our total power dissipated here? 32 watts -- right from our VIRP Table.0716

Taking a look at another series circuit, we have a 50-ohm resistor, an unknown resistor, (R), a 120-volt source, and an ammeter connected as shown.0727

The ammeter reads half an amp. Calculate the equivalent resistance of the circuit, the resistance of resistor (R), and the power dissipated by the 50-ohm resistor.0739

Let us do this with a VIRP Table again.0749

If we call this R1, we will make that R2, then our table will have R1, R2, and total.0751

We do not need to add the ammeter in there because our ammeter should have a negligible effect on the circuit. 0767 All the ammeter does is to provide us information.0761

V, I, R, P -- And we will start by filling in what we know: R1 is 50-ohms; we know that we have a 120-volt source.0770

We know the current over here because the ammeter says it is half an amp and that means we must have half an amp going through R1 and R2, so, 0.5 A, 0.5 A, so we must have a total current of 0.5 A, so that must be the same.0790

Now, let us start down here. We know two things in this row: if R = V/I or 120/0.5, that is going to be 240, so our total resistance must be 240.0806

If our total resistance is 240 and R1 is 50-ohms -- they are in series -- what do we add to 50 to get 240?0820

Well, that must be 190-ohms.0828

We can figure out the voltages now -- V = I/R, so half of 50 is going to be 25.0831

Half of 190 is going to be 95, and of course, those potential drops will add up to our total potential drop.0837

And if we want the power here too, one more step -- V × I is half of 25, which is 12.5 W; half of 95 is 47.5 W, and half of 120 is 60 W, or add up 12 1/2 and 47 1/2.0845

Calculate the equivalent resistance of the circuit.0867

That is easy. The equivalent resistance is our total resistance there, 240.0870

The resistance of resistor (R) is R2 and its resistance is 190-ohms. We have answered that as well.0875

The power dissipated by the 50-ohm resistor, or by R1 = 12.5 W.0883

By filling out our VIRP table we have answered all these questions effectively.0890

Let us take a look at a voltmeter in a series circuit.0896

In the circuit represented in the diagram, what is the reading of voltmeter V?0899

It looks like we have 2 resistors, and if this looks confusing at first, pretend the voltmeter is not there. 0909 If it is hooked up correctly, it should not have any significant effect on your circuit.0903

As I take a look at this, let us call this R1, we will call that R2...0913

...and we will make our VIRP table -- R1, R2, total -- V, I, R, P.0919

Let us go and let us fill in what we know already -- R1 is 20-ohms, R2 is 10-ohms and our source is 60 volts.0939

As we look again, this is a series circuit again.0949

Current is going through R1 and R2, and we can assume very little current through (V) -- pretend it is not there -- it has a negligible effect on the circuit.0953

Therefore, we could find that for the total equivalent resistance, we can just add them for a series circuit of 20 + 10 = 30.0961

Once I have that, of course, I can figure out the current -- I = V/R or 60/30 = 2 A.0970

If we have 2 A going here, we must have 2 A through R1 and R2, so we can fill those in.0978

And now, it is pretty easy to go find the potential drop across R1 -- V = I/R by Ohm's Law or 2 × 20 = 40 -- 2 × 10 = 20, and of course, those add up to our total.0984

And while we are here, let us figure out the power -- 40 × 2 (Power = V × I) = 80 W; 20 × 2 = 40 W, and 60 × 2 = 120, or I could have added those up.0997

Now, to answer the question -- What is the reading of voltmeter V?1010

Voltmeter V is reading the potential drop across R1, so the potential drop across R1, I can just look up on my table and it is 40 volts, so our answer must be 40 volts.1015

Let us take a look now at some parallel circuits. Parallel circuits have multiple current paths.1030

Removal of a circuit element may allow other branches of the circuit to continue operating.1035

This is kind of like the wiring in your house.1040

If you looked at a circuit in a bedroom, you have a power supply, a resistor, maybe another resistor, like a lamp, an alarm clock, a stereo, or whatever it happens to be.1042

And with your power supply here -- (+/-)V -- if one of these gets interrupted or broken, the other ones continue operating because you still have a complete path here for the electricity to follow.1058

It just does not go through the one element that is broken, which happens when a light bulb goes out in your house, you do not lose everything in that room, you typically lose just that light bulb.1070

Now, basic parallel circuit analysis works very similar to what we did for series circuit analysis, and we are going to use VIRP tables again.1100

Here I have 3 resistors and let us call them R1, R2, and R3. I will make our VIRP Table -- R1, R2, R3, and a row for a total and our data: V, I, R, and P.1108

Our first step again is always filling in what we know: R1 is 2,000, R2 is 2,000, R3 is 2,000, and our total voltage is 12 volts.1135

Now, as we do this, there are a couple different ways we could go about doing this, or different ways to start. 1155 One is we could calculate the equivalent resistance for 3 resistors in parallel and put it down here.1150

You could do that, but there is another way to do this without having to go through that math.1161

Anywhere on a wire has the same potential, so, if this is 12-volts difference here, these are connected to the same wire, so that must be a 12-volt drop here, here, and here.1166

We have the same potential drop across all 3 resistors of 12 volts.1176

In a series circuit, the potential drops are all the same.1181

Now we could figure out the current through each of these -- I = V/R -- the current through here is going to be 12-volt drop/2,000-ohms or about .006 A; R2 is going to be the same and R3 the same.1185

As we look at these, if this is .006 A, we must have .006 A going that way, and if that is also .006, now we must have .012 at this branch in the circuit plus this .006 over here gives us .018, so all of the currents add together for the total.1201

Now, I could find R over here and I have V/I = 12/.018 is going to give us 667, which is the same thing we would have gotten if we calculated an equivalent resistance for the resistors in parallel using 1/R-equivalent = 1/R1 + 1/R2 + 1/R3. -- Try it, it works out.1222

For the powers -- well, that is just going to be V × I, or .072 W, which is the same math for all three of these, and for the total, we could add these three up or 12 × .018 = .216 W or 216 mW for the parallel circuit.1245

Let us take a look here at another parallel circuit problem.1265

We have a 15-ohm resistor, R1 and a 30-ohm resistor, R2 that are to be connected in parallel between points (A) and (B) in the circuit that contains a 90-volt battery.1269

Complete the diagram to show the two resistors connected in parallel between (A) and (B), so let us do that first. 1284 If they are in parallel, we must have two current paths, so let us make that one of them, and we will make that the other, so now current has two different directions to go here, R1 and R2.1278

Now, determine the potential difference across resistor R1 and calculate the current in resistor R2.1300

Well, the potential difference across R1 has to be the same as the battery here.1307

If this is a 90-volt difference between the two, then let us make this simple -- let us call the negative side of the battery 0 volts.1312

If we call that 0, then this side must be 90 higher, so that is 90.1319

We have 90 volts here on the same wire and over here we have 0 volts.1323

The potential difference across R1 is 90 volts, so V1 = 90 volts.1327

And the current in resistor R2 -- well, that should be easy.1334

I2 is going to be V2/R2, where the voltage drop across R2 is the same as it is in R1, 90 volts, so 90 volts/R2 = 30 ohms, and that is going to give us a current of 3 A -- That easy.1338

Equivalent resistance -- Three identical lamps are connected in parallel with each other.1360

If the resistance of each lamp is x-ohms, what is the equivalent resistance of this parallel combination?1365

1/R-equivalent is going to be 1/x + 1/x + 1/x which is equal to 3/x and if 1/R-equivalent is 3/x, then R-equivalent must be x/3-ohms - Answer B1372

Let us take a look at a circuit that has four parallel resistors in it.1396

The diagram below represents an electric circuit consisting of four resistors and a 12-volt battery.1399

What is the current measured by ammeter A, what is the circuit's equivalent resistance, and how much power is dissipated in a 36-ohm resistor?1404

A lot of questions, but again, if we make a VIRP table we will probably answer all of them just in filling out that table.1412

Let us call these R1, R2, R3, and R4.1418

We will make our table and we have elements: R1, R2, R3, R4, and total V, I, R, and P.1426

We will fill in our lines here before we fill in what information we know right away from the circuit.1440

What do we know right away? R1 is 6-ohms, R2 is 12, R3 is 36, and R4 is 18, and we also know our total voltage is 12.1453

You can also look at this battery -- remember if we called this the 0 side that means we have 0 volts here, here, here, here; they are all connected together and this is 12, 12, 12, 12; they are all on the same wire, so the voltage drop across each of these is 12 volts: 12, 12, 12, 12.1467

We can now fill in our currents -- I = V/R or 12/6 = 2, 12/12 = 1, 12/36 = 1/3 (.333), and 12/18 = 2/3 (.667).1487

And the total current in a parallel circuit adds together, or we could have used the equivalent resistance formula to figure out what that is going to be, but if I add these currents together, 2 + 1 + 1/3 + 2/3, it is going to give me 4 A, so, R = V/I or 12/4 and we get 3-ohms there.1500

Now, let us stop for a second and check.1518

We know the equivalent resistance of any parallel circuit has to be less than the smallest resistor in that configuration, so is 3-ohms less than all of our other resistors?1519

It most certainly is. We probably did something right.1534

Power is just V × I, so let us work our way right through here: 24, 12, 4, 12 × 2/3 = 8, and add them all together, or 12 × 4 = 48.1535

What is the circuit's equivalent resistance? R(eq) right from our table is 3-ohms.1552

What is the current measured by ammeter A? Well, A is measuring the current through R1, so, let us say that I1 must be 2 A, and finally, how much power is dissipated in the 36-ohm resistor?1561

That is the power through resistor 3, which is going to be 4 watts -- All right from our table.1576

Looking at an ammeter in a parallel circuit again -- In a circuit diagram shown below, ammeter A1 reads 10 amperes, so 10 A right there. 1595 What is the reading of ammeter A2?1588

Well, let us try a VIRP table solution again.1599

If we call this R1, and this one is R2, then we have R1, R2, and total, and V, I, R, and P.1601

We will make our table and start by filling in what we know: R1 is 20-ohms, R2 is 30-ohms, and our total current is 10 A because that is the combination current of what is going through our battery here.1618

As I look at this now, what is my next step going to be?1639

Well, there is a lot of different things I could do here, but what I am going to do first, since we have not done it this way yet, is I am going to find the equivalent resistance of the circuit.1643

I am going to say that R-equivalent with only two resistors is going to be R1R2/R1 + R2, so that is going to be 20 × 30/20 + 30, which is 50, which is going to give me an equivalent resistance 600/50 or 12-ohms.1652

My potential drop then, V = IR must be 120 volts -- parallel circuit, which means we have the same voltage drop across these other elements -- 120.1673

If I want the current flow, I = V/R, that is 120/20 or 6 and 120/30, that is 4.1685

What is the reading of ammeter A2?1693

The current through A2 is the current through resistor 1, which is going to be 6 A, so the reading of ammeter A2 reads 6 A, and did not even have to fill in the power on this one to keep going.1702

If we wanted to though it would be pretty easy to say that the power here is 720 W, 480 W, and a total of 1200 W.1718

What happens if your circuit is not completely series or parallel but it has a combination of these different elements?1730

Well, first thing I like to do is look for portions of the circuit that have parallel elements and see if you can replace those by an equivalent resistance until you get it into a series circuit configuration and analyze with a VIRP Table.1736

Or, work back to your original circuit using KCL and KVL until you can find all of those unknowns.1748

It is a little bit easier to show than it is to explain.1755

Here we have a combination circuit -- 10 volts -- we have R1, and now we have two resistors, R2 and R3, which are in parallel and then back to series for R4.1761

What I would probably do first thing is draw an equivalent circuit where I am going to put R2 and R3, and I am going to replace those by an equivalent resistor.1770

I would draw this circuit as -- we have our 10 volts here, we have R1, which is still 20-ohms; we have our equivalent resistance between R2 and 3, and we still have R4 down here which is 20-ohms.1780

To find out R2-3 -- since it is in parallel -- it is going to be R2 × R3 = 30 × 50/30 + 50, which is 80...1805

...gives us 1500/80 and that is going to be about 18.75-ohms -- That is a much easier circuit to analyze.1817

As we look at this, we will go back to our VIRP Table now.1830

We have R1, R2, R3, and R4, and V, I, R, and P...1833

...R1 is 20-ohms, R2 is 30, R3 is 50, R4 is 20, and our total voltage is going to be 10 volts.1856

We know our total resistance because these are all in series -- 20 + 18.75 + 20 will give us our total, so 40 + 18.75 gives us a total resistance of 58.75.1876

That means our total current, (I) must be V/R, which is going to be about .170 A.1893

If that is .170 A, right there -- let us think about it -- On this version that is .170 A and it all goes through there.1901

It is going to split here, but as it comes back through R4, we have the total current again .170 A.1910

We can fill in .170 here, and we can fill in .170 here.1917

We will figure out what else we can do right now -- V = IR, so the voltage drop across R1 or 20 × .17 is going to be about 3.4, and R4 -- same math -- 20 × .17 = 3.4.1923

Now, as I look at this, if we start here at 10 volts, I am going to call that 'bottom side,' the negative side zero, and that means this is 10, and across R1 we drop 3.4.1940

If we had 10 and we dropped to 3.4, that means we must have 6.6 over here.1951

Down here at our fourth, this is zero side and it dropped to 3.4, so this side must be 3.4.1960

So, what is the potential difference across R2 and R3?1967

Well that is going to be 6.6 - 3.4, which is 3.2, so R2 and R3 have the same voltage drop.1970

Current flow now I can gets from Ohm's Law: I = V/R, 3.2/30 is going to be .107 and 3.2/50 is going to be .064 and with the exception of a little bit of rounding error there, if we add these two together we are going to get .17...1980

...which we should because if we have .17 coming this way through R2 now, we have 0.107 and that gets most of it, the remainder 0.64 comes through here and then they re-combine again to give you .170 -- they add up.1997

Now, to go finish this off, let us calculate our powers: V × I (0.578), VI down here, 0.341 watts; 3.2 × 0.064 = 0.205 W; 3.4 × 0.17 = 0.578 W again...2011

...and our total is 10 × .170 = 1.7 W, which is what I should get when I add all of these up -- and I do.2031

So that is how you could analyze a combination circuit.2040

Simplify it until you can figure out some more of your unknowns and use your VIRP table to help organize your thoughts.2043

So far we have been dealing with ideal voltage sources, batteries and so on, but in reality, voltage sources typically have some amount of real internal resistance.2052

Hopefully fairly small, but they have some amount of that.2061

The terminal voltage of a voltage source is actually reduced slightly by the potential drop of current flowing through this internal resistance, so if we wanted to look at a real voltage source, we could model it as a source of emf (electromotive force).2065

That is not really a force, it is another term for potential, but what it really is is that is the maximum voltages could put out and then you have this internal resistance.2080

Your terminal voltage (VT) is what you actually measure across the terminals of the battery when you have some current flowing through here, and because you current flowing, you are going to drop a little bit of your potential, your emf is going to be reduced a little bit by this internal resistance.2090

Terminal voltage is going to be E - I times your internal resistance.2106

Let us take a look at a problem with two voltage sources here. We have not done one of these yet.2117

Find the current flowing through R3 if R3 has a value of 6 ohms. What is the power dissipated in R3?2121

Well to do this, the way I am going to start is I am going to set up my circuit and think for a minute.2131

I am going to call that point 0 volts because that is on the negative side of the battery, so that is going to be 12 and we will say that we have some current flowing, so let us call that I1 flowing through R1.2136

Over here we have 0 volts on this side of the battery, which are connected by a wire, so they have to be the same.2147

The positive side, we will call 16 volts and we will say that the current flowing this way through R2, is what we will call I2.2153

That means that if I1 is flowing this way and I2 is flowing this way -- let us call this current3, and it should be pretty easy to see by Kirchhoff's Current Law at this point that I3 = I1 + I2.2160

Now that we have established that, let us see if we can apply Kirchhoff's Voltage Law around some of these loops to get us some more information.2177

If I apply Kirchhoff's Voltage Law around just this loop here, what that says is that some of the potential drops around that loop must be equal to 0.2185

So what I am going to do is I am going to list the positive and negative sides of each of these -- this will be the positive side of the battery of the resistor -- the current is flowing and dropping potential this way -- plus, minus, plus, minus, plus, minus.2194

Now as I make my loop around here, if I start down here I always look at what sign I see first -- if I am going this way up, I see the negative sign of that battery first.2210

So I am going to write -12 volts plus -- the next potential drop is going to be V = IR, or our current flow times our resistance by Ohm's Law, so this will be 8 ohms × I1, so plus 8I1 and as I come around to this part of the loop, I have I3 × R3.2222

That is going to be plus 6I3, and at that point, I am back to where I started -- it must be equal to 0.2245

I can do the same thing over here with this loop. Let us say we go this way around the loop to get us another equation.2253

If I start down here, I see the negative side of this power supply first so I could write -16 + 12I2, is what I come to next, + 6I3, and now I am back to where I started, which equals 0.2260

So now I have a system of equations with several different unknowns.2276

A lot of different ways to solve them, but let us just work through this one in a sort of the brute-force method.2281

Over here, let us start with this: -12 + 8I1 + 6I3, well I3 = I1 + I2...2287

...so that will be 6 × (I1 + I2) = 0, or -12 + 8I1 +6I1 + 6I2 = 0...2297

...or if I put that together, we could say that that is 14I1, adding 8 and 6I1 + 6I2 is going to be equal to 12.2317

I got that from my first loop combined with Kirchhoff's Current Law up here.2330

Now let us take a look at this equation and see what we can do with that.2335

We will start by writing it as -16 + 12I2 + 6, and I am going to replace I3 again with I1 + I2 = 0.2339

Therefore, -16 plus -- well we are going to have 6I1 plus we will have 6I2 + 12I2 is going to give us 18I2 = 0...2355

...so I could write that then as -- well we have 6I1, we have 18I2, and all that must be equal to 16.2370

All right. So I have two equations, two unknowns. How am I going to solve this?2383

Well I see a nice and easy way to do that right here.2388

What I am going to do is I am going to take and I am going to multiply that whole equation by -3 and rewrite it down here.2391

If I multiply both sides by -3, I keep that equality -- that is a fair thing to do algebraically.2398

So -3 × 14 is going to be -42I1; 6 × -3 is going to give us -18I2, and -3 × 12 will be -36 on that side.2404

Why did I do that? Well if you look here now, if I add these two equations, if I add up the left-hand sides and I add up the right-hand sides, I can keep that equality.2419

When I do that, here is what I get: 6I1 - 42I1 -- well that is going to give me -36I1, 18I2 and -I2 gives me 0, and that must be equal to 16 + (-36) = -20, so now I can easily solve for I1, which is going to be -20/-36 or about .556 A.2429

I know I1. I was able to get my first variable.2455

Now what I can do is I can take that value and I can plug it back into one of my previous equations over here.2459

What I am going to do is take that and let us come over here and I am going to start with this 14I1 + 6I2 = 12, but now 14I1 is .556 + 6I2 = 12.2466

14 × .556 + 6I2 = 12 -- fairly easy to solve that to say then that I2 is going to be equal to .703 A.2486

I know I1, I know I2, and I3 is just I1 + I2 -- so I3 = .556 + I2 (0.703), or I find that I3 is going to be equal to 1.26 A.2499

Find the current flowing through R3? That is I3, so we have done one of those.2520

Let us make sure we box our answers so we do not lose it.2525

Now what is the power dissipated in R3?2528

Well for the power dissipated in R3, power3, well I know (I) and I know (R), so I can use power = I2R, where my I is 1.26 A2 times the resistance of R3 (6 ohms) or 9.5 W, so there is my other key answer.2532

The current flowing through R3? -- 1.26 A; and the power dissipated by R3? -- 9.5 W.2555

Let us do a problem with internal resistance now.2566

We have a 50-ohm and a 100-ohm resistor, connected as shown, to a battery with an emf of 40 volts and an internal resistance of (R).2570

So there it is. Here, this entire thing is our battery.2578

Find the value of (R) if the current of the circuit is 1 A. What is the battery's terminal voltage?2580

Well over here I have two resistors and parallels, so the first thing I am going to do is I am going to re-draw this as a nice series circuit, or I am replacing these by their equivalent resistance.2589

So, we will have our 40 volts here, we still have our internal resistance (R), and our R-equivalent between 100 and 50?2600

Well R-equivalent is going to be 100 × 50/100 + 50, so 100 × 50 = 5000/150 -- R-equivalent is about 33.3 ohms.2614

I will put that in here, 33.3 ohms, and our circuit just became a whole lot simpler.2631

Now we know the current flowing through here is 1 A, and if that is the case, the current flowing through here is 1 A as well.2640

So as I run through and use Kirchhoff's Voltage Law around this loop -- positive side and negative side of my battery -- the first thing I am going to see is -40, then I have 1 A × R, so that is going to be +1R or +R, + 33.3 × 1 A, which is 33.3, so that must equal 0.2649

It is pretty easy to solve for this -- R is going to be equal to 40 - 33.3 or 6.7 ohms. We found the value of R.2672

What is the battery's terminal voltage?2685

Well if we want the terminal voltage of our battery, Vterminal is the battery's emf - IR.2688

That is going to be our 40 volts - I (1 A) times the internal resistance (6.67 ohms), so 40 - 6.7 is going to be 33.3 volts.2695

Because our battery has some internal resistance, you do not get the whole 40 volts out when the circuit is in operation, you get 33.3 volts across the terminals of our battery.2709

Let us take a look at a complex circuit with meters.2723

Given the schematic diagram below, determine the reading of both the ammeter and the voltmeter.2726

Well what I am going to do to start this off -- we have a couple of power supplies here -- is just look at this for a minute and see what we can figure out.2732

We will call this the zero side of our battery, so that is 30 volts, that must be 30 volts here, we have current flowing, we will call this I1 flowing through R1.2739

Over here we have +5 volts -- well I am going to call this side 0 volts again because it is on the same wire, and this must be 5 lower so that must be -5 volts over there.2753

If this is 0, we must have 0 volts over here as well, and we are trying to find the reading of both the ammeter and the voltmeter.2760

Let us add I2 for the current flow through there and we must have I1 flowing through here as well.2773

That would be an I3, so let us see what we have as we apply Kirchhoff's Voltage Law around the loop.2781

What we are going to do is we are going to start here as I apply Kirchhoff's Voltage Law, I am going to see -30 first, plus 10I1 + 20I1, then I see the -5 before I get back to where I started, which equals 0.2789

Well I have one equation and one unknown: this just became relatively simple.2810

What I can do then is, with a little bit of Algebra here, and say that I have 30I1 must equal 35, therefore I1 = 35/30 or about 1.17 A.2815

I1 is what goes through the ammeter, so there is our first answer.2834

Let us try and find the reading on the voltmeter.2840

Well the voltage drop across this R1 is going to be I1 × R1, so V1 = I1 × R1.2844

That drop then, I1 (1.17 A) × r1 (10 ohms) is going to give us a drop of 11.7 volts.2855

If this side is 30 and we drop 11.7, that must mean we have 18.3 volts left over here and the voltmeter measures the difference from this point to that point, that is how it is attached.2865

The difference between 18.3 and 0 volts is just 18.3 volts, so the voltmeter reads 18.3 volts -- our second answer.2879

That was not nearly as bad as I expected when we first looked at it.2896

Let us take a look at one more nice, simple problem to round this out.2901

Three resistors: 4 ohms, 6 ohms and 8 ohms are connected in parallel in an electric circuit.2907

The equivalent resistance of the circuit is...?2912

Well right away if they are in parallel I know that my equivalent resistance must be less than 4 ohms.2916

Oh wait, there is our answer right there -- less than 4 ohms. All of our other choices are larger than 4 ohms.2920

Very little thinking required, it is just knowing that formula and a couple of facts.2927