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Current & Resistance

Slide Duration:

Section 1: Electricity
Electric Charge & Coulomb's Law

30m 48s

Intro
0:00
Objective
0:15
Electric Charges
0:50
Matter is Made Up of Atoms
0:52
Most Atoms are Neutral
1:02
Ions
1:11
Coulomb
1:18
Elementary Charge
1:34
Law of Conservation of Charge
2:03
Example 1
2:39
Example 2
3:42
Conductors and Insulators
4:41
Conductors Allow Electric Charges to Move Freely
4:43
Insulators Do Not Allow Electric Charges to Move Freely
4:50
Resistivity
4:58
Charging by Conduction
5:32
Conduction
5:37
Balloon Example
5:40
Charged Conductor
6:14
Example 3
6:28
The Electroscope
7:16
Charging by Induction
7:57
Bring Positive Rod Near Electroscope
8:08
Ground the Electroscope
8:27
Sever Ground Path and Remove Positive Rod
9:07
Example 4
9:39
Polarization and Electric Dipole Moment
11:46
Polarization
11:54
Electric Dipole Moment
12:05
Coulomb's Law
12:38
Electrostatic Force, Also Known as Coulombic Force
12:48
How Force of Attraction or Repulsion Determined
12:55
Formula
13:08
Coulomb's Law: Vector Form
14:18
Example 5
16:05
Example 6
18:25
Example 7
19:14
Example 8
23:21
Electric Fields

1h 19m 22s

Intro
0:00
Objectives
0:09
Electric Fields
1:33
Property of Space That Allows a Charged Object to Feel a Force
1:40
Detect the Presence of an Electric Field
1:51
Electric Field Strength Vector
2:03
Direction of the Electric Field Vector
2:21
Example 1
3:00
Visualizing the Electric Field
4:13
Electric Field Lines
4:56
E Field Due to a Point Charge
7:19
Derived from the Definition of the Electric Field and Coulomb's Law
7:24
Finding the Electric Field Due to Multiple Point Charges
8:37
Comparing Electricity to Gravity
8:51
Force
8:54
Field Strength
9:09
Constant
9:19
Charge Units vs. Mass Units
9:35
Attracts vs. Repel
9:44
Example 2
10:06
Example 3
17:25
Example 4
24:29
Example 5
25:23
Charge Densities
26:09
Linear Charge Density
26:26
Surface Charge Density
26:30
Volume Charge Density
26:47
Example 6
27:26
Example 7
37:07
Example 8
50:13
Example 9
54:01
Example 10
1:03:10
Example 11
1:13:58
Gauss's Law

52m 53s

Intro
0:00
Objectives
0:07
Electric Flux
1:16
Amount of Electric Field Penetrating a Surface
1:19
Symbol
1:23
Point Charge Inside a Hollow Sphere
4:31
Place a Point Charge Inside a Hollow Sphere of Radius R
4:39
Determine the Flux Through the Sphere
5:09
Gauss's Law
8:39
Total Flux
8:59
Gauss's Law
9:10
Example 1
9:53
Example 2
17:28
Example 3
22:37
Example 4
25:40
Example 5
30:49
Example 6
45:06
Electric Potential & Electric Potential Energy

1h 14m 3s

Intro
0:00
Objectives
0:08
Electric Potential Energy
0:58
Gravitational Potential Energy
1:02
Electric Potential Energy
1:11
Electric Potential
1:19
Example 1
1:59
Example 2
3:08
The Electron-Volt
4:02
Electronvolt
4:16
1 eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:26
Conversion Ratio
4:41
Example 3
4:52
Equipotential Lines
5:35
Topographic Maps
5:36
Lines Connecting Points of Equal Electrical Potential
5:47
Always Cross Electrical Field Lines at Right Angles
5:57
Gradient of Potential Increases As Equipotential Lines Get Closer
6:02
Electric Field Points from High to Low Potential
6:27
Drawing Equipotential Lines
6:49
E Potential Energy Due to a Point Charge
8:20
Electric Force from Electric Potential Energy
11:59
E Potential Due to a Point Charge
13:07
Example 4
14:42
Example 5
15:59
Finding Electric Field From Electric Potential
19:06
Example 6
23:41
Example 7
25:08
Example 8
26:33
Example 9
29:01
Example 10
31:26
Example 11
43:23
Example 12
51:51
Example 13
58:12
Electric Potential Due to Continuous Charge Distributions

1h 1m 28s

Intro
0:00
Objectives
0:10
Potential Due to a Charged Ring
0:27
Potential Due to a Uniformly Charged Desk
3:38
Potential Due to a Spherical Shell of Charge
11:21
Potential Due to a Uniform Solid Sphere
14:50
Example 1
23:08
Example 2
30:43
Example 3
41:58
Example 4
51:41
Conductors

20m 35s

Intro
0:00
Objectives
0:08
Charges in a Conductor
0:32
Charge is Free to Move Until the
0:36
All Charge Resides at Surface
2:18
Field Lines are Perpendicular to Surface
2:34
Electric Field at the Surface of a Conductor
3:04
Looking at Just the Outer Surface
3:08
Large Electric Field Where You Have the Largest Charge Density
3:59
Hollow Conductors
4:22
Draw Hollow Conductor and Gaussian Surface
4:36
Applying Gaussian Law
4:53
Any Hollow Conductor Has Zero Electric Field in Its Interior
5:24
5:35
Electric Field and Potential Due to a Conducting Sphere
6:03
Example 1
7:31
Example 2
12:39
Capacitors

41m 23s

Intro
0:00
Objectives
0:08
What is a Capacitor?
0:42
Electric Device Used to Store Electrical Energy
0:44
Place Opposite Charges on Each Plate
1:10
Develop a Potential Difference Across the Plates
1:14
Energy is Stored in the Electric Field Between the Plates
1:17
Capacitance
1:22
Ratio of the Charge Separated on the Plates of a Capacitor to the Potential Difference Between the Plates
1:25
Units of Capacitance
1:32
1:37
Formula
1:52
Calculating Capacitance
1:59
Assume Charge on Each Conductor
2:05
Find the Electric Field
2:11
Calculate V by Integrating the Electric Field
2:21
Utilize C=Q/V to Solve for Capitance
2:33
Example 1
2:44
Example 2
5:30
Example 3
10:46
Energy Stored in a Capacitor
15:25
Work is Done Charging a Capacitor
15:28
Solve For That
15:55
Field Energy Density
18:09
Amount of Energy Stored Between the Plates of a Capacitor
18:11
Example
18:25
Dielectrics
20:44
Insulating Materials Place Between Plates of Capacitor to Increase The Devices' Capacitance
20:47
Electric Field is Weakened
21:00
The Greater the Amount of Polarization The Greater the Reduction in Electric Field Strength
21:58
Dielectric Constant (K)
22:30
Formula
23:00
Net Electric Field
23:35
Key Take Away Point
23:50
Example 4
24:00
Example 5
25:50
Example 6
26:50
Example 7
28:53
Example 8
30:57
Example 9
32:55
Example 10
34:59
Example 11
37:35
Example 12
39:57
Section 2: Current Electricity
Current & Resistance

17m 59s

Intro
0:00
Objectives
0:08
Electric Current
0:44
Flow Rate of Electric Charge
0:45
Amperes
0:49
Positive Current Flow
1:01
Current Formula
1:19
Drift Velocity
1:35
Constant Thermal Motion
1:39
Net Electron Flow
1:43
When Electric Field is Applied
1:49
Electron Drift Velocity
1:55
Derivation of Current Flow
2:12
Apply Electric Field E
2:20
Define N as the Volume Density of Charge Carriers
2:27
Current Density
4:33
Current Per Area
4:36
Formula
4:44
Resistance
5:14
Ratio of the Potential Drop Across an Object to the Current Flowing Through the Object
5:19
5:23
Resistance of a Wire
6:05
Depends on Resistivity
6:09
Resistivity Relates to the Ability of a Material to Resist the Flow of Electrons
6:25
Refining Ohm's Law
7:22
Conversion of Electric Energy to Thermal Energy
8:23
Example 1
9:54
Example 2
10:54
Example 3
11:26
Example 4
14:41
Example 5
15:24
Circuits I: Series Circuits

29m 8s

Intro
0:00
Objectives
0:08
Ohm's Law Revisited
0:39
Relates Resistance, Potential Difference, and Current Flow
0:39
Formula
0:44
Example 1
1:09
Example 2
1:44
Example 3
2:15
Example 4
2:56
Electrical Power
3:26
Transfer of Energy Into Different Types
3:28
Light Bulb
3:37
Television
3:41
Example 5
3:49
Example 6
4:27
Example 7
5:12
Electrical Circuits
5:42
Closed-Loop Path Which Current Can Flow
5:43
Typically Comprised of Electrical Devices
5:52
Conventional Current Flows from High Potential to Low Potential
6:04
Circuit Schematics
6:26
Three-dimensional Electrical Circuits
6:37
Source of Potential Difference Required for Current to Flow
7:29
Complete Conducting Paths
7:42
Current Only Flows in Complete Paths
7:43
Left Image
7:46
Right Image
7:56
Voltmeters
8:25
Measure the Potential Difference Between Two Points in a Circuit
8:29
Can Remove Voltmeter from Circuit Without Breaking the Circuit
8:47
Very High Resistance
8:53
Ammeters
9:31
Measure the Current Flowing Through an Element of a Circuit
9:32
Very Low Resistance
9:46
Put Ammeter in Correctly
10:00
Example 8
10:24
Example 9
11:39
Example 10
12:59
Example 11
13:16
Series Circuits
13:46
Single Current Path
13:49
Removal of Any Circuit Element Causes an Open Circuit
13:54
Kirchhoff's Laws
15:48
Utilized in Analyzing Circuits
15:54
Kirchhoff's Current Law
15:58
Junction Rule
16:02
Kirchhoff's Voltage Law
16:30
Loop Rule
16:49
Example 12
16:58
Example 13
17:32
Basic Series Circuit Analysis
18:36
Example 14
22:06
Example 15
22:29
Example 16
24:02
Example 17
26:47
Circuits II: Parallel Circuits

39m 9s

Intro
0:00
Objectives
0:16
Parallel Circuits
0:38
Multiple Current Paths
0:40
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
0:44
Draw a Simple Parallel Circuit
1:02
Basic Parallel Circuit Analysis
3:06
Example 1
5:58
Example 2
8:14
Example 3
9:05
Example 4
11:56
Combination Series-Parallel Circuits
14:08
Circuit Doesn't Have to be Completely Serial or Parallel
14:10
Look for Portions of the Circuit With Parallel Elements
14:15
Lead to Systems of Equations to Solve
14:42
Analysis of a Combination Circuit
14:51
Example 5
20:23
Batteries
28:49
Electromotive Force
28:50
Pump for Charge
29:04
Ideal Batteries Have No Resistance
29:10
Real Batteries and Internal Resistance
29:20
Terminal Voltage in Real Batteries
29:33
Ideal Battery
29:50
Real Battery
30:25
Example 6
31:10
Example 7
33:23
Example 8
35:49
Example 9
38:43

34m 3s

Intro
0:00
Objectives
0:17
Capacitors in Parallel
0:51
Store Charge on Plates
0:52
Can Be Replaced with an Equivalent Capacitor
0:56
Capacitors in Series
1:12
Must Be the Same
1:13
Can Be Replaced with an Equivalent Capacitor
1:15
RC Circuits
1:30
Comprised of a Source of Potential Difference, a Resistor Network, and Capacitor
1:31
RC Circuits from the Steady-State Perspective
1:37
Key to Understanding RC Circuit Performance
1:48
Charging an RC Circuit
2:08
Discharging an RC Circuit
6:18
The Time Constant
8:49
Time Constant
8:58
By 5 Time Constant
9:19
Example 1
9:45
Example 2
13:27
Example 3
16:35
Example 4
18:03
Example 5
19:39
Example 6
26:14
RC Circuits: Transient Analysis

1h 1m 7s

Intro
0:00
Objectives
0:13
Charging an RC Circuit
1:11
Basic RC Circuit
1:15
Graph of Current Circuit
1:29
Graph of Charge
2:17
Graph of Voltage
2:34
Mathematically Describe the Charts
2:56
Discharging an RC Circuit
13:29
Graph of Current
13:47
Graph of Charge
14:08
Graph of Voltage
14:15
Mathematically Describe the Charts
14:30
The Time Constant
20:03
Time Constant
20:04
By 5 Time Constant
20:14
Example 1
20:39
Example 2
28:53
Example 3
27:02
Example 4
44:29
Example 5
55:24
Section 3: Magnetism
Magnets

8m 38s

Intro
0:00
Objectives
0:08
Magnetism
0:35
Force Caused by Moving Charges
0:36
Dipoles
0:40
Like Poles Repel, Opposite Poles Attract
0:53
Magnetic Domains
0:58
Random Domains
1:04
Net Magnetic Field
1:26
Example 1
1:40
Magnetic Fields
2:03
Magnetic Field Strength
2:04
Magnets are Polarized
2:16
Magnetic Field Lines
2:53
Show the Direction the North Pole of a Magnet Would Tend to Point if Placed on The Field
2:54
Direction
3:25
Magnetic Flux
3:41
The Compass
4:05
Earth is a Giant Magnet
4:07
Earth's Magnetic North Pole
4:10
Compass Lines Up with the Net Magnetic Field
4:48
Magnetic Permeability
5:00
Ratio of the magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
5:01
Free Space
5:13
Permeability of Matter
5:41
Highly Magnetic Materials
5:47
Magnetic Dipole Moment
5:54
The Force That a Magnet Can Exert on Moving Charges
5:59
Relative Strength of a Magnet
6:04
Example 2
6:26
Example 3
6:52
Example 4
7:32
Example 5
7:57
Moving Charges In Magnetic Fields

29m 7s

Intro
0:00
Objectives
0:08
Magnetic Fields
0:57
Vector Quantity
0:59
Tesla
1:08
Gauss
1:14
Forces on Moving Charges
1:30
Magnetic Force is Always Perpendicular to the Charged Objects Velocity
1:31
Magnetic Force Formula
2:04
Magnitude of That
2:20
Image
2:29
Direction of the Magnetic Force
3:54
Right-Hand Rule
3:57
Electron of Negative Charge
4:04
Example 1
4:51
Example 2
6:58
Path of Charged Particles in B Fields
8:07
Magnetic Force Cannot Perform Work on a Moving Charge
8:08
Magnetic Force Can Change Its Direction
8:11
Total Force on a Moving Charged Particle
9:40
E Field
9:50
B Field
9:54
Lorentz Force
9:57
Velocity Selector
10:33
Charged Particle in Crosses E and B Fields Can Undergo Constant Velocity Motion
10:37
Particle Can Travel Through the Selector Without Any Deflection
10:49
Mass Spectrometer
12:21
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
12:26
Used to Determine the Mass of An Unknown Particle
12:32
Example 3
13:11
Example 4
15:01
Example 5
16:44
Example 6
17:33
Example 7
19:12
Example 8
19:50
Example 9
24:02
Example 10
25:21
Forces on Current-Carrying Wires

17m 52s

Intro
0:00
Objectives
0:08
Forces on Current-Carrying Wires
0:42
Moving Charges in Magnetic Fields Experience Forces
0:45
Current in a Wire is Just Flow of Charges
0:49
Direction of Force Given by RHR
4:04
Example 1
4:22
Electric Motors
5:59
Example 2
8:14
Example 3
8:53
Example 4
10:09
Example 5
11:04
Example 6
12:03
Magnetic Fields Due to Current-Carrying Wires

24m 43s

Intro
0:00
Objectives
0:08
Force on a Current-Carrying Wire
0:38
Magnetic Fields Cause a Force on Moving Charges
0:40
Current Carrying Wires
0:44
How to Find the Force
0:55
Direction Given by the Right Hand Rule
1:04
Example 1
1:17
Example 2
2:26
Magnetic Field Due to a Current-Carrying Wire
4:20
Moving Charges Create Magnetic Fields
4:24
Current-Carrying Wires Carry Moving Charges
4:27
Right Hand Rule
4:32
Multiple Wires
4:51
Current-Carrying Wires Can Exert Forces Upon Each Other
4:58
First Right Hand Rule
5:15
Example 3
6:46
Force Between Parallel Current Carrying Wires
8:01
Right Hand Rules to Determine Force Between Parallel Current Carrying Wires
8:03
Find Magnetic Field Due to First Wire, Then Find Direction of Force on 2nd Wire
8:08
Example
8:20
Gauss's Law for Magnetism
9:26
Example 4
10:35
Example 5
12:57
Example 6
14:19
Example 7
16:50
Example 8
18:15
Example 9
18:43
The Biot-Savart Law

21m 50s

Intro
0:00
Objectives
0:07
Biot-Savart Law
0:24
Brute Force Method
0:49
Draw It Out
0:54
Diagram
1:35
Example 1
3:43
Example 2
7:02
Example 3
14:31
Ampere's Law

26m 31s

Intro
0:00
Objectives
0:07
Ampere's Law
0:27
Finds the Magnetic Field Due to Current Flowing in a Wire in Situations of Planar and Cylindrical Symmetry
0:30
Formula
0:40
Example
1:00
Example 1
2:19
Example 2
4:08
Example 3
6:23
Example 4
8:06
Example 5
11:43
Example 6
13:40
Example 7
17:54
Magnetic Flux

7m 24s

Intro
0:00
Objectives
0:07
Magnetic Flux
0:31
Amount of Magnetic Field Penetrating a Surface
0:32
Webers
0:42
Flux
1:07
Total Magnetic Flux
1:27
Magnetic Flux Through Closed Surfaces
1:51
Gauss's Law for Magnetism
2:20
Total Flux Magnetic Flux Through Any Closed Surface is Zero
2:23
Formula
2:45
Example 1
3:02
Example 2
4:26

1h 4m 33s

Intro
0:00
Objectives
0:08
0:44
0:46
Direction of the Induced Current is Given by Lenz's Law
1:09
Formula
1:15
Lenz's Law
1:49
Lenz's Law
2:14
Lenz's Law
2:16
Example
2:30
Applying Lenz's Law
4:09
If B is Increasing
4:13
If B is Decreasing
4:30
Maxwell's Equations
4:55
Gauss's Law
4:59
Gauss's Law for Magnetism
5:16
Ampere's Law
5:26
5:39
Example 1
6:14
Example 2
9:36
Example 3
11:12
Example 4
19:33
Example 5
26:06
Example 6
31:55
Example 7
42:32
Example 8
48:08
Example 9
55:50
Section 4: Inductance, RL Circuits, and LC Circuits
Inductance

6m 41s

Intro
0:00
Objectives
0:08
Self Inductance
0:25
Ability of a Circuit to Oppose the Magnetic Flux That is Produced by the Circuit Itself
0:27
Changing Magnetic Field Creates an Induced EMF That Fights the Change
0:37
Henrys
0:44
Function of the Circuit's Geometry
0:53
Calculating Self Inductance
1:10
Example 1
3:40
Example 2
5:23
RL Circuits

42m 17s

Intro
0:00
Objectives
0:11
Inductors in Circuits
0:49
Inductor Opposes Current Flow and Acts Like an Open Circuit When Circuit is First Turned On
0:52
Inductor Keeps Current Going and Acts as a Short
1:04
If the Battery is Removed After a Long Time
1:16
Resister Dissipates Power, Current Will Decay
1:36
Current in RL Circuits
2:00
Define the Diagram
2:03
Mathematically Solve
3:07
Voltage in RL Circuits
7:51
Voltage Formula
7:52
Solve
8:17
Rate of Change of Current in RL Circuits
9:42
Current and Voltage Graphs
10:54
Current Graph
10:57
Voltage Graph
11:34
Example 1
12:25
Example 2
23:44
Example 3
34:44
LC Circuits

9m 47s

Intro
0:00
Objectives
0:08
LC Circuits
0:30
Assume Capacitor is Fully Charged When Circuit is First Turned On
0:38
Interplay of Capacitor and Inductor Creates an Oscillating System
0:42
Charge in LC Circuit
0:57
Current and Potential in LC Circuits
7:14
Graphs of LC Circuits
8:27
Section 5: Maxwell's Equations
Maxwell's Equations

3m 38s

Intro
0:00
Objectives
0:07
Maxwell's Equations
0:19
Gauss's Law
0:20
Gauss's Law for Magnetism
0:44
1:00
Ampere's Law
1:18
Revising Ampere's Law
1:49
Allows Us to Calculate the Magnetic Field Due to an Electric Current
1:50
Changing Electric Field Produces a Magnetic Field
1:58
Conduction Current
2:33
Displacement Current
2:44
Maxwell's Equations (Complete)
2:58
Section 6: Sample AP Exams
1998 AP Practice Exam: Multiple Choice Questions

32m 33s

Intro
0:00
0:11
Multiple Choice 36
0:36
Multiple Choice 37
2:07
Multiple Choice 38
2:53
Multiple Choice 39
3:32
Multiple Choice 40
4:37
Multiple Choice 41
4:43
Multiple Choice 42
5:22
Multiple Choice 43
6:00
Multiple Choice 44
8:09
Multiple Choice 45
8:27
Multiple Choice 46
9:03
Multiple Choice 47
9:30
Multiple Choice 48
10:19
Multiple Choice 49
10:47
Multiple Choice 50
12:25
Multiple Choice 51
13:10
Multiple Choice 52
15:06
Multiple Choice 53
16:01
Multiple Choice 54
16:44
Multiple Choice 55
17:10
Multiple Choice 56
19:08
Multiple Choice 57
20:39
Multiple Choice 58
22:24
Multiple Choice 59
22:52
Multiple Choice 60
23:34
Multiple Choice 61
24:09
Multiple Choice 62
24:40
Multiple Choice 63
25:06
Multiple Choice 64
26:07
Multiple Choice 65
27:26
Multiple Choice 66
28:32
Multiple Choice 67
29:14
Multiple Choice 68
29:41
Multiple Choice 69
31:23
Multiple Choice 70
31:49
1998 AP Practice Exam: Free Response Questions

29m 55s

Intro
0:00
0:14
Free Response 1
0:22
Free Response 2
10:04
Free Response 3
16:22

• ## Related Books

### Current & Resistance

• Current is the flow rate of electric charge. Conventional current flows in the direction that a positive charge moves. If negative electrons are the charge carriers, conventional current flows opposite the direction of electron flow.
• In a conductor, electrons are in constant thermal motion. The net electron flow, however, is zero because the motion is random. When an electric field is applied, a small net flow in a direction opposite the electric field is observed. The average velocity of these electrons due to the electric field is known as electron drift velocity.
• Resistance is the ratio of the potential drop across an object to the current flowing through the object.
• Objects which have a fixed resistance are known as ohmic materials and follow Ohm’s Law (R=V/I).
• The current density through a surface is the current per area, and is a vector quantity (J).
• The resistance of a wire depends on the geometry of the wire as well as the resistivity of the wire, a material property relating to the ability of the material to resist the flow of electrons.

### Current & Resistance

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 0:08
• Electric Current 0:44
• Flow Rate of Electric Charge
• Amperes
• Positive Current Flow
• Current Formula
• Drift Velocity 1:35
• Constant Thermal Motion
• Net Electron Flow
• When Electric Field is Applied
• Electron Drift Velocity
• Derivation of Current Flow 2:12
• Apply Electric Field E
• Define N as the Volume Density of Charge Carriers
• Current Density 4:33
• Current Per Area
• Formula
• Resistance 5:14
• Ratio of the Potential Drop Across an Object to the Current Flowing Through the Object
• Ohmic Materials Follow Ohm's Law
• Resistance of a Wire 6:05
• Depends on Resistivity
• Resistivity Relates to the Ability of a Material to Resist the Flow of Electrons
• Refining Ohm's Law 7:22
• Conversion of Electric Energy to Thermal Energy 8:23
• Example 1 9:54
• Example 2 10:54
• Example 3 11:26
• Example 4 14:41
• Example 5 15:24

### Transcription: Current & Resistance

Hello, everyone, and welcome back to www.educator.com.0000

I'm Dan Fullerton and in this lesson we are going to talk about current and resistance.0003

Our objectives include understanding the definition of electric current.0008

Relating magnitude and direction of the current to the rate of flow of electric charge.0013

Relating current flow with drift velocity and the density of charge carriers in a conductor.0017

Relating current and voltage for a resistor.0022

Writing a relationship between electric field strength and current density in a conductor.0025

Describing how the resistance of a resistor depends upon its length and cross sectional area, as well as the material it is made out of.0029

Finding the resistance of a resistor of uniform cross section from its dimensions and the resistivity of that material.0036

Let us dive right in.0044

An electric current is the flow rate of electric charge, units are in C/s0046

which we also know as amperes which are given the symbol A and oftentimes you will hear that referred to as amps.0051

Positive current flow is the direction of the flow of positive charges.0059

It can be a little bit confusing realizing that in most of the circuits we are going to talk about is actually electrons which are moving.0063

The direction of the charge carrier flow in most circuits, electrons is opposite what we call the direction of positive current flow.0070

Formally, current I is the amount of charge passing through a point at a given time.0079

Or DQ DT the time rate of change of charge.0086

Let us talk a little bit about drift velocity.0096

In a conductor, electrons are in constant thermal motion.0099

Net electron flow, however is 0, because that motion is in all directions.0103

It is random so they all cancel out.0107

When an electric field is applied, a small net flow in a direction opposite the electric field is observed.0109

The average velocity of these electrons due to the electric field is known as the electron drift velocity VD.0115

This is typically much smaller than that is the speed of the constant random thermal motion.0121

To give you an idea, let us take a look at the derivation of current flow.0129

Consider a uniform conductor of cross sectional area A and apply some electric field E.0135

Let us try to draw that in here, an electric field.0142

We will define the N as the volume density of charge carriers in this material.0148

Electrons in the conductor move randomly with thermal velocities.0153

We talked about that on the last slide.0157

Roughly 1,000,000 m/s, they are moving pretty quick but it is on random directions.0159

When we apply this electric field however, there is some small net movement of electrons opposite the direction of the electric field.0164

And that speed might be on the order say ½ cm/s compared to the thermal motion of 1,000,000 m/s.0172

If we define N as that volume density of charge carriers, that means the electrons contained in some volume, let us highlight it here in yellow.0180

Let us say that that is their drift velocity, VD × some time interval Δ T × that cross sectional area A.0191

The electrons in that volume are going to pass surface A in time T.0200

From that, the total charge it is passing, A is equal to the product of the volume passing surface A.0207

The carrier density and the charge on each carrier, which we are going to call e.0214

We have got this amount and we have to deal with the VD TA.0218

If they want the charge that passes A in that period of time, that is going to be that carrier density ×0224

the charge e that goes with each of those charged carriers.0231

Typically, an elementary charge × that volume VD TA.0236

Since current is charge per unit time, we can say that current flow then is going to be N ×0243

our elementary charge × that drift velocity × that cross sectional area.0252

Or I oftentimes write this E as Q as well, so you may see in this form NQ VD A, the current flow derivation.0260

We can also look at this from the perspective of current density.0273

Current density through a surface is the current per area and it is a vector quantity usually given the symbol J.0276

J is the current density would be that carrier density × the amount of charge per carrier × the drift velocity VD,0284

which implies then as well that current flow I, is going to be the integral / that cross sectional surface of J ⋅ DA.0297

You can relate current flow to current density.0310

Resistance is the ratio of the potential drop across an object, the current flowing through the object.0318

Objects which have a fixed resistance that is not a function of the current potential drop are known as Ohmic materials.0324

And they are said to follow Ohm’s law, an empirical law.0330

Now R = V/ I, therefore, Ohm’s law V = IR, just a rearrangement of that.0335

The potential drop across a resistor is equal to the current flowing through it × its resistance.0346

This is a constant slope, a constant resistance regardless of the current or potential drop, we say that the material is Ohmic.0351

If we did not have a straight line, we would call that material a non Ohmic material.0360

What happens when you have a wire?0366

The resistance of the wire depends on the geometry of the wire.0369

As well as the property of the material the wire is made out of, known as its resistivity given the symbol ρ.0371

The units of ρ are ohm’s ω × m.0378

Resistivity relates to the ability of a material to resist the flow of electrons.0386

If we have a resistor of some length L and cross sectional area A, we can find its resistance R0390

is the resistivity × its length ÷ that cross sectional area.0399

You can almost think of it to look kind of like water in a pipe.0405

If you have a thicker diameter pipe, you have less resistance to water flow.0411

Thicker diameter wire, less resistance.0419

A is in the denominator.0424

The longer it is, the harder it is to push things out, the higher the resistance.0426

Same thing with the water pipe, the longer the pipe the more resistance to water flow.0431

Very similar and a nice analogy for helping to understand these qualitatively.0436

Let us see if we can refine Ohm’s law just a little bit.0442

We start with V = IR but we also just said that R = ρ L / A, our cylindrical resistor.0444

Then we have V = I ρ L ÷ A.0456

But we also know, because we have a uniform material that the electric field is going to be the potential drop ÷ the length.0462

That our electric field then is going to be ρ × I / A.0470

But this I/ A current per area is the current density.0478

This implies then because current density = current flow ÷ area, we can write then that our electric field0482

is equal to our resistivity × our current density vector.0492

Going further, we can even talk about the conversion of electrical energy to thermal energy.0504

The work done or energy used is charge × potential difference which implies that the time rate of change of that,0510

the rate of change of the work done with respect to time is going to be the derivative with respect to time of QV.0519

We also know that power is the time rate of change of work done, DW DT.0527

We could write then that power is equal to, potential should be a constant V DQ DT.0535

DQ DT we said that was current flow.0544

Therefore, we can write that power is current × voltage.0551

Or using Ohm’s law, V = IR, replacing V with IR power = I² R.0557

Or using Ohm’s law rearranged again.0567

If I = V/ R, let us replace I² with V²/ R².0570

We determine that power is also D² / R.0575

We have a couple different derivations for the rate of change at which energy is expanded which we call power.0579

Let us take a look at an example having to do with a silver wire.0591

The silver wire with 1/2 mm radius cross section is connected to the terminals of a 1V battery.0596

If the wire is 0.1 m long, determine the resistance of the wire.0602

It gives us some information, the resistivity of silver, its molar mass, and its mass density.0606

Resistance is ρ L / A, where our resistivity here is 1.59 × 10⁻⁸ ohm meters, our length is 0.1 m and our cross sectional area0612

is going to be π × our radius² which is 0.0005 m² for resistance of 0.00202 ohms.0632

Let us see if we can extend this example a little bit further.0650

A silver wire with 1/2 mm radius cross section connected to the same battery, same length of wire, determine the current flowing through the wire.0656

Current is potential ÷ resistance.0665

We have a 1V potential and we just found our resistance 0.00202 ohms, gives us a current flow of around 494 amps.0670

Let us take this even further in a slightly more detailed calculation.0685

The same wire but now we are asked to find the drift velocity of the free electrons and the wire assuming 1 free electron per atom.0692

In order to find the drift velocity, we first need to know the charge carrier density and0702

we will determine this by dividing Avogadro’s number by the volume of a mol of silver.0708

Then, we can find the drift velocity from our formula for current.0712

Let us start there with our charge carrier density is Avogadro’s number ÷ our volume which implies then,0715

since we know the resistivity of silver or molar density of silver is going to be our molar mass ÷ volume.0731

Or volume then is going to be our molar mass ÷ ρ.0742

Therefore, N is going to be equal to Avogadro’s number ρ silver / its molar mass.0749

We can look at the current flow I, we know as N × the charge for carrier V drift velocity A.0759

We want drift velocity so VD drift velocity will be I ÷ N EA.0768

But we just found N up here, so we will plug that in to determine that VD = IM/ NA ρ silver EA.0777

Or solving numerically that is going to be, we have got our 494 amps for our current.0797

We have our molar mass 0.1079 kg/ mol, making sure to put this into our standard units.0803

By the way, 10.5 g/ cc that is going to be 10,500 kg/ m³.0815

We have got to divide all this by Avogadro’s number 6.02 × 10 ⁺23 × our mass density for silver which we said 10,500 kg/ m³ ×0828

our charge per carrier, that is our elementary charge 1.6 × 10 ⁻19 C × our area which is π R².0848

Π × 0.0005².0856

Put that all very carefully in your calculator, I come up with a drift velocity of about 0.067 m/ s.0861

A little bit more to do on that one.0874

Alright let us go on step further here with a silver wire.0878

Determine the average time required for electrons to pass from the negative terminal of the battery to the positive terminal.0884

We found the drift velocity and velocity is distance ÷ time.0892

Then time is going to be distance ÷ drift velocity.0897

And if we have to cross 0.1 m and our velocity is 0.067 m/ s,0903

that means it is going to take right about 1.5, 1.49 s for those electrons to travel that distance.0912

Let us take a look at one last example problem.0923

The 12 gauge aluminum wire with a cross sectional area of 3.31 × 10⁻⁶ m² carries a 4 amp current.0927

The density of aluminum is 2.7 g/ cc.0935

Find the drift velocity of the electrons and the wire assuming each aluminum atom supplies 1 conduction electron.0939

Starting off with what we know, our area is 3.31 × 10⁻⁶ m².0946

Our current is 4 amps, our ρ is going to be 2.7 g/ cc our density.0955

Or if we convert that into kg/ m³ that is going to be 2700 kg/ m³ standard units.0967

And our molar mass is 27 g/ mol for aluminum which is 0.027 kg/ mol.0976

We can go back to what we did in example 3 to give us at least part way there in this problem.0988

We know that is current is N EV DA.0993

We went through and we also found then that the drift velocity is current × that molar mass /0998

Avogadro’s number × our density of aluminum × our charge per charge carrier × A.1007

And if I substitute in my values, we end up with our current 4 amps, our molar mass was 0.027 kg/ mol.1017

Avogadro’s number 6.02 × 10 ⁺23.1031

We had our density 2700 kg/ m³, our charge per carrier 1.6 × 10 ⁻19 C our elementary charge.1036

And our cross sectional area it gives it to us here 3.31 × 10⁻⁶ m².1049

I come up with a drift velocity of right around 1.25 × 10⁻⁴ m/ s.1056

Thank you so much for watching www.educator.com.1074

We will see a very soon, make it a great day everyone.1076

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