Unit V:

Essential Questions: What is charge? How do charges behave?

What is an electric field? How is electricity created? What is resistance? How do circuits work?

I.

A. Electric Nature of Matter1. Sketch:

2. Concept Map: the Atom

The study of electric charges at rest along with their electric fields and potentials

Mass of

SymbolSymbol Symbol

Charge is

Charge is

Mass of

Mass of

Charge is

Inside Nucleus

Outside Nucleus

B. The Elementary Charge: the magnitude of charge on a proton or an

electron 1. Symbol: e

2. Protons and Electrons have equal but opposite charges

• Protons are 1 positive elementary charge:

• Electrons are 1 negative elementary charge:

e

e

3. Any object may only have a charge that is a multiple of e

i.e.:

4. Charge is said to be quantized comes in discreet bundles or

packages

e3 e2 e e e2 e3

C. Charged Objects1. Objects with excess electrons or a deficit of electrons

As the amount of electrons increases, the charge of an object becomes more

___________

2. Atoms that have gained or lost electrons are called ___________

Electrons are removed when an atom gains energy

NEGATIVE

IONS

(Friction, Heat, Light)

3. Like charges ___________ while opposite charges ____________

The charges exert __________ on each other

4. Charge is Conserved! Neither created nor destroyed, only transferred

REPELATTRACT

Force

Law of Conservation of Charge

5. Charge will spread itself out evenly over objects in contact!

6. Grounding: All charges seek the path of least resistance to the ground

(where they can “get away from each other”)

most objects that are connected to the ground will allow charge to pass through

Including YOU!

7. Charge has Units!

Coulombs (C) 1 Coulomb = 6.25 x 1018 elementary

charges

1 elementary charge = 1.6 x 10-19 C How can you remember these

numbers? PRT’s !! (Front Cover)

Example: Charges

If an object contains 3.45 x 1013 elementary charges, how many Coulombs of charge are on the object? How many MICROCoulombs is the equal

to?How many elementary charges make up an –8.0 Coulomb charge? What is causing the charge for this

object?

Journal # 11/18

A sphere has an excess of 1.5625 x 1017 elementary charges.• How many Coulombs of charge exist on the sphere?• How many Microcoulombs of charge does the sphere posses?• Calculate the electrostatic force that would exist if the sphere were brought within 0.5 meter of an identical NEGATIVELY charged sphere.

8. Charge is Transferablea. Conductors: objects that allow

charge to move freely through

b. Insulators: objects that slow or prevent the flow of charge

Examples: metal, tap water, YOU

Examples: most plastic, rubber, distilled water

c. Conduction: transfer of charge by contact between objects

electrons move between objects

d. Induction: transfer of charge between two objects without contact

electrons move to/from the ground

D. Coulomb’s Law:

quantifies electrostatic force between charges

1. As the magnitude of the charges increases the

force between them _______________increases

2. As the distance between the charges increases

the force between them __________________decreases (by a lot)

3. Equation:

2

21

r

qkqFe

r

q

k

FeElectrostatic Force (N)

Coulomb’s Constant ( )Magnitude of Charge (C)Separation of Charges (m)

N • m2/C2

NOT RADIUS!

Electrostatic Constant or

4. Units:

2

21

r

qkqFe

2

22

)(

))()((

m

CCCmNFe

NFe 5. Electrostatic Force is a vector quantity

has magnitude and direction

• What is the electrostatic force between a charged boy and girl at the Homecoming possessing net charges of +2.0 microcoulombs and –3.0 microcoulombs if the lovers are 10 meters apart?

• Is the force attractive or repulsive?

mr

Cq

Cq

CmNk

Fe

10

100.3

100.2

1099.8

?

6

2

6

1

229

2

21

r

qkqFe

NFe

4104.5 2

66229

)10(

)100.3)(100.2)(1099.8(

m

CCCmNFe

Example: Coulomb’s Law

Example: Converting Charge

How many Coulombs are in 850 microcoulombs?

How many microcoulombs are in 2.8 x 10-6 C?

How many microcoulombs are in 0.003 C?

How many meters are in 80 cm?

E. Electric Fields

1. Electric fields are shown with electric field lines

a. lines are drawn along the path a “positive test charge” would move in the field

b. all lines are directed toward the negative charge

Region around a charged object in which force is exerted on another charged object

Fields

2. Examples of electric fieldsa. Positive Point Charge

b. Negative Point Charge

c. Positive and Negative Spheres

d. Positive Sphere vs. Positive Sphere

e. Negative Sphere vs. Negative Sphere

f. Oppositely Charged Parallel Plates

F. Potential Difference

1. When work is done on a charge, there is a change in its electric potential energy

The work done by moving a charge in an electric field

2. Potential Difference (V) is equal to the work done (W) per unit charge (q)

3. Equation:

4. Units:

q

WV PRT’s !!

(Electricity Section)

q

WV

C

J

V 111 orVoltC

J

Moving a charge of 3.2 x 10-19 C between two points in an electric field requires 4.8 x 10-18 J of energy. What is the potential difference between these points?

Cq

JW

V

19

18

102.3

108.4

?

q

WV

C

J19

18

102.3

108.4

CJV 15

V15V

Example 1: Potential Difference

6. In order to bring like charges closer together, Work must be done! Same is true for separating unlike charges!

q

WV VqW

7. Potential Difference can also be used to find the work done in moving a charge

No Work Done Here!

Work IS Done Here!

Example 2: Potential Difference

How much charge is in a wire containing 1.5625 x 1018 elementary charges?How much work is done to move these charges through a potential difference of 120V?

9. Potential Difference is measured with a Voltmeter

Example: Electric Fields

Identify the sign of the charges that exist on the spheres in the following situation:

II.

A. Electric Current:

1. Conditions necessary for electric current:

a potential difference (V) must exist a closed circuit (pathway) must

exist the pathway must be a conductor

Provides a pathway for charges to flow

The rate at which charge is allowed to flow past a given point (over time)

2. Equation:

3. Units:

t

qI

t

qI

I = Electric Current

Δq = total charge

t = time

s

C

Ampere)(1 As

C11

4. Direction of Current Flowa. Only electrons are allowed to

move freely – toward positive charge!

b. Current is usually understood as flowing from positive to negative

Conventional Current

5. In general, As the potential difference increases, the electric current will ___________

6. Electric Current is measured with an Ammeter

increase

Potential Difference (V)

Curr

en

t (A

)

Direct Relationship

7. Direct vs. Alternating Currenta. Direct Current: electrons flow in

one direction only produced bybatteries, cells, and

automobiles

weakens considerably when resistance is present length of

wire temperature

b. Alternating Current: switches direction of electron flow with a determined frequency

requires high potential differences to drive the current

used to deliver electricity to end users

allows current to maintain strength over large distances

B. Circuit Symbols and Diagrams makes it possible to represent circuits easily wire is shown as lines

the rest of the symbols we use are in the PRT’s!PRT’s:

Electricity Section

Acts as a resistor

Slows down current

Measures potential difference Measures

current

Adjustable (Rheostat)

Journal #23 11/21

A 12 Volt battery is used to power a circuit with a switch and three light bulbs. 100 Coulombs of charge move through the circuit in 20 seconds.

How much work is done to move this charge?What is the electric current?Draw a circuit diagram!

Ammeters must be placed in SERIES so that all current passes through in order to measure current!

Voltmeters must be placed in PARALLEL (across) a circuit item to measure the Voltage

Example: Circuit Diagram

Draw a circuit with three light bulbs (one after the other) that also contains a switch, a battery, and a properly placed ammeter and voltmeter.

C. Resistance:

1. A potential difference is created by resistance and current is slowed down

Opposition a conductor or device offers to electric current

2. Equation:

3. Units:

I = Electric Current

V = Potential Diff.

R = Resistance

I

VR

Ohm’s Law

I

VR

AV

Ohm) (1 AV

11

Journal #24 11/22

A 120 Volt outlet is used to power a circuit with some resistance.

If 60 Coulombs of charge move through the circuit in 10 seconds, what is the electric current?How much work is done by the outlet moving the charge?What is the internal resistance of the circuit?How long will it take for 400 Coulombs of charge to flow through the circuit?

4. Factors Affecting Resistancea. Length of Wire

b. Thickness of Wire

Related to diameter of wire!

Thicker wire = less resistance

Longer wire = more resistance

c. Resistivity:

Depends on material

How well a material conducts electrons

PRT’s: Electricity Section

d. Temperature of conductor (wire) Warmer temperatures increase

collisions of electrons with other particles/atoms and slows down current!

Warmer temperatures increase resistance

D. Series Circuits:

1. Each resistor will cause a “potential drop”

sum of potential drops will be the total voltage across the series circuit

All Components are connected in sequence (one after another)

...321 VVVV

2. Each individual resistance can be added together to find the total equivalent resistance for the series circuit (AKA effective resistance)

...321 RRRReq

1030eqR

40eqR

3. All current must pass through each component wired in series

Current settles at a certain rate that is the same throughout the series circuit

...321 IIII

AI 0.3

What is the effective resistance of the circuit? ...321 RRRReq

54eqR

9eqR

Example: Series Circuit

Example of a Series Circuit Continued…

What is the current in the circuit?

I

VR

eqR

VI

0.9

0.9 VA0.1

Example of a Series Circuit Continued…

What is potential difference across the 4 Ω resistor?

I

VR

1IRV )0.4)(0.1( A V0.4 What is potential difference across the 5 Ω resistor?

I

VR

2IRV )0.5)(0.1( A V0.5

Journal #25 12/2

A 10 Ohm resistor, a 15 Ohm resistor, and a 5 Ohm resistor are connected in series across a 90 Volt battery. Sketch the circuit diagram!!!

What is the equivalent resistance in the circuit?

What is the electric current in the circuit?

SHOW ALL WORK!

E. Parallel Circuits:

1. Potential difference is the same in each branch of the circuit

Components are connected so current “splits up”

...321 VVVV

2. Current splits into each branch of the circuit

Amount of current in each branch depends on the resistance in each

branch Currents from each branch will add

up to the total current

...321 IIII

1A 2

A3A

3. Resistance in a parallel circuit behaves very strangely (see derivation)

...

1111

321

RRRReq

21

111

RRReq

10

1

30

11

eqR

30

41

eqR

5.7eqR

4. Increasing the number of parallel branches decreases the equivalent resistance of the circuit

More current is forced to flow through from the source so the resistance drops

321

1111

RRRReq

20

1

10

1

30

11

eqR

60

111

eqR

5.5eqR

20Ω

5. Elements CAN BE removed from a parallel circuit and current will still flow through other branches

This does NOT work in series circuits

What is the effective resistance of the circuit?

21

111

RRReq

30

1

20

11

eqR

60

51

eqR

12eqR

Example: Parallel Circuit

Example of a Parallel Circuit Continued…

What is the potential difference in each branch the circuit?

21 VVV

V121 V

V12V

V122 V

Example of a Parallel Circuit Continued…

What is the current in each branch the circuit and the total current?

I

VR R

VI 1

R

VI 2

20

12V

30

12V

A6.0

A4.0

Example of a Parallel Circuit Continued…

Check yourself!!

I

VR

eq

T R

VI

12

12VA1

AA 4.06.0 21 IIIT A1

Journal #26 12/3

Three resistors of 60 Ω, 30 Ω, and 20 Ω are connected in parallel across a 90 V batteryDraw a schematic of the circuit! Include ammeters in each branch Draw a voltmeter as it needs to be

placed to measure the potential drop across the 20 Ω resistor

Find the equivalent resistance in the circuit.Find the current in each resistor.Find the TOTAL current in the circuit.

F. Law of Conservation of Charge:

1. Can be used with known electric currents to find unknown electric currents in circuit branches

The total current entering a junction must equal the total current leaving the junction

What is the reading on Ammeter A1?

What is the reading on Ammeter A5?

15 A

30 A

Example: Junctions

Por Ejemplo

Which of the following junctions is possible?

III.

A. Electric Power:

1. Equation:

2. Units:

Remember: Power is the Work done per unit time

t

WP

product of the potential difference and electric currentVIP

B. Ohm’s Law and Power Recall each form of Ohm’s Law:

1. Substitute Ohm’s Law for Voltage into the electric power equation:

I

VR

R

VI IRV

VIP IIR)( RI 2 This is the power generated as a resistor slows down current

2. Substitute Ohm’s Law for Current into the electric power equation:

VIP R

V 2

R

VV

PRT’s: Electricity Section

Example: Electric Power

So there’s this light bulb…

What is Power of the bulb if the outlet provides a voltage of 120 V and a current of 0.5 A? What is the resistance of the bulb?

(Show two ways to do this!)If the user changes the bulb to 100 W, what is the new current in the bulb?What is the new resistance of the 100 W bulb?

Journal #27 12/3

Assume two lights are plugged into a 120 V household outlet. One has a 40 W bulb and the other has a 75 W bulb.

What is the resistance of each bulb?What is the current in each bulb?Make a rule about Power (wattage) of a device and it’s current and resisistance. (As the…)What makes a bulb brighter?

IV.

A. Take any equation for electrical power and multiply by time (t) to get energy!

the product of the power consumed and the time of charge flow

PtW

R

tVRtIVItW

22

Units: Joules (J)

B. Electric companies charge for ELECTRICAL ENERGY USED, not Power.

Joules are not used (too small) Formula Used: PtW Units: ))(( sW W

Divide by 1000 watts/kilowatt Divide by 3600 seconds/hour Becomes:

hrW kW to go back to SI units multiply by 1000 & 3600

Example: Electric Energy

So there’s this other light bulb…

What is Power of the bulb if the outlet provides a voltage of 120 V and a current of 0.83 A? How much energy does the bulb use after a period of 1 hour?If the user changes the bulb to 40 W, what is the new current in the bulb?How much energy does the 40 W bulb use after a period of 1 hour?