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?
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