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ResourcesChapter menu
Chapter Presentation
Transparencies Sample Problems
Visual Concepts
Standardized Test Prep
Resources
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ResourcesChapter menu
Section 1 Electric Potential
Section 2 Capacitance
Section 3 Current and Resistance
Section 4 Electric Power
Electrical Energy and CurrentChapter 17
Table of Contents
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Objectives
• Distinguish between electrical potential energy, electric potential, and potential difference.
• Solve problems involving electrical energy and potential difference.
• Describe the energy conversions that occur in a battery.
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Electrical Potential Energy
• Electrical potential energy is potential energy associated with a charge due to its position in an electric field.
• Electrical potential energy is a component of mechanical energy.
ME = KE + PEgrav + PEelastic + PEelectric
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Electrical Potential Energy, continued
• Electrical potential energy can be associated with a charge in a uniform field.
• Electrical Potential Energy in a Uniform Electric Field
PEelectric = –qEdelectrical potential energy = –(charge) (electric field strength)
(displacement from the reference point in the direction of the field)
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ResourcesChapter menu
Chapter 17
Electrical Potential Energy
Section 1 Electric Potential
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Potential Difference
• Electric Potential equals the work that must be performed against electric forces to move a charge from a reference point to the point in question, divided by the charge.
• The electric potential associated with a charge is the electric energy divided by the charge:
V
PEelectric
q
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Potential Difference, continued
• Potential Difference equals the work that must be performed against electric forces to move a charge between the two points in question, divided by the charge.
• Potential difference is a change in electric potential.
change in electric potential energy
potential differenceelectric charge
electricPEV
q
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ResourcesChapter menu
Chapter 17
Potential Difference
Section 1 Electric Potential
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Potential Difference, continued
• The potential difference in a uniform field varies with the displacement from a reference point.
• Potential Difference in a Uniform Electric Field
∆V = –Ed
potential difference = –(magnitude of the electric field displacement)
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Sample ProblemPotential Energy and Potential Difference
A charge moves a distance of 2.0 cm in the direction of a uniform electric field whose magnitude is 215 N/C.As the charge moves, its electrical potential energy decreases by 6.9 10-
19 J. Find the charge on the moving particle. What is the potential difference between the two locations?
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Sample Problem, continuedPotential Energy and Potential Difference
Given:
∆PEelectric = –6.9 10–19 J
d = 0.020 m
E = 215 N/C
Unknown:
q = ?
∆V = ?
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Sample Problem, continuedPotential Energy and Potential Difference
Use the equation for the change in electrical potential energy.
PEelectric = –qEd
Rearrange to solve for q, and insert values.
–19
–19
(–6.9 10 J)– –
(215 N/C)(0.020 m)
1.6 10 C
electricPEq
Ed
q
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Sample Problem, continuedPotential Energy and Potential Difference
The potential difference is the magnitude of E times the displacement.
– –(215 N/C)(0.020 m)
–4.3 V
V Ed
V
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Potential Difference, continued
• At right, the electric poten-tial at point A depends on the charge at point B and the distance r.
• An electric potential exists at some point in an electric field regardless of whether there is a charge at that point.
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ResourcesChapter menu
Section 1 Electric PotentialChapter 17
Potential Difference, continued• The reference point for potential difference near a
point charge is often at infinity.
• Potential Difference Between a Point at Infinity and a Point Near a Point Charge
• The superposition principle can be used to calculate the electric potential for a group of charges.
value of the point chargepotential difference = Coulomb constant
distance to the point charge
C
qV k
r
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ResourcesChapter menu
Chapter 17Section 1 Electric Potential
Superposition Principle and Electric Potential
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Objectives
• Relate capacitance to the storage of electrical potential energy in the form of separated charges.
• Calculate the capacitance of various devices.
• Calculate the energy stored in a capacitor.
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Capacitors and Charge Storage
• A capacitor is a device that is used to store electrical potential energy.
• Capacitance is the ability of a conductor to store energy in the form of electrically separated charges.
• The SI units for capacitance is the farad, F, which equals a coulomb per volt (C/V)
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Capacitors and Charge Storage, continued
• Capacitance is the ratio of charge to potential difference.
magnitude of charge on each platecapacitance =
potential difference
QC
V
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ResourcesChapter menu
Chapter 17
Capacitance
Section 2 Capacitance
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Capacitors and Charge Storage, continued
• Capacitance depends on the size and shape of a capacitor.
• Capacitance for a Parallel-Plate Capacitor in a Vacuum
–12 2
0
0
area of one of the platescapacitance = permittivity of a vacuum
distance between the plates
of the medium 8.85 10 C /N mpermittivity
AC
d
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Capacitors and Charge Storage, continued
• The material between a capacitor’s plates can change its capacitance.
• The effect of a dielectric is to reduce the strength of the electric field in a capacitor.
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ResourcesChapter menu
Chapter 17
Capacitors in Keyboards
Section 2 Capacitance
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ResourcesChapter menu
Chapter 17
Parallel-Plate Capacitor
Section 2 Capacitance
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Energy and Capacitors
• The potential energy stored in a charged capacitor depends on the charge and the potential difference between the capacitor’s two plates.
1electrical potential energy = (charge on one plate)(final potential difference)
2
1
2electricPE Q V
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ResourcesChapter menu
Section 2 CapacitanceChapter 17
Sample ProblemCapacitance
A capacitor, connected to a 12 V battery, holds 36 µC of charge on each plate. What is the capacitance of the capacitor? How much electrical potential energy is stored in the capacitor?
Given:
Q = 36 µC = 3.6 10–5 C
∆V = 12 V
Unknown:
C = ? PEelectric = ?
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ResourcesChapter menu
Chapter 17
Sample Problem, continuedCapacitance
To determine the capacitance, use the definition of capacitance.
–5
–6
3.6 10 C
12 V
3.0 10 F 3.0 µF
QC
V
C
Section 2 Capacitance
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ResourcesChapter menu
Chapter 17
Sample Problem, continuedCapacitance
To determine the potential energy, use the alternative form of the equation for the potential energy of a charged capacitor:
2
–6 2
–4
1( )
21
(3.0 10 F)(12 V)2
2.2 10 J
electric
electric
electric
PE C V
PE
PE
Section 2 Capacitance
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Objectives
• Describe the basic properties of electric current, and solve problems relating current, charge, and time.
• Distinguish between the drift speed of a charge carrier and the average speed of the charge carrier between collisions.
• Calculate resistance, current, and potential difference by using the definition of resistance.
• Distinguish between ohmic and non-ohmic materials, and learn what factors affect resistance.
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Current and Charge Movement
• Electric current is the rate at which electric charges pass through a given area.
charge passing through a given area
electric current = time interval
QI
t
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ResourcesChapter menu
Chapter 17
Conventional Current
Section 3 Current and Resistance
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Drift Velocity
• Drift velocity is the the net velocity of a charge carrier moving in an electric field.
• Drift speeds are relatively small because of the many collisions that occur when an electron moves through a conductor.
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ResourcesChapter menu
Chapter 17
Drift Velocity
Section 3 Current and Resistance
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Resistance to Current
• Resistance is the opposition presented to electric current by a material or device.
• The SI units for resistance is the ohm (Ω) and is equal to one volt per ampere.
• Resistance
potential difference
resistancecurrent
VR
I
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Resistance to Current, continued
• For many materials resistance is constant over a range of potential differences. These materials obey Ohm’s Law and are called ohmic materials.
• Ohm’s low does not hold for all materials. Such materials are called non-ohmic.
• Resistance depends on length, cross-sectional area, temperature, and material.
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ResourcesChapter menu
Chapter 17
Factors that Affect Resistance
Section 3 Current and Resistance
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ResourcesChapter menu
Section 3 Current and ResistanceChapter 17
Resistance to Current, continued
• Resistors can be used to control the amount of current in a conductor.
• Salt water and perspiration lower the body's resistance.
• Potentiometers have variable resistance.
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ResourcesChapter menu
Section 4 Electric PowerChapter 17
Objectives
• Differentiate between direct current and alternating current.
• Relate electric power to the rate at which electrical energy is converted to other forms of energy.
• Calculate electric power and the cost of running electrical appliances.
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ResourcesChapter menu
Section 4 Electric PowerChapter 17
Sources and Types of Current
• Batteries and generators supply energy to charge carriers.
• Current can be direct or alternating.– In direct current, charges move in a single
direction.– In alternating current, the direction of charge
movement continually alternates.
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ResourcesChapter menu
Section 4 Electric PowerChapter 17
Energy Transfer
• Electric power is the rate of conversion of electrical energy.
• Electric power
P = I∆V
Electric power = current potential difference
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ResourcesChapter menu
Chapter 17
Energy Transfer
Section 4 Electric Power
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ResourcesChapter menu
Section 4 Electric PowerChapter 17
Energy Transfer, continued
• Power dissipated by a resistor
• Electric companies measure energy consumed in kilowatt-hours.
• Electrical energy is transferred at high potential differences to minimize energy loss.
22 ( )V
P I V I RR
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ResourcesChapter menu
Chapter 17
Relating Kilowatt-Hours to Joules
Section 4 Electric Power
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ResourcesChapter menu
Multiple Choice
1. What changes would take place if the electron moved from point A to point B in the uniform electric field?A. The electron’s electrical potential energy would increase; its electric potential would increase.B. The electron’s electrical potential energy would increase; its electric potential would decrease.C. The electron’s electrical potential energy would decrease; its electric potential would decrease.D. Neither the electron’s electrical potential energy nor its electric potential would change.
Standardized Test PrepChapter 17
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ResourcesChapter menu
Multiple Choice, continued
1. What changes would take place if the electron moved from point A to point B in the uniform electric field?A. The electron’s electrical potential energy would increase; its electric potential would increase.B. The electron’s electrical potential energy would increase; its electric potential would decrease.C. The electron’s electrical potential energy would decrease; its electric potential would decrease.D. Neither the electron’s electrical potential energy nor its electric potential would change.
Standardized Test PrepChapter 17
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ResourcesChapter menu
Multiple Choice, continued
2. What changes would take place if the electron moved from point A to point C in the uniform electric field?F. The electron’s electrical potential energy would increase; its electric potential would increase.G. The electron’s electrical potential energy would increase; its electric potential would decrease.H. The electron’s electrical potential energy would decrease; its electric potential would decrease.J. Neither the electron’s electrical potential energy nor its electric potential would change.
Standardized Test PrepChapter 17
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ResourcesChapter menu
Multiple Choice, continued
2. What changes would take place if the electron moved from point A to point C in the uniform electric field?F. The electron’s electrical potential energy would increase; its electric potential would increase.G. The electron’s electrical potential energy would increase; its electric potential would decrease.H. The electron’s electrical potential energy would decrease; its electric potential would decrease.J. Neither the electron’s electrical potential energy nor its electric potential would change.
Standardized Test PrepChapter 17
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 3–4.A proton (q = 1.6 10–19 C) moves 2.0 10–6 m in the direction of an electric field that has a magnitude of 2.0 N/C.
3. What is the change in the electrical potential energy associated with the proton?A. –6.4 10–25 JB. –4.0 10–6 VC. +6.4 10–25 JD. +4.0 10–6 V
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 3–4.A proton (q = 1.6 10–19 C) moves 2.0 10–6 m in the direction of an electric field that has a magnitude of 2.0 N/C.
3. What is the change in the electrical potential energy associated with the proton?A. –6.4 10–25 JB. –4.0 10–6 VC. +6.4 10–25 JD. +4.0 10–6 V
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 3–4.A proton (q = 1.6 10–19 C) moves 2.0 10–6 m in the direction of an electric field that has a magnitude of 2.0 N/C.
4. What is the potential difference between the proton’s starting point and ending point?F. –6.4 10–25 JG. –4.0 10–6 VH. +6.4 10–25 JJ. +4.0 10–6 V
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 3–4.A proton (q = 1.6 10–19 C) moves 2.0 10–6 m in the direction of an electric field that has a magnitude of 2.0 N/C.
4. What is the potential difference between the proton’s starting point and ending point?F. –6.4 10–25 JG. –4.0 10–6 VH. +6.4 10–25 JJ. +4.0 10–6 V
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
5. If the negative terminal of a 12 V battery is grounded, what is the potential of the positive terminal?
A. –12 V
B. +0 V
C. +6 V
D. +12 V
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Multiple Choice, continued
5. If the negative terminal of a 12 V battery is grounded, what is the potential of the positive terminal?
A. –12 V
B. +0 V
C. +6 V
D. +12 V
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Multiple Choice, continued
6. If the area of the plates of a parallel-plate capacitor is doubled while the spacing between the plates is halved, how is the capacitance affected?
F. C is doubled
G. C is increased by four times
H. C is decreased by 1/4
J. C does not change
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Multiple Choice, continued
6. If the area of the plates of a parallel-plate capacitor is doubled while the spacing between the plates is halved, how is the capacitance affected?
F. C is doubled
G. C is increased by four times
H. C is decreased by 1/4
J. C does not change
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Multiple Choice, continued
Use the following passage to answer questions 7–8.
A potential difference of 10.0 V exists across the plates of a capacitor when the charge on each plate is 40.0 µC.
7. What is the capacitance of the capacitor?
A. 2.00 10–4 F
B. 4.00 10–4 F
C. 2.00 10–6 F
D. 4.00 10–6 F
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Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 7–8.
A potential difference of 10.0 V exists across the plates of a capacitor when the charge on each plate is 40.0 µC.
7. What is the capacitance of the capacitor?
A. 2.00 10–4 F
B. 4.00 10–4 F
C. 2.00 10–6 F
D. 4.00 10–6 F
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Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 7–8.
A potential difference of 10.0 V exists across the plates of a capacitor when the charge on each plate is 40.0 µC.
8. How much electrical potential energy is stored in the capacitor?
F. 2.00 10–4 J
G. 4.00 10–4 J
H. 2.00 10–6 J
J. 4.00 10–6 J
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ResourcesChapter menu
Standardized Test PrepChapter 17
Multiple Choice, continued
Use the following passage to answer questions 7–8.
A potential difference of 10.0 V exists across the plates of a capacitor when the charge on each plate is 40.0 µC.
8. How much electrical potential energy is stored in the capacitor?
F. 2.00 10–4 J
G. 4.00 10–4 J
H. 2.00 10–6 J
J. 4.00 10–6 J
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Multiple Choice, continued
9. How long does it take 5.0 C of charge to pass through a given cross section of a copper wire if I = 5.0 A?
A. 0.20 s
B. 1.0 s
C. 5.0 s
D. 25 s
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Multiple Choice, continued
9. How long does it take 5.0 C of charge to pass through a given cross section of a copper wire if I = 5.0 A?
A. 0.20 s
B. 1.0 s
C. 5.0 s
D. 25 s
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Multiple Choice, continued
10. A potential difference of 12 V produces a current of 0.40 A in a piece of copper wire. What is the resistance of the wire?
F. 4.8 Ω
G. 12 Ω
H. 30 Ω
J. 36 Ω
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Standardized Test PrepChapter 17
Multiple Choice, continued
10. A potential difference of 12 V produces a current of 0.40 A in a piece of copper wire. What is the resistance of the wire?
F. 4.8 Ω
G. 12 Ω
H. 30 Ω
J. 36 Ω
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Multiple Choice, continued
11. How many joules of energy are dissipated by a 50.0 W light bulb in 2.00 s?
A. 25.0 J
B. 50.0 J
C. 100 J
D. 200 J
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Multiple Choice, continued
11. How many joules of energy are dissipated by a 50.0 W light bulb in 2.00 s?
A. 25.0 J
B. 50.0 J
C. 100 J
D. 200 J
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Multiple Choice, continued
12. How much power is needed to operate a radio that draws 7.0 A of current when a potential difference of 115 V is applied across it?
F. 6.1 10–2 W
G. 2.3 100 W
H. 1.6 101 W
J. 8.0 102 W
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Standardized Test PrepChapter 17
Multiple Choice, continued
12. How much power is needed to operate a radio that draws 7.0 A of current when a potential difference of 115 V is applied across it?
F. 6.1 10–2 W
G. 2.3 100 W
H. 1.6 101 W
J. 8.0 102 W
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Short Response
13. Electrons are moving from left to right in a wire. No other charged particles are moving in the wire. In what direction is the conventional current?
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Standardized Test PrepChapter 17
Short Response, continued
13. Electrons are moving from left to right in a wire. No other charged particles are moving in the wire. In what direction is the conventional current?
Answer: right to left
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Short Response, continued
14. What is drift velocity, and how does it compare with the speed at which an electric field travels through a wire?
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Short Response, continued
14. What is drift velocity, and how does it compare with the speed at which an electric field travels through a wire?
Answer: Drift velocity is the net velocity of a charge carrier moving in an electric field. Drift velocities in a wire are typically much smaller than the speeds at which changes in the electric field propagate through the wire.
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Short Response, continued
15. List four factors that can affect the resistance of a wire.
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Short Response, continued
15. List four factors that can affect the resistance of a wire.
Answer: length, cross-sectional area (thickness), temperature, and material
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Extended Response
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
a. Assuming that the capacitor is operating in a vacuum and that the permittivity of a vacuum (0 = 8.85 10–
12 C2/N•m2) can be used, determine the capacitance of the capacitor.
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
a. Assuming that the capacitor is operating in a vacuum and that the permittivity of a vacuum (0 = 8.85 10–
12 C2/N•m2) can be used, determine the capacitance of the capacitor.
Answer: 3.10 10–13 F
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
b. How much charge will be stored on each plate of the capacitor when the capacitor’s plates are connected across a potential difference of 0.12 V?
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
b. How much charge will be stored on each plate of the capacitor when the capacitor’s plates are connected across a potential difference of 0.12 V?
Answer: 3.7 10–14 C
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
c. What is the electrical potential energy stored in the capacitor when fully charged by the potential difference of 0.12 V?
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
c. What is the electrical potential energy stored in the capacitor when fully charged by the potential difference of 0.12 V?
Answer: 2.2 10–15 J
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
d. What is the potential difference between a point midway between the plates and a point that is 1.10 10–4 m from one of the plates?
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
d. What is the potential difference between a point midway between the plates and a point that is 1.10 10–4 m from one of the plates?
Answer: 3.4 10–2 V
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Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
e. If the potential difference of 0.12 V is removed from the circuit and the circuit is allowed to discharge until the charge on the plates has decreased to 70.7 percent of its fully charged value, what will the potential difference across the capacitor be?
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Standardized Test PrepChapter 17
Extended Response, continued
16. A parallel-plate capacitor is made of two circular plates, each of which has a diameter of 2.50 10–3 m. The plates of the capacitor are separated by a space of 1.40 10–4 m.
e. If the potential difference of 0.12 V is removed from the circuit and the circuit is allowed to discharge until the charge on the plates has decreased to 70.7 percent of its fully charged value, what will the potential difference across the capacitor be?
Answer: 8.5 10–2 V
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Section 2 CapacitanceChapter 17
Charging a Capacitor
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Section 2 CapacitanceChapter 17
A Capacitor With a Dielectric
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Section 2 CapacitanceChapter 17
Factors That Affect Resistance