Electrical Potential Energy
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Transcript of Electrical Potential Energy
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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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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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Chapter 17
Electrical Potential Energy
Section 1 Electric Potential
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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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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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Chapter 17
Potential Difference
Section 1 Electric Potential
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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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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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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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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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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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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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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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Chapter 17Section 1 Electric Potential
Superposition Principle and Electric Potential
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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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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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Chapter 17
Capacitance
Section 2 Capacitance
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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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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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Chapter 17
Capacitors in Keyboards
Section 2 Capacitance
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Chapter 17
Parallel-Plate Capacitor
Section 2 Capacitance
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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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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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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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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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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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Chapter 17
Conventional Current
Section 3 Current and Resistance
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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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Chapter 17
Drift Velocity
Section 3 Current and Resistance
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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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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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Chapter 17
Factors that Affect Resistance
Section 3 Current and Resistance
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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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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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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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Chapter 17
Energy Transfer
Section 4 Electric Power
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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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Chapter 17
Relating Kilowatt-Hours to Joules
Section 4 Electric Power