Download Section 1 Electric Potential Chapter 17 Electrical Potential Energy

Chapter 17
Section 1 Electric Potential
Preview
• Objectives
• Electrical Potential Energy
• Potential Difference
• Sample Problem
Chapter 17
Section 1 Electric Potential
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.
Chapter 17
Section 1 Electric Potential
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
Chapter 17
Section 1 Electric Potential
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 = –qEd
electrical potential energy = –(charge)  (electric field strength) 
(displacement from the reference point in the direction of the field)
Chapter 17
Section 1 Electric Potential
Electrical Potential Energy
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Visual Concept
Chapter 17
Section 1 Electric Potential
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:
PEelectric
V
q
Chapter 17
Section 1 Electric Potential
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.
PEelectric
V 
q
change in electric potential energy
potential difference 
electric charge
Chapter 17
Section 1 Electric Potential
Potential Difference
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Visual Concept
Chapter 17
Section 1 Electric Potential
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)
Chapter 17
Section 1 Electric Potential
Sample Problem
Potential 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?
Chapter 17
Section 1 Electric Potential
Sample Problem, continued
Potential Energy and Potential Difference
Given:
∆PEelectric = –6.9  10–19 J
d = 0.020 m
E = 215 N/C
Unknown:
q=?
∆V = ?
Chapter 17
Section 1 Electric Potential
Sample Problem, continued
Potential Energy and Potential Difference
Use the equation for the change in electrical potential
energy.
PEelectric = –qEd
Rearrange to solve for q, and insert values.
PEelectric
(–6.9  10 –19 J)
q–
–
Ed
(215 N/C)(0.020 m)
q  1.6  10 –19 C
Chapter 17
Section 1 Electric Potential
Sample Problem, continued
Potential Energy and Potential Difference
The potential difference is the magnitude of E times
the displacement.
V  – Ed  –(215 N/C)(0.020 m)
V  –4.3 V
Chapter 17
Section 1 Electric Potential
Potential Difference, continued
• At right, the electric potential 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.
Chapter 17
Section 1 Electric Potential
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
q
V  kC
r
potential difference = Coulomb constant 
value of the point charge
distance to the point charge
• The superposition principle can be used to calculate
the electric potential for a group of charges.
Chapter 17
Section 1 Electric Potential
Superposition Principle and Electric Potential
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Visual Concept
Chapter 17
Section 2 Capacitance
Preview
• Objectives
• Capacitors and Charge Storage
• Energy and Capacitors
• Sample Problem
Chapter 17
Section 2 Capacitance
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.
Chapter 17
Section 2 Capacitance
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)
Chapter 17
Section 2 Capacitance
Capacitors and Charge Storage, continued
• Capacitance is the ratio of charge to potential
difference.
Q
C
V
magnitude of charge on each plate
capacitance =
potential difference
Chapter 17
Section 2 Capacitance
Capacitance
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Visual Concept
Chapter 17
Section 2 Capacitance
Capacitors and Charge Storage, continued
• Capacitance depends on the size and shape of a
capacitor.
• Capacitance for a Parallel-Plate Capacitor in a
Vacuum
A
C  0
d
capacitance = permittivity of a vacuum 
area of one of the plates
distance between the plates
 0  permittivity of the medium  8.85  10 C /N  m
–12
2
Chapter 17
Section 2 Capacitance
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.
Chapter 17
Section 2 Capacitance
Capacitors in Keyboards
Chapter 17
Section 2 Capacitance
Parallel-Plate Capacitor
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Visual Concept
Chapter 17
Section 2 Capacitance
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.
PEelectric 
electrical potential energy =
1
2
1
QV
2
(charge on one plate)(final potential difference)
Chapter 17
Section 2 Capacitance
Sample Problem
Capacitance
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 = ?
Chapter 17
Section 2 Capacitance
Sample Problem, continued
Capacitance
To determine the capacitance, use the definition of
capacitance.
Q
3.6  10 –5 C
C

V
12 V
C  3.0  10 –6 F  3.0 µF
Chapter 17
Section 2 Capacitance
Sample Problem, continued
Capacitance
To determine the potential energy, use the
alternative form of the equation for the potential
energy of a charged capacitor:
1
C ( V )2
2
1
 (3.0  10 –6 F)(12 V)2
2
PEelectric 
PEelectric
PEelectric  2.2  10 –4 J
Chapter 17
Section 3 Current and
Resistance
Preview
• Objectives
• Current and Charge Movement
• Drift Velocity
• Resistance to Current
Chapter 17
Section 3 Current and
Resistance
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.
Chapter 17
Section 3 Current and
Resistance
Current and Charge Movement
• Electric current is the rate at which electric charges
pass through a given area.
I
electric current =
Q
t
charge passing through a given area
time interval
Chapter 17
Section 3 Current and
Resistance
Conventional Current
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Visual Concept
Chapter 17
Section 3 Current and
Resistance
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.
Chapter 17
Section 3 Current and
Resistance
Drift Velocity
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Visual Concept
Chapter 17
Section 3 Current and
Resistance
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
V
I
potential difference
resistance 
current
R
Chapter 17
Section 3 Current and
Resistance
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.
Chapter 17
Section 3 Current and
Resistance
Factors that Affect Resistance
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Visual Concept
Chapter 17
Section 3 Current and
Resistance
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.
Chapter 17
Section 4 Electric Power
Preview
• Objectives
• Sources and Types of Current
• Energy Transfer
Chapter 17
Section 4 Electric Power
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.
Chapter 17
Section 4 Electric Power
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.
Chapter 17
Section 4 Electric Power
Energy Transfer
• Electric power is the rate of conversion of electrical
energy.
• Electric power
P = I∆V
Electric power = current  potential difference
Section 4 Electric Power
Chapter 17
Energy Transfer
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Visual Concept
Chapter 17
Section 4 Electric Power
Energy Transfer, continued
• Power dissipated by a resistor
2
(

V
)
P  I V  I 2R 
R
• Electric companies measure energy consumed in
kilowatt-hours.
• Electrical energy is transferred at high potential
differences to minimize energy loss.
Chapter 17
Section 4 Electric Power
Relating Kilowatt-Hours to Joules
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Visual Concept