Download Chapter 17: Electrical Energy and Current1 Electric Potential Energy

Chapter 17: Electrical Energy and Current1
Section 1: Electric Potential
Electric Potential Energy
When 2 charges interact, there is an electric
force between them.
Also an electrical potential energy – results
from the interaction of two objects’ charges,
not their masses
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Component of mechanical energy
ME is conserved as long as friction and
radiation are not present
ME = KE + PEgrav + PEelastic + PEelectric
Remember: any time a force is used to move
an object, work is done on the object
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True for charges moved by electric
force
Whenever a charge moves because of
the electric field produced by another
charge(s), work is done on the charge
that moves
Tesla Coil – contains a plate in the
center where negative electric charges
build up.

Electrical potential energy of
each charge decreases as the
charge moves from the plate to
the walls, and then to the
ground
Electrical potential energy
Consider a positive charge in a uniform electric
field. The charge is displaced at a constant
velocity in the same direction as the electric
field.
A uniform electric field is a field that
has the same value and direction at
all points.
Change in the electrical potential energy
associated with the charge’s new position in
the electric field.
Change depends on
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the charge, q
strength of the electric field, E
displacement, d
ΔPEelectric = -qEΔd
Electric PE = —(charge x electric field strength
x displacement from a reference point in the
direction of the field)
Negative sign indicates that the PE will
increase if the charge is negative and
decrease if the charge is positive.
Chapter 17: Electrical Energy and Current2
Like all forms of potential energy …
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It is the difference in electrical
potential energy that is important
o If the initial position is chosen as
a reference point (zero level),
then the initial electrical
potential energy is zero, which
changes the equation to:
ΔPEelectric = -qEd
o Equation only works in a uniform
electric field
o d is the magnitude of the
displacement’s component in the
direction of the electric field
o Any displacement perpendicular
to the field does not change
PEelectric
SI unit for PEelectric is the joule (J)
Think about gravitational potential
energy:
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Gravitational field is vertical
Only movement parallel to the
gravitational field affects PEg. All
other movement perpendicular
(horizontal) to the field has no
effect.
Work and potential energy
Remember, W = Fd

Electric field does work on a positive
charge by moving the charge in the
direction E
o Final potential energy is less than
initial PE
o Negative charge is opposite –
negative charge undergoes a force in
the opposite direction
Potential Difference
Electrical potential energy increases as the magnitude of the charge increases.
Electric potential allows us to express the potential energy in a way that is independent
of the test charge.
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Electric potential: electrical potential energy associated with a charged particle
in an electric field divided by the charge of the particle
V = PEelectric
Unit: volt, V, = J/coulomb
q
Potential difference is a measure of the difference in the electrical potential
energy between 2 positions in space divided by the charge.
Chapter 17: Electrical Energy and Current3
Potential difference is a change in electric
potential energy
As a 1 C charge moves through a potential
difference of 1 V, the charge gains 1 J of
energy
Electric potential is represented by V
Potential difference (change in electric
potential) is represented by ΔV and is
sometimes referred to as voltage.
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Reference point for measuring
electrical potential energy is arbitrary
Reference point for measuring
electrical potential is also arbitrary
o Only changes in electric
potential is significant
Electrical potential energy is a
quantity of energy, measured in
joules
o Both electric potential and
potential difference are both
measures of energy per unit
charge, measured in volts
o Potential difference describes a
change in energy per unit
charge
Potential difference in a uniform field
varies with the displacement from a
reference point
Combining the equation for potential
difference with the equation for
electrical potential energy results in
equations that are simpler to apply in
some situations.
PEelectric = —qEd
ΔV = ΔPEelectric = Δ(—qEd)
q
q
As the charge moves in a uniform
electric field, the quantity in the
parentheses does not change from the
reference point.
Potential difference in a uniform
electric field
ΔV = —Ed
Potential difference = —(magnitude of
the electric field x displacement)
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d is the displacement parallel
to the field
motion perpendicular to the
field does not change the
electrical potential energy.
Reference point for potential difference near a point charge is often at infinity
To calculate the potential difference between 2 points in the field of a point charge:
[scenario: point charge q2 at point A in the electric field of a point charge q1 at point B, r
distance away]
1. Calculate the electric potential associated with each point:
VA = PEelectric = kCq1q2 = kCq1
q2
rq2
r
a. Keep up with the 2 charges and don’t confuse them. q1 is responsible for the
electric potential at point A.
b. An electric potential exists at some point in an electric field regardless of
whether there is a charge at that point.
Chapter 17: Electrical Energy and Current4
Continuing on with the example …
2. Electric potential at a point depends only on the charge responsible for the electric
potential, and the distance, r, from this charge to the point in question.
a. If the 2 distances are r1 and r2, then the potential difference between these 2
points is:
𝟏
𝟏
ΔV = kCq1 — kCq1 = kCq1 𝒓𝟐
− 𝒓𝟏
r2
r1
b. If the distance r1 is large enough, it is assumed to be infinitely far from the
charge q1. If so, then 1/r1 is considered to be zero.
3. Equation becomes: ΔV = kCq
r
potential difference = Coulomb constant x value of the point charge
distance to the point charge
This equation looks identical to the one for electric potential associated with a point
charge because we have chosen a special reference point from which to measure
the potential difference.
4. Application for potential difference is the operation of electric circuits. The
reference point for determining electric potential is arbitrary and must be defined.
a. Earth is frequently designated as having an electric potential of zero
b. When an electrical device is grounded (connected to Earth), a possible
reference point is created which allows you to measure the electric potential
in an electric circuit.
Sample 17A
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 x 10-19J. Find the charge on the moving particle. What is the potential difference
between the two locations?
Chapter 17: Electrical Energy and Current5
Superposition principle

Can be used to calculate the electric potential for a group of charges
o The total electric potential at some point near several point charges is the
sum of all the electric potentials from each charge
o Summation here is easier than with electric field because these are scalar, not
vector, quantities.
o Keep track of signs – the electric potential near a positive charge is positive;
near a negative charge is negative.
Battery does work to move charges
Battery – energy-storage device; provides a constant potential difference between its
two terminals.
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AA battery: + terminal has a potential difference of 1.5 V higher than the
potential difference of the — terminal.
Chemical reaction produces electrons (negative charges) that collect on the
negative terminal.
o Chemical reaction does work on the charges when moving them from the
positive to the negative terminal
o Every coulomb of charge that leaves the + terminal has 1.5 J of electrical
potential energy
Negative charges move from the positive to the negative terminal through a
potential difference of ΔV = -1.5 V.
When in an electrical device, 1 C of charge moves through the device toward the
positive terminal of the battery
o 1.5 J of electrical is given to the device
o When the charge reaches the + terminal, the charge’s electrical potential
energy = 0.
o Electrons return to the + terminal for the chemical reaction to occur.
http://regentsprep.org/Regents/physics/phys03/apotdif/default.htm
Section 2: Capacitance
Terms:
Capacitor: device used to store electrical potential energy.
Energized (or charged) capacitor: charged capacitor whose energy can be used for a
specific purpose.
Parallel-plate capacitor: typical design of a capacitor consisting of 2 metal plates
separated by a small distance. Charge refers to the magnitude of charge on either plate.
Chapter 17: Electrical Energy and Current6
Capacitance expresses
how much charge the
capacitor plates have
relative to the
potential difference
between the plates.
The farad (F) is
named for Michael
Faraday. Most
capacitors have
capacitances ranging
from microfarads
(1x10-6 F)to
picofarads (1x10-12 F)
ε (epsilon) represents
permittivity of the
medium (how
responsive the
medium is to an
electric field).
ε0 indicates a vacuum
and has a magnitude
of 8.85 x 10-12C2/N•m2
Capacitance: ability of a conductor to store energy in the
form of electrically separated charges.
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Ratio of the net charge on each plate to the potential
difference created by the separated charges
C=Q
measured in C/V (also called the farad, F)
ΔV
Capacitance = magnitude of charge on each plate
potential difference
Capacitance
Capacitance of a parallel-plate capacitor with no material
between the plates is determined by:
C = ε0A
d
Capacitance = permittivity of a vacuum x area of one plate
distance b/t plates
Combining capacitance with equation for charge:
Q = ε0AΔV
d
From this equation, we learn:
For a given potential difference (ΔV), the charge on the
plate is proportional to the area of the plates and inversely
proportional to the distance (separation) between the
plates.
Chapter 17: Electrical Energy and Current7
Material between the plates of a capacitor
can change its capacitance.
Dielectric – material occupying the space
between the plates of a parallel-plate
capacitor.
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Insulating material (such as air,
rubber, glass, or waxed paper)
Capacitance increases with dielectric
o Plates can store more charge
for a given potential
difference
o Problems in our book assumes
no dielectrics (ε0)
Discharging a capacitor
1. Charge a capacitor by connecting it to
a battery
a. Once charged, the battery can
be removed
b. Capacitor will hold its charge
until connected to a circuit
2. Connect a capacitor to a circuit and it
will discharge
a. Ex. Flash in a camera
i. Faster than using a
battery
b. Ex. Computer keyboard
Energy and Capacitors
A charged capacitor stores electrical potential energy because it requires work to move
charges through a circuit to the opposite plates of a capacitor.
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Initially uncharged, both plates are neutral
Requires almost no work to move a small amount of charge
Once charge has been transferred, a small potential difference exists between the
plates
Requires more work to move additional charge through the potential difference,
so electrical potential energy increases
Electrical potential energy stored in a capacitor that is charged from zero to some
charge, Q:
PEelectric = ½QΔV
Using the equation C = Q/ΔV, we get the following alternative forms:
PEelectric = ½C(ΔV)2
PEelectric = Q2
2C
Sample 17B
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?
Chapter 17: Electrical Energy and Current8
Section 3: Current and Resistance
Current and charge movement
Sample 17C
Current – movement of electric charge
The current in a light bulb is 0.835 A. how
long does it take for a total charge of 1.67 C
to pass through the filament of the bulb?
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Technology
Appliances
Bodies! (electric currents
transmit messages between body
muscles and the brain)
Electric current – rate at which charges
move through a cross section of wire

I = ∆Q
∆t
Electric current moves opposite
the movement of the negative
charges.
measured in ampere, A = 1C/s
Electric current = charge passing area
time interval
Conventional current
Moving charges that make up a current
can be:
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Negative (moving electrons in
solid conductors)
Positive (protons are set in
motion in particle accelerators)
Combination (in gases and
dissolved salts, + charges move in
one direction, ― charges move in
the opposite direction
Positive and negative charges in motion
are called charge carriers.
Conventional current is defined in terms
of the flow of positive charges.
Negative charge carriers (electrons)
would have a conventional current
opposite their physical motion.
Electric field in a material sets charges
in motion.
Conductors: charge carriers move
easily
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Metals – large number of free
electrons
Body fluids – contain ions
Electrolytes – solute that
dissolves in water and conducts
electric charge
Chapter 17: Electrical Energy and Current9
Drift Velocity
You turn on a light switch, and light appears almost instantly. Many people believe that
electrons must flow very rapidly from the switch to the bulb for the light to appear so
quickly. This is NOT true!
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Electron motion near the switch changes the electric field there
Change in the electric field moves through the wire very rapidly
o Nearly the speed of light
o Charges move more slowly
When a potential difference is applied across a conductor, the electrons do not move in
straight lines in the opposite direction of the electric field.
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Repeated collisions with the vibrating atoms of the conductor
Energy transferred from the electrons to the metal atoms increases the
vibrational energy of the atoms
Conductor’s temperature increases
Electrons gain kinetic energy as they are accelerated by the electric field
Electrons lose kinetic energy because of the collisions
Individual electrons move slowly along the conductor, in the opposite direction of
the electric field  velocity is known as the drift velocity, vdrift
Drift speeds are very small
o Ex. 10.0A of current, drift speed is 2.46 x 10-4 m/s it would take 68
minutes to move 1 meter!
Resistance
In a circuit of a light bulb connected to a
battery:
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Battery determines the potential
difference that lights the bulb
Current in the bulb causes the bulb to
light
Wires (conductors) and the filament in
the bulb also affect the current
reaching the bulb and the brightness of
the light
Resistance: opposition to the motion of
charge through a conductor
Resistance = potential difference
current
R = ∆V
I
unit: ohm (Ω) = V/A
Ohm’s Law: Resistance is constant over
a wide range of applied potential
differences.
∆V = constant
I
Can also be expressed as ∆V = IR
Chapter 17: Electrical Energy and Current10
Ohm’s law
Resistance
Ohm’s law is not a fundamental law of
nature
Resistance occurs because of the internal
collisions between the charges as they are
moved along by the potential difference.
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Valid only for certain materials
Materials with a constant resistance
over a wide range of potential
differences are ohmic
o Graph of current versus
potential difference is linear
o I/∆V (inverse of Ohm’s law) is
inversely proportional to
resistance
o Non-ohmic materials have a
graph that is curved (not
constant); resistance varies.
 Diode (small resistance for
currents in one direction;
large resistance for currents
in the opposite direction
 Diodes are used in circuits to
control the direction of
current
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Internal friction
Factors that affect resistance:
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Length – longer has greater
resistance
Cross-sectional area – (skinny has
greater resistance)
Temperature – higher temperature
= greater resistance
Material
Resistors – Ways to adjust the current in a
conductor:
When potential difference (∆V) remains
constant:

Current decreases when resistance
increases
o Replace the wire with one of
greater resistance
o Use a longer, thinner wire
o Connect a resistor to the circuit
 A simple electrical
element that provides a
specified resistance
Chapter 17: Electrical Energy and Current11
Sample 17D
Human Body Resistance
The resistance of a steam iron is 19.0 Ω.
What is the current in the iron when it is
connected across a potential difference of
120 V?

When dry, human skin has a
resistance of 500,000 Ω

When wet, specifically soaked in salt
water, human skin has a resistance as
low as 100 Ω
o Ions in salt water readily
conduct electric charge
Danger exists if a large potential
difference is applied between parts of
the body because current increases as
resistance decreases.
Specifics
Current level
Probable effect on human body
•
1 mA
•
Slight tingling sensation
•
5 mA
•
Slight shock is felt; can ―let go‖
•
6-30 mA
•
Painful shock; muscular control is
lost. Freezing current or ―let go‖
range.
•
50-150 mA
•
Extreme pain, respiratory arrest,
severe muscular contractions.
Cannot let go. Death possible.
•
1000-4300 mA
•
Pumping action of the heart ceases.
Nerve damage. Death.
•
10,000 mA
•
Cardiac arrest, severe burns,
DEATH.
Perspiration contains ions that conduct
electric charge.
Galvanic skin response (GSR), used in
stress tests and “lie detector” tests,
have a small potential difference set up
across the body. When stressed (or
lying), perspiration increases and
decreases the resistance of the body.
Potentiometers
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Special type of resistor
Contains an adjustable, sliding contact
that allows the user to adjust resistance
Dimmer switches, volume control, game
controllers (1 for x direction, 1 for y)
Chapter 17: Electrical Energy and Current12
Section 4: Electric Power
Sources and Types of Current
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When a potential difference is applied across a conductor, charges will move from a
position of higher electrical potential to a position of lower electrical potential
Batteries convert chemical energy to electrical potential energy, which can be
converted into kinetic energy
o KE allows collisions to occur between the moving charges and the remaining
material in the circuit elements
o Collisions transfer energy (in the form of heat) back to the circuit.
Generators convert mechanical energy into electrical energy
o Hydroelectric power plant converts KE of falling water into electrical potential
energy
Current can be either alternating (AC) or direct (DC).
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Direct – charges only flow in 1 direction; negative charges move from a lower to
higher electric potential
o Conventional current is directed from the positive terminal to the negative
terminal of the battery
o Electrons actually move in the opposite direction
Alternating – the terminals of the source of potential difference constantly change
sign
o No net motion of the charge carriers; the charge carriers vibrate back-forth
o If the vibration were slow enough, you would see lights flicker; in the US, AC
oscillates 60x/second  frequency is 60 Hz.
o Current transferred to homes/businesses by power companies is AC
Energy Transfer
1. Energy from battery is converted
to internal energy due to collisions
between charge carriers and other
particles in conductor.
2. Disregard the resistance of the
connecting wire, and no loss of
energy occurs as the charge moves
from A to B.
3. B to C, loss of electrical energy due to the
resistance in the bulb filament.
Chapter 17: Electrical Energy and Current13
Continuing on with the circuit
4. In the filament, electrical energy is converted to internal energy; the filament warms
up and glows.
5. Charge returns to the battery; potential energy is 0.
a. Battery does work on the charge
6. Charge moves between the terminals of the battery (D to A), electrical potential
energy increases by Q∆V (where ∆V is the potential difference across the battery
terminals.
a. Battery’s chemical energy decreases by the same amount.
Electrical power is the rate of conversion of electrical energy
Electrical power is the rate at which charge carriers do work

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rate at which charge carriers convert electrical PE to nonelectrical forms of energy
P = W = ∆PE
∆t
∆t

∆V = ∆PE
∆PE = q∆V
q
Substitute equation into power equation:
P = q∆V
(q/∆t = I),
∆t
P = I∆V
Electric power = current x potential difference
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Unit for power is the watt (W) = J/s. How do those units work out?
Because ∆V = IR, power can be rewritten in other terms:
P = I∆V = I(IR) = I2R
P = I∆V = ∆V∆V = (∆V)2
R
R
Practice 17E
An electric space heater is connected across a 120 V outlet. The heater dissipates 1320 W of
power in the form of electromagnetic radiation and heat. Calculate the resistance of the
heater.
Chapter 17: Electrical Energy and Current14
Electric companies
Electric power is the rate of energy transfer.
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Power companies charge for energy used, not power.
Unit of energy used by power companies is the kilowatt-hour (kW•h)
o Energy delivered in 1 hour at the constant rate of 1kW
Electrical energy to you …
Electrical companies want to deliver energy to you with as little loss as possible
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Conversion of electrical energy to internal energy in a resistant material is called
joule heating, and is referred to as an I2R loss (from power formula where ∆V is
replaced with IR).
Decrease current or resistance
o Wires have little resistance, but resistance increases with length
o Energy loss is proportional to the square of the current I2R, so decreasing
current is more important than decreasing resistance
Power can be transported either at high current and low potential difference or
vice versa.
o To minimize loss, power companies transport electrical energy at very high
potential differences (up to 765,000 V).
o Transformers reduce the potential difference to about 4000 V
o Within our homes, potential difference is reduced again to about 120 V by
another transformer.