Download electrical potential

Electrical Energy and Electrical Potential
Two different things that sound alike!
Recall Work: W = F d cos(q)
In order to bring two like charges together work must be done.
In order to separate two opposite charges, work must be done.
As the monkey does + work on the positive
charge against electric force, he increases the
energy of that charge. The closer he brings it,
the more electrical potential energy it has.
This work done by external force against
electrical force is stored as electrical PE, U.
When he let it go, the charge will gain kinetic energy and can do a work.
Try the same thing with grav. force. It is the same!!!! charge → mass
So essentially, potential energy is capacity for doing
work which arises from position or configuration.
Greater amount of charge → greater force needed →
greater work done → greater stored potential energy U.
→ introducing the electrical potential energy per unit charge,
known as electrical potential, which doesn’t depend on
the amount of charge.
If a charge q at point P (in electric field E) has electric
potential energy U, the electric potential V at that point is:
electric potential 
U
V
q
electric potential energy
charge
1J
1V 
1C
The SI unit of electric
potential is the volt.
• Note important difference between energy and potential:
• A point has potential, charge placed there has electric potential energy
+++++
+
+
++++
+
++
+
+ +
+++
Two points that are at the same distance from
the charged object have the same potential.
++ +
++
So, when two charged object are placed
there, they are at the same potential,
but the one with more charge on it has
higher electric potential energy – could
do more work.
Potential Difference Between Two Points (ΔV = VB – VA)
The difference between the potentials at two different
points, A & B, is equal to the change in electric potential
energy between these two points or the work done per
unit of positive charge in order to move it from one point
to the other.
∆U W
∆V=
=
q
q
Law of conservation of energy:
change in potential energy = change in kinetic energy
To place a charge in electric field a work has to be done on the charge.
That work is stored as potential energy, U, of the charge. The point
where the charge is, has potential V (charge q placed there has
potential energy U = qV). Charge placed in electric field E will
experience electric force, F= qE. If the charge is free to move it will
accelerate, it will gain kinetic energy and can do a work.
For things like batteries, we specify the potential difference between the
contacts (poles) on the batery. So a "D-cell" has a rating of 1.5 volts
which means that every 1C of charge (electrons) that moves from the
negative side of the cell to the positive side will do 1.5 Joules work.
1. Potential difference = 1.5 V →
2. Potential energy of 1 C electrons relative to positive
pole is 1.5 J.
3. That energy is being converted into kinetic energy on
the way to positive pole.
4. Kinetic energy is being converted into work due to
collisions with atoms within conductor. That is what
makes bulb (and wires unfortunately too) to heat up
and give off light (not wires, hopefuly)
5. Electrons reach positive pole completely exausted without
any energy, ready to reenergize again in the cell.
The AA-cell may only light a light bulb for 15 minutes while the D-cell may
keep the same bulb lit for several hours (simply more charge).
In the 12 volt car battery, every coulomb of charge that moves from one
side to the other does 12 Joules worth of work.
In a 120 volt electrical outlet, every Coulomb of charge does 120 Joules
worth of work as it moves from one side of the outlet to the other.
surprise, surprise ! We use the same name for different things, and even
worse we use couple of different names to express the same thing, like:
1. The variable we use for potential, potential difference, and the unit
for potential difference (volts) is V. Cute!!!!!
2. Don't let that confuse you when you see V = 1.5V
3. Electric potential energy is not the same as electrical potential.
4. The electron volt is not a smaller unit of the volt, it's a smaller unit of
the Joule.
5. Electrical potential can also be described by the terms, potential
difference, voltage, potential drop, potential rise, electromotive force,
and EMF. These terms may differ slightly in meaning depending on
the situation.
Electrical Energy Storage
◊ We can store electric energy in a capacitor :
◊ Found in nearly all electronic circuits eg. in photo-flash units.
◊ Simplest is: two close but separated parallel plates.
When connected to a battery electrons get transferred from
one plate to the other until the potential difference between
them = voltage of battery.
◊ How?
Positive battery terminal attracts electrons on LH plate; these
are then pumped through battery, through the terminal to the
opposite plate. Process continues until no more potential
difference btn plate and connected terminal.
◊ Discharging: when conducting path links the two charged plates.
◊ Discharging is what creates the flash in a camera.
♦If very high voltages (eg caps in tv’s), its dangerous if you are this path!
Potential difference or Voltage (symbol V)
• When the ends of an electric conductor are at different
electric potential, charge flows from one end to the other.
Voltage is what causes charge to move in a conductor.
Charge moves toward lower potential energy the same way
as you would fall from a tree.
• Voltage plays a role similar to pressure in a pipe; to get
water to flow there must be a pressure difference between
the ends, this pressure difference is produced by a pump
• That’s why we call voltage “electric pressure”
• A battery is like a pump for charge, it provides the energy for
pushing the charges around a circuit
Voltage and current are not the same thing
• You can have voltage, but without a
path (connection) there is no current.
An
electrical
outlet
voltage
Current– flow of electric charge
If I connect a battery to the ends of the copper bar the
electrons in the copper will be pulled toward the positive
side of the battery and will flow around and around.
 this is called current – flow of charge
copper
An electric circuit!
Duracell
+
Electric current (symbol I)
◊ the flow of electric charge q that can occur in solids, liquids and gases.
q
• DEF: the rate at which charge flows
by a given cross-section.
• measured in amperes (A)
q
I=
t
1C
1A =
1s
Solids – electrons in metals and graphite, and holes in semiconductors
Liquids – positive and negative ions in molten and aqueous electrolytes
Gases – electrons and positive ions stripped from gaseous molecules
by large potential differences.
Electrical resistance (symbol R)
• Why is it necessary to keep pushing the charges to make
them move?
• The electrons do not move unimpeded through a
conductor. As they move they keep bumping into the ions
of crystal lattice which either slows them down or bring
them to rest.
path
atoms
(actually
positive ions)
free electron
.
The resistance (R) is a measure of the degree to
which the conductor impedes the flow of current.
Resistance is measured in Ohms ()
OHM’S LAW - Current, Voltage and Resistance
• DEF: Current through resistor (conductor) is
proportional to potential difference on the resistor
if the temperature of a resistor is constant
(than the resistance of a conductor is constant).
Other way:
V
I=
R
current =
voltage
resistance
• if resistance R is constant/ temperature is constant
• I – current
V – potential difference across R
Examples
• If a 3 volt flashlight bulb has a resistance of 9 ohms, how
much current will it draw?
• I = V / R = 3 V / 9  = 1/3 Amps
• If a light bulb draws 2 A of current when connected to a
120 volt circuit, what is the resistance of the light bulb?
• R = V / I = 120 V / 2 A = 60 
Effects of electric current on the BODY- electric shock
Current (A)
Effect
0.001
can be felt
0.005
painful
0.010
involuntary muscle contractions (spasms)
0.015
loss of muscle control
0.070
if through the heart, serious disruption; probably
fatal if current lasts for more than 1 second
questionable circuits: live (hot) wire ? how to avoid being electrified?
1. keep one hand behind the body (no hand to hand current through the body)
2. touch the wire with the back of the hand. Shock causing muscular contraction
will not cause their hands to grip the wire.
human body resistance varies:
100 ohms if soaked with salt water;
moist skin - 1000 ohms;
normal dry skin – 100 000 ohms,
extra dry skin – 500 000 ohms.
What would be the current in your body if you touch the
terminals of a 12-V battery with dry hands?
I = V/R = 12 V/100 000  = 0.000 12 A
quite harmless
But if your hands are moist (fear of AP test?) and you
touch 24 V battery, how much current would you draw?
I = V/R = 24 V/1000  = 0.024 A
a dangerous amount of current.
Factors affecting resistance
Conductors, semiconductors and insulators differ
in their resistance to current flow.
Wires, wires, wires
The resistance of a wire can be completely ignored – if it
is a thin wire connecting two, three or more resistors, or
can become very important if it is a long, long wire as in
the case of iron, washing machine, toaster ……
The resistance of a conducting wire depends on four main
factors: • length • cross-sectional area • resistivity • temperature
Resistance of a wire when the temperature is kept constant is:
R=ρ
L
A
L – length
A – cross-sectional area
Of course, resistance depends on the material being used.
The resistivity, ρ (the Greek letter rho), is a value that only
depends on the material being used. It is tabulated and you can
find it in the books. For example, gold would have a lower value
than lead or zinc, because it is a better conductor than they are.
The unit is Ω•m.
In conclusion, we could say that a short fat cold wire makes
the best conductor.
If you double the length of a wire, you will double the
resistance of the wire.
If you double the cross sectional area of a wire you will cut
its resistance in half.
Example
A copper wire has a length of 160 m and a diameter of 1.00 mm. If the wire is
connected to a 1.5-volt battery, how much current flows through the wire?
The current can be found from Ohm's Law, V = IR. The V is the battery
voltage, so if R can be determined then the current can be calculated.
The first step, then, is to find the resistance of the wire:
L = 1.60 m.
r = 1.00 mm
r = 1.72x10-8 m, copper - books
The resistance of the wire is then:
R = r L/A = (1.72x10-8 m)(1.67)/(7.85x10-7m2 ) = 3.50 
The current can now be found from Ohm's Law:
I = V / R = 1.5 / 3.5 = 0.428 A
Ohmic and Non-Ohmic conductors
How does the current varies with potential difference for some typical devices?
current
potential
difference
diode
current
filament lamp
current
metal at const. temp.
potential
difference
I = 1 is const.  R is const.
V
R
Devices for which current through them is directly
proportional to the potential difference across device
are said to be ‘ohmic devices’ or ‘ohmic conductors’ or
simply resistors. There are very few devices that are
trully ohmic. However, many useful devices obey the
law at least over a reasonable range.
potential
difference
devices are non-ohmic if
resistance changes
Power dissipation in resistors
DEF: Electric power is the rate at which energy
is supplied to or used by a device.
DEF: Power is the rate at which electric energy is converted
into another form such as mechanical energy, heat, or light.
When a current is flowing through a load such as a resistor, it
dissipates energy in it. In collision with lattice ions electrons’
kinetic energy is transferred to the ions, and as a result the
amplitude of vibrations of the ions increases and therefore the
temperature of the device increases.
That thermal energy (internal energy) is then transferred as heat
(to the air, food, hair etc.) by convection, or radiated as light
(electric bulb).
Where is that energy coming from?
This energy is equal to the potential energy lost by the charge as
it moves through the potential difference that exists between the
terminals of the load.
Power is measured in J s-1 called watts W.
If a vacuum cleaner has a power rating of 500 W, it means
it is converting electrical energy to mechanical, sound
and heat energy at the rate of 500 J s-1. A 60 W light globe
converts electrical energy to light and heat energy at the
rate of 60 J s -1.
Appliance
Power rating
Blow heater
Kettle
Toaster
1.2 kW
Iron
Vacuum cleaner
Television
2 kW
1.5 kW
850 W
1.2 kW
250 W
Deriving expressions for determining power
Basic definition of power:
Remember: W = qV → P =
W
P=
t
qV
t
P=IV
P = IV = V2/R = I2 R
and I = q/t, so
1W =
1J
= 1A 1V
1s
In USA you can not get direct information on power of appliance you buy.
Look at your hair dryer. If label says “10 A”, that means that the power of the
hair dryer is 10x120=1200 W, or 1.2 kW (using a standard US 120 V outlet).
Comparison of US and other countries that use voltage of 240 V.
As the power of appliances is the roughly the same, the
appliances in USA have to draw a greater current, hence have to
have less resistance. As the consequence the wires (both used
for connecting and in appliances) are thicker in USA.
example
• How much current is drawn by a 60 Watt light bulb connected to a
120 V power line?
P = 60 W = I V = I x 120
so I = 0.5 A
• What is the resistance of the bulb?
I = V/R
R = V/I = 120 V/0.5 A
R = 240 
Paying for electricity
• You pay for the total amount of electrical energy (not power) that
is used each month
• In Irving the cost of electric energy used is 14 ¢ per kilowatt-hour.
• How do we get kilowatt-hour and what is that?
• Power = energy/time
• Energy = power x time, so energy can be expressed in units
watts x second what is simply a joule.
Physicists measure energy in joules, but utility companies
customarily charge energy in units of kilowatt-hours (kW h), where :
Kilowatt-hour (kWh) = 103 W x 3600 s
1 kWh = 3.6 x 106 J
1W x 1s = 1J
$$$ example $$$
• At a rate of 14 cents per kWh, how much does it cost to keep a 100 W
light bulb on for one day?
• energy (kWh) = power (kW) x time (h)
• energy (kWh) = 0.1 kW x 24 h = 2.4 kWh
cost / day = 2.4 kWh x 14 cents/kWh = 33.6 ¢
 for one month that amounts to $ 10.1.
Direct Current (DC) electric circuits
• a circuit containing a battery is a DC circuit
• in a DC circuit the current always flows in the same direction.
• The direction of the current depends on how you connect the battery
Either way the bulb will be on.
• a circuit must provide a closed path for the
current to circulate around
• when the electrons pass through the light
bulb they loose some of their energy 
the conductor (resistor) heats up
• the battery is like a pump that re-energizes
them each time they pass through it
Duracell
+
The electrons go one way but the
current flows the opposite to the
direction that the electrons travel.
That’s convention.
hystoric explanation
click me
Drift speed
When a battery is connected across the ends of a metal
wire, an electric field is produced in the wire. All free
electrons in the circuit start moving at the same time.
Free electrons are accelerated along their path
reaching enormous speeds of about 106 ms-1. They
collide with positive ions of crystal lattice generating
heat that causes the temperature of the metal to
increse. After this event, they are again accelerated
because of the electric field, until the next collision
occurs. Due to the collisions with positive ions of crystal
lattice, hence changing direction, it is estimated that the
drift velocity is only a small fraction of a metre each
second (about 10-4 m s-1).
example: in an el. circuit of a car, electrons have
average drift speed of about 0.01 cm/s, so it takes
~ 3 hour for an electron to travel through 1m.
it’s not even a snail’s pace!!!!!
• the electricity that you get from the power company is not DC it is AC
(alternating) created by an AC electric generator.
• In an AC circuit the current reverses direction periodically
AC movement of electrons in a wire
_
+
The current in AC electricity alternates in direction. The back-and-forth motion
occurs at freq. of 50 or 60 Hz, depending on the electrical system of the country.
!!!!!!! the source of electrons is wire itself – free electrons in it !!!!!!
If you are jolted by electric shock, electrons making up the current in your body
originate in your body. They do NOT come from the wire through your body into
the ground. Alternating electric field causes electrons to vibrate. Small
vibrations – tingle; large vibrations can be fatal.
current
How does the voltage and current change in time?
DC does not change
direction over time;
DC
current
time
AC
time
the actual voltage in
a 120-V AC circuit
varies between
+170V and -170V
peaks.
AC vs. DC current
• for heaters, hair dryers, irons, toasters, waffle makers,
the fact that the current reverses makes no difference.
They can be used with either AC or DC electricity.
• battery chargers (e.g., for cell phones) convert the AC
to DC
• Why do we use AC ?? DC seems simpler?
• late 1800’s  the war of the currents
• Edison (DC) vs Tesla (Westinghouse) (AC)
• Edison opened the first commercial power plane for
producing DC in NY in 1892
• Tesla who was hired by George Westinghouse
believed that AC was superior
• Tesla was right, but Edison never gave up!
Why AC is better than DC
• DC power is provided at one voltage only
• The major advantage: AC voltages can be transformed
to higher or lower voltages (can be stepped up or down
to provide any voltage required)
• This means that the high voltages used to send
electricity over great distances from the power station
can be reduced to a safer voltage for use in the house.
• This is done by the use of a transformer.
• DC is very expensive to transmit over large distances
compared to AC (more loss to heat), so many plants are
required
• DC power plants must be close to users
• AC plants can be far outside cities
• by 1895 DC was out and AC was in
D.C. circuit analysis
Electric Circuits: Any path along which electrons can
flow is a circuit. For a continuous flow of electrons,
there must be a complete circuit with no gaps. A gap is
usually provided by an electric switch that can be
opened or closed to either cut off or allow electron flow.
An electric circuit has three essential components
1. A source of emf.
2. A conducting pathway obtained by conducting
wires or some alternative.
3. A load to consume energy such as a filament
globe, other resistors and electronic components.
When the switch is closed, a current exists almost immediately in all
circuit. The current does not “pile up” anywhere but flows through the
whole circuit. Electrons in all circuit begin to move at once. Eventually
the electrons move all the way around the circuit. A break anywhere in
the path results in an open circuit, and the flow of electrons ceases.
In the mid-nineteenth century, G.R. Kirchoff
(1824-1887) stated two simple rules using the
laws of conservation of energy and charge to
help in the analysis of direct current circuits.
These rules are called Kirchoff’s rules.
1. Junction rule – conservation of charge.
‘The sum of the currents flowing into a point in a circuit
equals the sum of the currents flowing out at that point’.
I1 + I2 = I3 + I 4 + I 5
2. loop rule – conservation of energy principle: Energy supplied
equals the energy released in this closed path
‘In a closed loop, the sum of the emfs equals
the sum of the potential drops’.
V = V1 + V2 + V3
Resistors in Series
• connected in such a way that all components
have the same current through them.
• Burning out of one of the lamp filaments or simply
opening the switch could cause such a break.
Equivalent or total or effective resistance is the one that
could replace all resistors resulting in the same current.
Req = R1+ R2 + R3
logic: the total or effective resistance would have length L1+ L2+ L3
and resistance is proportional to the length
Resistors in Parallel
• Electric devices connected in parallel are
connected to the same two points of an electric
circuit, so all components have the same
potential difference across them.
• The current flowing into the point of splitting is
equal to the sum of the currents flowing out at
that point: I = I1 + I2 + I3.
• A break in any one path does not interrupt the flow of charge in the
other paths. Each device operates independently of the other devices.
The greater resistance, the smaller curent.
1
1
1
1
=
+
+
Req R1 R2 R3
equivelent resistance
is smaller than the
smallest resistance.
RESISTORS IN COMPOUND CIRCUITS
Now you can calculate current, potential drop and
power dissipated through each resistor
http://www.saaphysics.com/CircuitsPractic
eQuiz.htm
http://www.glencoe.com/qe/science.php?qi
=2246
http://phet.colorado.edu/en/simulation/circu
it-construction-kit-dc-virtual-lab
Ammeters and voltmeters
In practical use, we need to be able to measure currents through
components and voltages across various components in electrical
circuits. To do this, we use AMMETERS and VOLTMETERS.
An ammeter – measures current passing through it
• is always connected in series with a component we want to
measure in order that whatever current passes through the
component also passes the ammeter.
• has a very low resistance compared with the
resistance of the circuit so that it will not alter the
current the current being measured.
• would ideally have no resistance with no potential
difference across it so no energy would be dissipated in it.
A voltmeter – measures voltage drop between two points
• is always connected across a device (in parallel).
• has a very high resistance so that it takes very little
current from the device whose potential difference
is being measured.
• an ideal voltmeter would have infinite resistance with
no current passing through it and no energy would be dissipated in it.