Download current - Uplift Hampton

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.
animation ????
♦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
• 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
past 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
(the resistance of a conductor is constant).
◊ math def:
V
I=
R
voltage
current =
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.
DEF: The electrical resistance of a piece of material is
defined by the ratio of the potential difference across
the material to the current that flows through it.
V
R=
I
The units of resistance are volts per ampere (VA-1).
However, a separate SI unit called the ohm Ω is defined
as the resistance through which a current of 1 A flows
when a potential difference of 1 V is applied.
Wires, wires, wires
As you are going to see, the resistance of a wire can be
completely ignored – if it is a thin wire connecting two,
three or more resistors, or becoming very important if it is
a long, long wire as in the case of iron, washing machine,
toaster ….., where it becomes resistor itself.
The resistance of a conducting wire depends on four main
factors: • length • cross-sectional area • resistivity • temperature
Cross Sectional Area (A)
The cross-sectional area of a conductor (thickness) is similar to the cross section
of a hallway. If the hall is very wide, it will allow a high current through it, while a
narrow hall would be difficult to get through. Notice that the electrons seem to be
moving at the same speed in each one but there are many more electrons in the
larger wire. This results in a larger current which leads us to say that the resistance
is less in a wire with a larger cross sectional area.
Length of the Conductor (L)
The length of a conductor is similar to the length of a hallway.
A shorter hallway will result in less collisions than a longer one.
Temperature
To understand the effect of temperature you must picture what happens in a
conductor as it is heated. Heat on the atomic or molecular scale is a direct
representation of the vibration of the atoms or molecules. Higher temperature
means more vibrations. In a cold wire ions in crystal lattice are not vibrating much so
the electrons can run between them fairly rapidly. As the conductor heats up, the
ions start vibrating. As their motion becomes more erratic they are more likely to get
in the way and disrupt the flow of the electrons. As a result, the higher the
temperature, the higher the resistance.
At extremely low temperatures, some materials, known as superconductors, have no
measurable resistance. This is called superconductivity. Gradually, we are creating
materials that become superconductors at higher temperatures and the race is on to
find or create materials that superconduct at room temperature. We are painfully far
away from the finish line.
Resistance also depends on temperature, usually
increasing as the temperature increases.
At low temperatures some materials, known as superconductors,
have no resistance at all. Resistance in wires produces a loss of
energy (usually in the form of heat), so materials with no resistance
produce no energy loss when currents pass through them.
And that means, once set up in motion (current) you don’t
need to add additional energy in oder to keep them going.
The dream: current without cost!!!!!!!!! Both in money and
damage to environment!!!!!!!!
Of course, resistance depends on the material being used.
Resistance of a wire when the temperature is kept constant is:
L
R=ρ
A
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
Do Now
Answer the following
1) What is power? What is unit for power?
2) Can you figure out 2 reasons for this year Nobel prize in physics?
It is an invention of greatest benefit to mankind
“for the invention of efficient blue light-emitting diodes which has
enabled bright and energy-saving white light sources"
The main advantage is efficiency. In conventional tungsten/wolfram
bulbs, the light-production process involves generating a lot of heat
(the filament must be warmed). This is completely wasted energy,
unless you're using the lamp as a heater, because a huge portion of
the available electricity isn't going toward producing visible light. LEDs
generate very little heat, relatively speaking. A much higher percentage
of the electrical power is going directly to generating light, which cuts
down on the electricity demands considerably.
https://www.youtube.com/watch?v=oCEKMEeZXug
By the End of Today’s Class You Should Be Able
To…
• Define and calculate electric power
• Describe the difference between current and electron flow
• Contrast DC and AC current
• Differentiate between real and drift speed of electrons
• Calculate how much your parents pay for devices you use
Agenda…
Do Now
10
minutes
INM: Using Electrical Energy 20 minutes
Guided Practice Problems 20 minutes
Independent Practice
30 minutes
Closing, Exit Ticket
10 minutes
Electrical Energy, Resistance, and Power
Energy supplied to a circuit can be transformed in many useful ways.
However not all of the electrical energy
delivered ends up in useful form.
The light bulb to the left transforms some of
the electrical energy from the battery into
thermal energy
Remember that current moving through
a resistor increases its thermal energy because flowing electrons collide
with lattice ions of the resistor.
• As a result the amplitude of vibrations of the ions increases and
therefore the temperature of the device increases. We say device
dissipates energy in it.
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 device.
Power dissipation in resistors
DEF: Power is the rate at which electric energy is converted
into another form such as mechanical energy, heat, or light.
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
Blow heater
Kettle
Toaster
Iron
Vacuum cleaner
Television
Power rating
2 kW
1.5 kW
1.2 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
CFU
Comparison of US and other countries that use voltage of 240 V.
• The power of appliances must be roughly the same
• Voltage in USA is 120V and in other countries 120 V.
• Which appliances have to draw a greater current?
A) in USA,
B) other countries
• Which appliances have less resistance?
A) in USA,
B) other countries
• Which countries use thicker wire (both used for connecting and in appliances)?
A) in USA,
B) other countries
So, 220V was an economically more meaningful choice.
There is really not too much safety difference between
getting zapped by 110V or 220V !!!
CFU
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 
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.
• a circuit must provide a closed path for the
current to circulate around
• when the electrons pass through the light
bulb they loose energy  the bulb gives light
and heats up
• the battery is like a pump that re-energizes
them each time they pass through it
Duracell
+
Direction of Current
Current is defined as the direction positive charges would flow
• From + side of battery to – side of battery
Fun Fact
Benjamin Franklin defined
current in this manner long
before we knew much about
charges.
Now, we know that positive
charges stay put and negative
charges flow. So, electrons
actually flow opposite current.
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 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 increase.
• After that, 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 0.1mm/s).
example: it takes ~ 3 hour for an electron to travel
through 1m in an electric circuit of a car.
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
_
+
AC current alternates in direction. The back-and-forth motion occurs at frequency
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
There is energy lost in a power line due to dissipation of energy to heat
throughout the length of the cable.
So DC power plants must be close to users
The major advantage of AC: AC voltages can be transformed to higher or
lower voltages (can be stepped up or down to provide any voltage required)
by the use of the transformers.
This means that low voltage produced in a generator can be stepped up to
higher voltage. High voltages in power lines are actually needed for sending
power from one place to another over great distances.
Power is equal to the current times the voltage. That means that if you want
to send a lot of power you can use:
a) high current
b) high voltage
if you use high current, resistance should be small. To reduce the resistance
of power lines becomes very expensive since, in order to do this, bigger
cables must be used (heavier cables aren’t very safe either).
To avoid a lot of the power to be lost to the resistance in the wires it is much
better to use high voltage since the currents are smaller then!
•
•
•
•
Electrical energy sent at high voltage over great distances from
the power station can be eventually reduced to a safer voltage for
use in the house.
Some long distance power lines use voltages of more than
500,000 V
AC plants can be far outside cities
by 1895 DC was out and AC was in
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 12 ¢ per kilowatt-hour.
• How do we get kilowatt-hour and what is that?
• Power = energy/time
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
1W x 1s = 1J
1 kWh = 3.6 x 106 J
Model $$$Problem$$$:
A digital clock has a resistance of 12,000 Ω and is plugged into a 115 V outlet.
a) How much current does it draw?
𝐼=
𝑉
𝑅
𝐼 = 0.0096 A or 9.6 mA
a)
How much power does it use?
P=𝐼V
P = 1.10 W
b) If the owner of the clock pays $0.12 per kWh, how much does it cost to
operate the clock for 30 days?
amount of power in kW used by the clock over 30 days
E = Pt ;
where time is in hours and P is in kW
cost = E($.12)
Cost = $0.10
Agenda…
Do Now
10 minutes
INM: Using Electrical Energy
20 minutes
Guided Practice Problems
20 minutes
Independent Practice
30 minutes
Closing, Exit Ticket
10 minutes
As you work with a partner, take 10 minutes to answer
the problems on the handout.
we will finish together as a whole group and review
our progress.
Guided Practice
Answer the following problems
1) A 15 ohm electric heater operates on a 120 V outlet.
a) What is the current running through the heater?
I = 8.0 A
b) How much energy is used by the heater in 30.0 s?
E = 2.9x104 J
c) How much thermal energy is liberated in this time?
E = 2.9x104 J
2) An electric space heater draws 15.0 A from a 120 V source.
It is operated, on the average, for 5.0 h each day.
a) How much power does the heater use?
P = 1.8 kW
b) How much energy in kWh does it consume in 30 days?
E = 270 kWh
c) At $0.12 per kWh, how much does it cost to operate the heater for 30 days?
$32.40
Agenda…
Do Now
10 minutes
INM: Using Electrical Energy
20 minutes
Guided Practice Problems
20 minutes
Independent Practice
30 minutes
Closing, Exit Ticket
10 minutes
Work in silence please.
Raise your hand if you have a question, I will help you but I will not just
give you the answer to any problem during this time.
Agenda…
Do Now
10 minutes
INM: Using Electrical Energy
20 minutes
Guided Practice Problems
20 minutes
Independent Practice
30 minutes
Closing, Exit Ticket
10 minutes
Electromotive force (emf – ε or E)
We have defined potential difference as the amount of
work that has to be done to move a unit positive charge
from one point to the other in an electric field.
W
ΔU
ΔV =
=
q
q
A battery or an electric generator that transforms one type of energy
into electric energy is called source of electromotive force
• DEF: emf (ε) of the source is the potential difference between
the terminals when NO current flows to an external circuit.
(IT IS A VOLTAGE NOT A FORCE).
In the true sense, electromotive force (emf)
is the work (energy) per unit charge
made available by an electrical source.
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.
Terminal voltage, emf and internal resistance
In the circuit the total energy supplied is determined by the value of the emf.
When electrons flow around a circuit, they gain potential energy in the cell
and then lose the energy in the resistors. In a closed circuits charge must
flow between the electrodes of the battery and there is always some
hindrance to completely free flow. So when the current I is drawn from the
battery there is some resistance called INTERNAL RESISTANCE (r ) of the
battery causing the voltage between terminals to drop below the maximum
value specified by the battery’s emf.
Thus the TERMINAL VOLTAGE
(the actual voltage delivered) is:
V = e - Ir
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 or 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
example: Find power of the source, current in each resistor, terminal potential,
potential drop across each resistor and power dissipated in each resistor.
I = ε/Req = 0.3 A
Req = 120 
terminal potential:
V = ε – Ir = 36 – 0.3x6.7 = 34 V
current through resistors 100Ω and 50Ω :
0.3 = I1 + I2
100 I1 = 50 I2
I = I1 + I2
→ I1 = 0.1 A
potential drops
V = IR
power dissipated
P = IV
80 Ω
0.3x80 = 24 V
0.3x24 = 7.2 W
100 Ω
0.1x100 = 10 V
0.1x10 = 1 W
50 Ω
0.2x50 = 10 V
0.2x10 = 2 W
6.7 Ω
0.3x6.7 = 2 V
0.3x2 = 0.6 W
I1R1 = I2R2
I2 = 0.2 A
ε = Σ all potential drops
36 V = 2 V + 24 V + 10 V
power dissipated in the circuit =
power of the source
0.6 + 2 + 1 + 7.2 = 0.3x36
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.
A potential divider
In electronic systems, it is often necessary to obtain smaller
voltages from larger voltages for the various electronic
circuits. A potential divider is a device that produces the
required voltage for a component from a larger voltage.
It consists of a series of resistors or a rheostat (variable
resistor) connected in series in a circuit.
Potential divider equation
I=
V
R1+R 2
V1 =
R1
V
R1+R2
V1 = IR1
example:
In the potential divider shown, calculate:
(a) the total current in the circuit
(b) the potential difference across each resistor
(c) the voltmeter reading if it was connected
between terminals 2 and 6.
(a) The total resistance
R = 12 Ω.
I = V / R = 12 V / 12 Ω = 1 A
(b) 6 x V = 12 V → V = 2 V
(12 V is equally shared by each 2 Ω resistor.
or
V = IR = 1x2 = 2 V
(c) R = 4 x 2 = 8 Ω
(Between terminals 2 and 6 there are 4 resistors)
potential difference between the terminals is
V = IR = 1 x 8 = 8 V
Potentiometer
Because resistance is directly proportional to the length of
a resistor, a variable resistor also known as a
potentiometer or as a “pot” can also be used to control the
potential difference across some device.
Sliding contact A can connect anywhere from one end
to the other of the resistor chain. This way it can
control voltage across a device and therefore the
current through it, from maximm down to zero.
1. step is to do a circuit without device and then adjust
point A in such a way that there is no current passing through potentiometer.
Potential difference across potentiometer is 6 V.
For some other battery point A would be somewhere else. If you include a lamp
into circuit and the pointer is at A, potential difference across the lamp is zero.
However, if the pointer is moved up to two-thirds the length of the potentiometer
as in the figure, then the output voltage across the filament lamp would be
⅔ × 6V = 4V.
Pots have a rotating wheel mounted in plastic and they are
commonly used as volume and tone controls in sound systems.
They can be made from wire, metal oxides or carbon compounds.