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Honors Physics
Part II: Electricity
San Dieguito Academy
2009 - 2010
Note: all situations described in this text are fictional and do not
represent the views of the school, its sponsors, or the S.P.C.A.
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Early Views of Electrictity
Ben Franklin, sometimes referred to as the father of electricity, saw charge very
differently than we do today. For him it was a fluid that was to be found in every object. An
object was electrically happy if it was filled to the brim with electric fluid. If electric fluid
was lacking he saw this as a negative thing. If there was too much fluid, this also was not good
but it was better than having too little. So, he called this situation positive. For him electric
fluid always sought equilibrium by flowing from containers that had too much charge toward
containers that were in need of charge. He saw water as the best analogy for studying
electricity.
The fact that water flows using the path of least resistance seemed
to parallel the flow of electricity; hence the terms resistance and resistor
were used to describe objects that restricted the free flow of electricity.
Early electricians latched onto this water analogy for describing
electricity. They often took it literally. For example some of the first
devices used to store electrical fluids were wine bottles, called Leyden
Jars. A metal straw was placed through the cork at the top of the bottle
and a spherical brass ball was added at the top of the straw.
It turns out that Franklin was wrong about electrical charge. Where
he felt there was only one type of charge we now believe that there are
two. Interestingly, the terms he coined; positive, negative, and neutral are
still used to describe charge. Only now we associate negative with the type
of charge found on the electron and positive with the type of charge found
on the proton.
1
Attraction and Repulsion
Every elementary student has heard the term opposites attract and likes
repel. This is particularly poignant as applies to electricity.
It turns out that the charge of an electron is the
same size (magnitude) as the charge of a proton.
Place a proton and an electron at a given distance
apart and they will feel a force of attraction. Place
two protons, or two electrons at the same distance
apart and they will feel the same magnitude of force.
Only it will be a repulsive force.
For examples see
http://www.shep.net/resources/curricular/physics/P30/Unit2/Topic1_Statics/Topic1-1_Charges.pdf
2
Coulomb’s Law
In 1784 Charles Augustine Coulomb designed an apparatus to determine the
relationship between charges and the distances they are apart. Below is a diagram of
the torsional balance he used for doing this. Check out this youtube video for a
demonstration of how it worked
http://www.youtube.com/watch?v=_5VpIje-R54
Coulomb’s pendulum was very sensitive. It could measure very small forces. From
this he was able to come up with what would later be called Coulomb’s Law.
q is the symbol for charge and it is measured in Coulombs.
r is the distance between the charges (in meters)
k is the electrical constant that gives forces in terms of Newtons.
( k = 9 x 109 )
Notice how similar it is to Newton’s Universal law of gravitation.
for more, see
http://www.shep.net/resources/curricular/physics/P30/Unit2/Topic2_CoulombLaw/Topic2_CoulombLaw.pdf
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Using Coulomb’s Law
To demonstrate just how strong electrical forces are compared to gravitational
forces let us investigate the forces of attraction when we take one mole of hydrogen
(each atom of hydrogen has one proton and one electron) and systematically remove
the electrons and put them into one container while placing the protons into another
container that is one meter away. For those of you who have not taken chemistry, a
mole of hydrogen has a mass of only 1 gram (one fifth of a nickel.) There are actually
a lot of hydrogen atoms in a mole.
One mole = 602,200,000,000,000,000,000,000 atoms ( 6.022e23 atoms.)
That means that there are 6.022e23 protons in each mole of hydrogen and an equal
number of electrons. The quantity of charge each electron carries is quite small.
Charge of one electron = 1.6e-19 Coulombs.
Given the information above find
1. How much total negative charge is in a mole of hydrogen?
_____________________________
2. How much total positive charge is in a mole of hydrogen?
_____________________________
3. Separate the charges by one meter. What is the force in Newtons?
_____________________________
4. On pound (lb) = 4.45 Newtons. How many pounds is this?
_____________________________
5.
4
Insulators
It turns out that some molecules and atoms keep a very tight grip on their charge and do not
easily let other charges flow through. These are called insulators. Below are some very good
insulators
Rubber
Glass
One of the very best insulators is
Most plastics
Oil
Dry air
Distilled water
If you drop a toaster into a bathtub of distilled water and nothing will happen
Conductors
Other materials do not have such a tight grip on their charges (most notably their electrons)
they are called conductors. Good conductors include:
Silver
A very good conductor is
Gold
Copper
Aluminum
Salt water
Drop a toaster into a bathtub of salt water and watch what happens.
When we are dealing with most materials it is the negative charge
that moves. For positive charges to move, the whole nucleus would
have to migrate. Also, if a proton were to move out of the nucleus of
an atom of mercury you would no longer have mercury, you would have
gold. This would be nice but it does not happen.
“Plasma” which is also a conductor. Plasma occurs when the temperature is very high.
Temperature is associated with molecular motion. At very high temperatures, collisions
between atoms are so forcefull that electrons are knocked off with such speeds that they
cannot reunite again. The sun’s outer atmosphere is plasma. The most common occurrence of
plasma on earth is inside lightening.
5
Fields
Mass has an associated gravitational field
Charge has an associated electrical field
While it is hard to see gravitational fields, it is easier to visualize electric fields.
A simple method is to place dust on or in an insulating solution and then bring a
charged object near it.
Above is a what happens when a charged sphere is placed in the solution. The dust
particles line up with the electric field that is associated with the charge.
This is what you get if two charged spheres with equal but opposite charges are
placed in the solution.
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Place a circular charged tube near a line of opposite charge and you get a very
neat electric field pattern. Michael Faraday predicted that there would be no
field inside of the tube. Do you see any field lines there?
This last picture demonstrates how the field tends to concentrate at the pointed
edge of an object.
For more see
www.shep.net/resources/curricular/physics/P30/Unit2/Topic3_ElectricFields/Topic3_Efields.pdf
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The Gold Leaf Electroscope
An electroscope consists of a conducting sheet attached to two conducting leaves
of gold. In our case two aluminum coated straws.
Charged rod
Electroscope
metal sheet
e
e
e
gold leaves
As we bring a positively charged insulator up to the electroscope, negative
charges are attracted from remote corners of the scope leaving a net positive
charge behind. The closer the rod gets the more charge gathers at each end.
There are two things to note here.
First, there are bazillions of positive and negative charges on the
electroscope. We only show locations were there are more positive (+) or
more negative charges (-)
Second, as a fraction of the total charge on the electroscope, we are
moving a tiny, tiny percentage.
Third, in every picture above, the net charge on the electroscope is
neutral. For every positive charge on the leaves, there is an equal amount
of negative charge on the top.
Check out this site for dramatization
http://www.shep.net/resources/curricular/physics/P30/Unit2/electroscope.html
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Now, lets see what happens when a negatively charged rod is brought up to an
electroscope. (Fill in the missing parts.)
Charged rod
Electroscope
metal sheet
gold leaves
Charging by Conduction
Charging by conduction happens when a charged object deposits its own excess
charge directly on the object to be charged.
Charged rod
insulator touches
and rubs
e
e
e
e
In the second picture where did the positive charges go?
Notice that for charges to move off of or on to an insulator you need to do more than just
touch. There must be some rubbing.
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Now, lets see what happens when a positively charged rod rubs against an electroscope. (Fill in
the missing parts)
Charged rod
insulator touches
and rubs
Remember that positive charge does not move. It is the negative charge that moves, making it
appear that the positive charge has moved.
Here is a very basic but accurate video that covers all of the previous info
http://www.shep.net/resources/curricular/physics/P30/Unit2/Videos/03ChargeInductionTVONTWeb.mov
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Another Approach to Charging by Conduction
Imagine two conducting spheres that started very far apart. On one sphere there were eight
excess electrons. Let us see what happens as we bring them together. (Fill in the blanks)
Two things to note:
1. When conductors touch they do not need to rub for charge to move
2. When charging by conduction the charging object must lose as much charge as
the other object gains.
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Charging by induction
As simple as charging by conduction is, it is much more common with electrical devices to charge
by induction. Induction occurs when the charging object influences charge distributions in
other objects.
ground
Notice that the ground can either give or receive charge. In this case the ground is allowing
negatives to flow as far away from the charging sphere as is possible.
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Lets see what happens when the charging abject is positively charged.
ground
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Charge Distribution and shape.
It turns out that on charged conductors. like charges congregate near points. The math behind
this effect is a bit complicated (AP Physics) However the effect was known as far back as Ben
Franklin’s time.
Below are three shapes with a sample charge of eight electrons on each one.
Sphere
Bulbus
Sphere
Teardrop
Ben Franklin used this fact to invent the lightning rod. Back east, during the winters, there
were (and are) a lot of house fires. There were several reasons for this.
First, cold air cannot hold much moisture in it, When this air is heated up inside of a
wooden home the warm, super dry, air absorbs all the moisture it can get from
people’s skins and from the wood inside of the house.. This desiccated wood makes
for wonderful kindling.
Second, because it snows in the winter, houses need to have steep roofs so that the
weight of the snow does not crush the house. These steep roofs have in sharp edges
at their tops. This Franklin knew was a bad situation during electrical storms as
lightning not only goes to the highest points but it also goes from and to the sharpest
points, which in this case are the gables of a house..
Third, wood is not a good conductor. As charges move across the top of the roof
toward the point where lightning strikes, they encounter a lot of friction. This
friction generates heat; enough heat to start fires.
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QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Above is the situation that plagues homes with sharp pointed roofs. Notice how the
charge build up along the top of the roof will need to travel to the right encountering
a great deal of friction as it moves.
Ben Franklin used a bit of reverse logic when he came up with the lightning rod. The
average person facing the dilemma of lightning strikes causing house fires would be
tempted to try to repel lightning from the house and attract it to locations some
distance away. Ben’s approach was to do exactly the opposite. He decided to make
the home an even more attractive target. He placed a conducting pointed metal rod
on the side of the house. Because charge is attracted to the sharpest points on an
object, most of the charge buildup would be there. Then he ran a conducting strap
(of lead) that ran down the side of the home and deep into the ground.. The thought
process was that electricity, like water, seeks the easiest path over which to travel.
Rather than moving across the rooftop charge would move straight up the conducting
strap.
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At that time the English looked down on everything made in America. When
Franklin’s discovery became known in England the British decided that Franklin made a
mistake because of his lack of understanding. Rather than putting a sharp point at the
top of the lightning rod they placed big metal spheres. The sphere is a good shape or
storing large amounts of charge. Unfortunately it is not the best shape for drawing a
spark. Sparks tend to jump from sharp points. What happened was that much more
charge was at the roof level than ever before. The result was that lightning would hit
the sharp rooftop and draw huge amounts of charge which generated immense amounts
of heat as it moved, causing more house fires than ever before.
It wasn’t long before sharp pointed lightning rods were put on homes in England.
Friction is the key to developing charge in insulators. It is believed that quickly
rising ice crystals in clouds is responsible for the buildup of charge in clouds. If you
have spent a winter back East or in the desert you probably have experienced shocks
when getting into or out of a car . Your clothing rubbing against the upholstery of the
seats is responsible for this. A fun game for many children is to shuffle across the
carpet and then call “Here kitty kitty.” In the picture below the shoes have a greater
electron affinity than the carpet and they rub electrons off the carpet leaving the
shoes and you negatively charged and the carpet positively charged.
16
A very effective way of building up a static charge used in the Van de Graaf
generator. This generator employs an insulating belt the rolls over two insulating
rollers. One roller, at the bottom of the belt, has a material with a strong
electron affinity. As the belt moves over it, friction rubs electrons off of the
belt and places it on the roller. The belt carries this charge until it reaches the
second roller (often a conductor). At the second roller is a metal comb that is
placed very close to the
belt. Negative charges are attracted to the points of the comb and jump off
toward the belt at the top roller as shown below. These charges come from a
large hollow metal sphere at the top of the Van de Graaf generator. They leave a
net positive charge on the top sphere.
e
Van de Graaf Generator
For positive charge to build up in one area, the top of the generator in this case,
there must be an equal build up of charge in another area. If you look at the base
you will notice that electrons ripped off of the belt repel each other and migrate
to the metal housing of the base.
17
A Van de graaf generator can move charge. But, how does one store it? Because
early electricians saw electricity as a fluid they decided to try to store it the way one
stores water or wine, in a bottle. Because it was first developed in the Leyden in 1745
and has become known as a Leyden Jar. The first Leyden Jars were filled with salt
water inside which the electricity would be stored. Electricians soon discovered that
the water could be replaced by a thin sheet of metal foil which would allow charge to
more easily into and out of the jar.
metal
sphere
Cork
Glass
metal
rod
metal
foil
metal
foil
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
metal
chain
Below is a series of pictures of a Leyden Jar. A positively charged piece of plastic is
brought up near the top of the jar and then taken away. Show the resulting motion of
charge and where it accumulates. (You will fill in the missing parts)
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Charging a Leyden Jar
If a charged insulating rod is brought down to a Leyden Jar and then rubbed across the
top conducting sphere the jar will take on a positive charge on the inside plates that is
equal to the quantity of charge lost by the insulator.
This charge will stay on the inside surface even after the insulator is removed. Explain
why it stays in this case and not when the charged insulator is only brought nearby and
then taken away as it was on the previous page.
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Introduction to Circuits
So far we have dealt with properties usually associated with static electricity, now we
will look into situations where electricity is in constant motion. For this class we will
work with DC (direct current) circuits where charge once flowing, flows at a constant
rate. We will be dealing with the following concepts.
1. Electric potential (Voltage)
Electrical pressure – It compares well to air pressure or water
pressure. Imagine that you have a little canister for air that attach
to your paint ball gun. For your gun to work you must put a lot of air
into the canister. The higher the pressure (think Voltage) you apply,
the more air is pushed into the canister. There is a lot of energy in a
fully charged system. Every time you convert some of this potential
energy to kinetic energy in the fired paint ball the canister loses some
of its pressure ( think Voltage drop)
2. Current (Amperage or Amps)
Current is a measure of the quantity of charge passing a given
point in a circuit. You will be tempted to think of current as
Kinetic Energy. Be careful and remember that KE is not solely
determined by an object’s velocity. It is also determined by how
much mass is moving. In circuits it turns out that most charge
moves very slowly even if there is a very large current flowing.
So where is the KE? Well it is in the shear volume of charge
that flows through wires. There can be so much charge flowing
that the wires get hot due to friction between the moving
charges and the stationary metal that makes up the wires. This
leads us to Resistance. The ampere is the basic unit of current it
is equal to one coulomb of charge per second. At an electron
level one Ampere is
6,241,500,000,000,000,000 electrons
passing a given point each second.
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3. Resistance
(Ohms or  )
Resistance is electrical friction. It occurs when charge tries to
move through a material. Some materials are naturally more
electrically slippery than others. They have lower resistance.
They allow more charge to flow through with less loss of energy
due to thermal frictional heating.
4. Power
(Watts or j/sec)
Power is a measure of how quickly energy is being used. It is
measured in Joules per second. For short we call one joule/sec a
Watt. Note: We used the same units of power in the mechanical
energy section of the last book.
All of the circuits that we will be dealing with must obey 4 simple laws
1.
Kirchoff’s junction law
(a junction is where wires come together)
Current in = Current out
This law states that the sum total of all current leaving a junction must
be exactly equal to the sum total of all current flowing into a junction.
It is the law of conservation of charge as applies to circuits.
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2. Kirchoff’s loop law
0 = Voltage gains – Voltage losses
This law states that as you progress around a circuit and find your way back
again to where you started. The sum of all voltage gains (going through
batteries, solar cells, etc.) and all voltage losses (resisters, light bulbs,
motors, etc.) must add up to zero. This is the law of conservation of energy
as applies to circuits.
3. Ohm’s law
V=I R
For any given circuit the more voltage (V) you apply the more current (I)
will flow through the circuit.
4. Power Law
P = I V
This is the easiest to remember. I will explain in class.
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The Battery
In 1800, Count Alessandro Volta found a way to chemically move charge from one
location to another. He called it his Voltaic Pile because it was simply a stack of coins
(silver and zinc or silver and copper ) sandwiched between paper that had been soaked in
salt water. The taller the stack of coins the more electrical pressure (Volts) that was
generated and the more current that could be produced.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Above is a modern recreation of Volta’s cell. Nowadays we call such cells batteries.
It is important to note that a battery does not create charge, it just pushes
charge from one location to another.
Flow of current out of battery
Battery
Flow of current into battery
23
Above is a circuit diagram of a battery with a wire attached to each terminal.
Notice how the symbol for a batter looks a lot like Volta’s pile. Notice also, that there
would be no flow of current if the wire did not make it all the way back to the battery.
We will go by the convention that current will flow out of the positive terminal ( +
) and into the negative terminal.
When dealing with electricity there are some terms that you have to know.
Term
Symbol
Units
Description
Charge
Voltage
Current
Resistance
Power
Last but not least there are some special symbols that will be used when we draw circuit
diagrams. You already have seen the symbol for a battery.
Battery =
Switch =
Resister =
Light bulb =
(special resister)
24
Ground =
25
Series Circuits
A series circuit is one in which electrons flowing through one section must
flow through every other sections before leaving the circuit.
B
A
C
Above is a schematic diagram of a circuit with three resisters in a series.
Any electrons that flow through resister A must go through B and C before
returning to the battery. The triangular shaped symbol at each end is called ground.
It represents two things at one time. First it is the reference point where we set
zero volts (similar to how we set an elevation for zero PEg in our energy problems).
Second, it is used to represent a physical connection between all other ground
locations without having to actually draw a wire.
Series circuits have the problem that if one component in the series fails then
the whole circuit fails. You might have experienced this with Christmas tree lights.
The nice and easy aspect about series circuits when it comes to resisters in
series is that the net resistance for the circuit is just the sum of the resistances
of each of its parts. Find the net resistance of the following series circuits..
10 
10 
R total
20 
10 
30 
R total
1k
1k
1k
R total
26
Analyzing simple circuit problems
When you study a circuit it is best to determine its net values first.
20 
12 V
10 
30 
V
net
I
net
R net
P
net
The net voltage and resistance are easy to find. To find current use V = I R
V
=
I
R
______ = ______ ________
The net power is found by using P = I V
P
=
I
V
______ = ______ ________
Find the net values for the following circuits.
12 V
200 
10 
30 
V
net
I
net
R net
12 V
2M
2M 
1M
1M 
P
net
V
net
I
net
R net
P
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net
Now lets look at what happens as current flows through each of the parts of a circuit.
10 
20 
12 V
A
B
30 
D
C
12 V
V
ne t
I
ne t
E
0.2 A
R ne t
60 
P
60 W
ne t
We want to find the Voltage at each of the locations (A, B, C, D, and E) Remember
that voltage is a measure of electrical pressure. Pressure is gained as current passes
through a battery and lost as current passes through a resistance. We will assume
that the wires have no resistance.
Voltage at points A, B, and E is self evident. To find the voltage at the other points
we will use V = IR which is sometimes written as Pd = I R where Pd stands or
potential drop. The potential drop across the 20 W resister is found below.
Pd
=
I
R
______ = ______ ________
If the potential difference is 4 volts. This is four volts less than at point B.
Therefore the voltage at point C = _________
A = ________ B = ________
C = ________
D = ________
E = ________
Try the following:
200 
12 V
A
B
10 
C
30 
D
E
V
net
I
net
R net
P
A = ________ B = ________
C = ________
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net
D = ________
E = ________
Parallel Circuits
So for we have looked at one type of circuit, the series circuit. There is
another type of circuit called the parallel circuit. Unlike the series circuit where
all charge must flow through every part of the circuit before returning to the
battery, in a parallel circuit current splits up. Some charge moves through one
part while other charge moves through other parts of the circuit. Below is an
example of a simple parallel circuit.
i2
12 V
30 
i1
i3
12 V
V
ne t
I
ne t
R ne t
60 
P
ne t
To find the net resistance of a parallel circuit we use the following equation:
1
1
______
=
1
_______
Rtot
+
_______
R1
1
_______
+
R2
+ . . . .
R3
Substituting resistances we get
1
______
Rtot
1
=
________
30
1
+
________
60
Rtot = _____________ Notice that the net resistance is less than either of
the resistors in the circuit? To get a visual representation of this imagine that
the electrons in the circuit are people and the resistors are doors of different
sizes through which they must pass through.
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Of the two resistors (30  and 60  which one would be the smaller door?
____________ Explain:
In terms of people and doors, explain why two resistors in parallel yields a smaller net
resistance.
For practice and visualization go to
http://phet.colorado.edu/simulations/sims.php?sim=Circuit_Construction_Kit_DC_
Only
30
Circuits Problems
Find the answers to the following:
30 
12 V
A
D
C
E
B
D
C
ne t
I
ne t
R ne t
P
30 
Find the voltage at A ______
V
ne t
B _______ C _______ D _______ E _______
30 
V
ne t
I
ne t
12 V
A
E
B
R ne t
30 
P
ne t
V
ne t
I
ne t
30 
30 
12 V
A
E
B
R ne t
30 
P
ne t
15 
Many circuits are compound circuits composed of both series and parallel.
30 
A
D
9
12 V
B
E
C
D
C
ne t
I
ne t
R ne t
P
30 
Find the voltage at A ______
V
ne t
B _______ C _______ D _______ E _______
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Circuit Problems
1. Imagine that you are given four resistors each with a resistance of 12 ohms each.
You are told to construct circuits using all four resistors. The circuits must give
different net resistances and some current must be able to flow through each
resistor. On the back side of this page draw as many of these circuits as you can
an determine their net resistance. Remember that each circuit must give a
different net resistance.
2.
To find the net values for the following circuit you need to determine the
resistances of each of the parts.
A
12 
12 V
15 
10 
30

B
120
20 
30 

80 
20 
Vnet = _______
Inet =______
Rnet = _______
3. In the problem above, find the voltages at points A and B.
VA = ______ 4 V VB = ______ 10.68V
4. Find the net values for the following:
15 
120 V
4
12 
10 
B
A
20 
10 
30 
20 
Vnet = _______
Inet =______
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Rnet = _______
Power and Common Circuits
1. You house supplies a potential difference at each outlet of approximately 120 Volts. A
laptop computer draws 65 Watts. How much current is this?
_______________
2. The computer cannot accept 120 volts. So, the voltage is reduced in a transformer down
to 12 Volts. To maintain the same amount of power the wire to the laptop supplies haw
many amps?
_______________
3. A 100 Watt incandescent light bulb has will draw more current than a laptop, How many
amps does it draw?
_______________
4. A hair blow drier draws a lot of power (1650 Watts) from the wall outlet at 120 volts
pressure. How much current is going through the cord?
_______________
5. A Prius has a mass of 1000 kg and it can go from 0 to 30 miles per hour using only its
batteries. If it can attain this speed in 6 seconds. On average how much power is needed
to do this? (A in watts and B in horsepower)
_______________
6. If the batteries of the prius supply a voltage of 500 volts, how much current is the
electric motor drawing as the car starts up?
_______________
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