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Chapter 3: Electricity
This chapter will present many of the basic principles of electricity. The goal of this chapter will
be to analyze electrical usage in your home and determine the cost of the electrical energy used.
Objectives
Upon completion of this chapter you should be able to:








Explain the basic properties of electricity
Solve problems using the power equation and Ohm’s Law
Explain the difference between series and parallel circuits
Explain the differences between AC and DC electricity
Explain why AC electricity is used in homes today
Demonstrate an understanding of the characteristics of the atom
Explain the principles of resistance
Calculate power consumption in your home
Basic Electrical Properties
From the lights, to the microwave, to the computer most devices
within your home require electricity. We will develop an
understanding of how electricity flows and is used within your
home. First we need understand the basic principles of
electricity.
Electricity is the flow of electrons. An electron is one of the
fundamental building blocks of an atom and has a very small
negative charge of -1.6 x 10-19 Coulomb (the Coulomb is a
foundation unit and cannot be broken into any other unit) and a
mass of 9.11 x 10-31kg. An atom is also composed of protons
that have a positive charge equal (but positive instead of
negative) to that of an electron and neutrons which are
uncharged. Protons and neutrons have approximately the same
mass of 1.67 x 10-27 kg. Electrons are about 2000 times less
massive. The protons and neutrons occupy the nucleus of the
atom and the electrons orbit the nucleus (this is a simplistic
view of the atom but is functional for our purposes). The
nucleus is very small in diameter compared to the size of the
Figure 3.1 Atom (ie model not
total atom. The charges of the electrons and protons are equal
to scale)
in magnitude (size) but are opposite in type of charge. Opposite
charges attract and like charges repel. The electrons and
protons do not combine due to the fact that the electrons are orbiting much like how the moon
orbits the earth. However the earth and moon are gravitationally attracted whereas electrons and
protons are electrically attracted. If the electrostatic force was not present the electrons would
fly off and not orbit the nucleus of the atom (the moon would do the same if it was not for the
gravitational force).
A neutral atom would have the same number of protons and electrons and thus have no net
charge since the charges of the electron and proton are equal in magnitude but opposite signed.
The number of protons that an atom has determines what the element is on the periodic table.
Therefore if the number of protons is increased or decreased in the atom the substance changes.
Some elements actually would like to gain another electron, thus giving them a net negative
charge. Other elements would like to lose an electron and thus giving a net positive charge to the
atom. An element is a pure substance only composed of atoms of one material (all having the
same number of protons). The number of protons determines the physical properties of the
material and the atomic number. The atomic mass is the sum of the number of protons and
neutrons. The chemical properties are determined by the number of electrons. The chemical
properties are items such as is the material a good or poor conductor and what elements will
combine easily together. A charged atom is called an ion. An atom is the smallest particle of
matter that has all the properties of the element. Compounds are composed of multiple
elements.
Figure 3.2 Periodic Table
Some substances allow charged particles (electrons) to flow
through them easily and other substances inhibit the flow of
electrical charge. The resistance of the material to the flow of
electrons depends upon several factors.
 The composition of the material (atomic make up)
 The length of the material (like how long a wire is for
example)
 The cross-sectional area of the material
The greater the length of the material (wire) the greater the
resistance to the flow of electricity, therefore the resistance and
length of the wire are directly proportional. The cross-sectional
Figure 3.3 End View of
Electric Wire
area of the material is indirectly proportional to resistance of the material. Therefore, a larger
diameter wire will have less resistance than a wire of small diameter. Think of a water hose; it is
easier to move water in a large diameter hose than in a small diameter one. Figure 3.3 is a
greatly enlarged and simplified end view of two electric wires. The green circles represent the
effective diameter of atoms. The one little red circle near the center represents an electron (This
is not to scale; a wire would have billions more atoms and the comparative size of the electron
and the atom is proportionally incorrect, the electron should be 100 times smaller). Only one
electron was placed in each wire. Of course this would be incorrect since the wires would have
billions and billions of electrons. As you look at the lower wire there are many more gaps that
the electron can easily pass through thus less resistance to the flow of current. As the diameter
of the wire is increased, more electrons can flow and there is less resistance per electron.
Therefore, resistance (R) is based on the following relationship:
R
l
A
(3.1)
The A represents the cross sectional area (r2, r is the radius of the wire), l is the length of the
wire and the Greek letter rho () is used to represent the electrical resistance of different
materials. Some of the materials with the lowest resistivities are gold, silver, copper and
aluminum. The resistivity and the resistance are directly proportional. Electrical conductivity is
the inverse of resistance and thus items with small resistance to the flow of electrons have larger
conductivity. The temperature of the material also changes the resistance of the material.
Temperature and resistance are directly proportional therefore the higher the temperature of the
wire the greater the resistance to the flow of electrons. This is because the atoms are moving
more rapidly (vibrating). This concept will be explored in more depth in Chapter 5. Some
materials as you make them very cold will lose all their resistance to the flow of electrons and
will become superconductors. If this technology can be perfected energy lost during
transmission of electricity will be reduced and less energy will be need to be produced creating a
cleaner environment (Most of the electricity produced in the United States comes from the
burning of coal.).
Current is defined as the number of electrons that move pass a given point in a given amount of
time. Current is defined in the units of the Ampere'. An Ampere' is one coulomb of charge
passing a point in a second.
I
q
t
Coulomb
I  ampere ' 
sec
I is the symbol for current.
It takes 6.25 x 1018 electrons to have one coulomb of charge.
(3.2)
(3.3)
qe is the charge of an electron
Therefore, a wire having a current of 1 Amp (ampere') would need to have 6.25 x 1018 electrons
per second moving through it.
Voltage is the push behind the electrons. Voltage (also referred to as potential difference) is the
amount of work done per charged particle.
V
W
q
(3.4)
V  Volt 
Joule
Coulomb
It is measured in the unit of the Volt; a Volt is one Joule per Coulomb. The greater the push
(voltage) the higher the current in the wire therefore these two items are proportional. The third
dependent factor is the resistance of the wire. The higher the resistance the harder you must push
to get the same current. This relationship is defined as Ohm’s Law:
V  IR
(3.5)
V represents the push, I the current and R is the resistance. This linear relationship is the
foundation of all electrical principles.
The unit of electrical resistance is the Ohm. An ohm is defined by equation (3.5) as the
following.
V  IR
V
R
I
(3.6)
Joule
Volt
Joule  Second
R  ohm 
 Coulomb 
Ampere Coulomb
Coulomb 2
Second
Electrical power is the amount of work per time. Work in this case is electrical energy used.
Work and energy are measured in the unit of the Joule. A Joule is the amount of work done by
lifting 100 grams approximately one meter in height (on earth 100 grams is approximately onequarter of a pound). The coulomb is the measurement of charge. We will use equations (3.2) and
(3.4) in the formation of a new equation.
W E

t
t
W
V
q
W  Vq
therefore
P
Vq
t
q
I
t
gives
P  VI
P
(3.7)
From unit analysis we get the following:
P  VI
joule coulomb
coulomb sec
joule
watt 
sec
watt 
(3.8)
The watt is the unit of power. If you lift 100 grams to the height of one meter in one second then
the power required to do this work was 1 watt (This will be explored in more depth in Chapter
6). We know that light bulbs are rated in watts, and we know that the power that the light uses is
related to the brightness of the bulb in general. Therefore, a 100 watt light bulb uses the same
amount of power as you would to lift 100 grams to a height of 100 meters in a second. Another
unit of power that is used in your everyday life is the horsepower. 1 horsepower is equal to 746
watts. You will learn more of the concept of work, energy and power in Chapter 6. When you
buy electricity you purchase kilowatt-hr (that is kilowatt times hours). A kilowatt is 1000 watts
(kilo always means 1000 times). The product of Power and time is energy. This can be seen in
equation (3.7). You therefore are actually paying for energy and not power on your home
electric bill.
Electric Circuits
The circuits within your home are
both in series and parallel. Simply
series circuit is when the electrical
flows from one item to the next.
break in the pathway will break the
electrons in the entire circuit and all
this circuit will cease to function.
wired
put a
current
Any
flow of
items on
Each
Figure 3.4 Series Circuit
circuit in your home is connected to a circuit breaker in the circuit breaker box. If a circuit
breaker trips (breaks the flow of electricity), everything on that circuit goes off, but all other
circuits in the home remain functional unless the main circuit breaker trips. If the main circuit
breaker trips then all the electricity to the entire home is disconnected and no electrical items
work within the home.
A parallel circuit is when the electricity flows to
multiple items at the same time. This is how your electrical outlets are wired. When one light
bulb on a circuit burns out all the other lights on the circuit continue to function properly. There
are multiple pathways for the electrical current to flow.
There are two different types of current, Direct (DC) and Alternating (AC). Direct current has a
non-changing current. This is what a battery or computer power supply produces. Alternating
current has a current that rapidly changes from positive to negative and back again. In the United
States it occurs 60 times per second and is known as 60 Hertz (Hertz is one cycle per second). If
you look on most electrical appliances in your home you will see a reference to this. During the
last parts of the 1800 there was a major debate on what type of electricity should be used. The
proponents of alternating current won the debate. So that is what flows through our homes.
Direct Current
Figure 3.6 Computer Power Supply – photographed by Emily DiNoto
Direct Current is used in your car, laptop, portable radio, etc. Any item that uses a battery is a
direct current device. Other devises also use direct current by converting alternating current into
direct current. The power supply in the computer pictured above is one such device that converts
AC to DC.
Alternating Current
Alternating Current is the type of electricity
that
enters your home and is transmitted by
power lines around your community and
across the country. Alternating current is
sinusoidal and changes from positive to
negative and back 60 times per second. The
electricity that enters your home comes in as
240
volts, and only a few of your electrical
devices use this voltage (electric heat pump,
air
conditioner, dryer, stove). Most items in
your
home use 120 volts. The voltage is split
Figure 3.7 Sinusoidal
before it is distributed to the wall outlets in
your
home. Similarly the voltage in power lines
is
much higher than can be used in your home and must be changed into a useable voltage of 240
volts before entering your home. A device known as a transformer is used to do this conversion.
Because a transformer is designed to be very efficient we can say the power before conversion is
equal to the power after conversion.
Therefore:
P1  P2
V1 I1  V2 I 2
(3.9)
If V2 decreases then I2 must increase to keep the proportion true. So if the voltage is stepped
down the current is stepped up and vise versa.
The power lines that run in your neighborhood carry lower currents so they will lose less energy.
This is because power lose is related to the square of the current. This relationship can be
obtained by using Ohm’s law (3.5) and the power equation (3.7) and by doing a substitution.
V  IR
P  VI
P   IR  I
(3.10)
P  I 2R
Let’s work examples using both equations (3.9) and (3.10). If the voltage in the power line is V1
= 10000 volts and the current in the power line is I1=6 Ampere’ and the voltage in your home is
240 volts (V2), what is the current that enters your home?
V1 I1  V2 I 2
10000volts  6amp    240volts  I 2
(3.11)
60000volts amp
240volts
I 2  250amp
I2 
How much power would be lost if the current was 6 amps? If it were 250 amps? We assume the
wire has a resistance of 1per mile of wire, and because we are comparing loses in the same
length of wire, we can ignore the length term. Losses of I2 and I1 can be determined by using
equation (3.10)
P1  I12 R1
P1   6amp  1 
2
P1  36watt
(3.12)
P2  I 22 R2
P2   250amp  1 
2
P2  62,500watts
It is clear that lower currents produce much smaller losses in power. This is why we transfer
electrical energy at high voltages and low currents. If the wires were superconducting (zero
resistance at very low temperatures) the losses would be reduced to nothing. Only alternating
current can make use of a transformer. For this reason we use alternating current in our homes
and convert as needed to DC. Alternating current is also used for the transportation of electrical
energy over long distances.
Fuses and Circuit Breakers
When the power enters your home it first enters either a fuse panel or a circuit breaker box. This
box contains main circuit breakers (or fuses) and individual circuit breakers (or fuses). The
purpose of a breaker (or fuse) is to limit the current flowing in a circuit. This is important
because if too much current flows in a circuit the wires will get hot to the point of causing a fire.
A circuit breaker (http://home.howstuffworks.com/circuit-breaker.htm) contains a metal strip and
when it gets too hot it will bend away from the contact thus opening the circuit which breaks the
pathway stopping the flow of the electricity. A fuse (http://auto.howstuffworks.com/wfc.htm) has
a thin metal strip and when to much current passes through the metal it melts. Circuit breakers
can be reset once the overload problem has been corrected, fuses will need to be replaced.
Blackout 2003
Joint U.S. - Canada Task Force Releases Power Outage Sequence of Events - pdf
(http://energy.gov/engine/doe/files/dynamic/1282003113351_BlackoutSummary.pdf)
Images from blackout and day after
(http://www.usatoday.com/news/gallery/2003/08-14-power/flash.htm)
Graphical descriptions of the blackout
(http://www.usatoday.com/news/graphics/powerfailure2/flash.htm)
Home Energy Usage
Every device that runs on electricity
consumes electrical energy. The amount
of energy used per second is the electrical
power consumption. The device that
measures energy consumption in your
home is the electric meter mounted on the
exterior of your home at the location
where electrical energy enters your home.
Go outside and observe the large rotating
dial (if it is a digital meter look at the right
most digit) then go inside to and turn on
an electrical appliance like a stove or air
conditioner that uses lots of energy.
Return to the meter to see if you can see a
change in the speed that the dial is rotating
Figure 3.8 Electric Meter
or the digits are moving. Most electric
Photographed by Emily DiNoto
meters have dials on them that measure
the amount of electricity you have used.
Some of the newer style meters have a digital read out. Each dial represents a digit measured in
kilowatt-hours. If you look at your electric bill it will state the number of kilowatt-hours that
were utilized during the billing period. A kilowatt is 1000 watts. There are 3600 seconds in an
hour. Therefore, a kilowatt-hour is a measure of the electrical energy used. Remember that
power is defined as:
E
t
E  Pt
P
(3.13)
Therefore 1 kilowatt hour is equal to
E  Pt
E  (1kilowatt )(1hr )
E  1000watts  3600s 
(3.14)
J

E  1000   3600s 
s

E  3, 600, 000 J
Therefore you truly are buying electrical energy when you pay for the kilowatt hours of
electricity. The Cost per kilowatt hour varies by electric company and where you live.
Home Electrical Audit
Let compute the cost of electricity from the following electric bill.
Figure 3.9 Electric Bill
cost
# of kilowatts
$43.63
cost per kilowatt-hour=
497
cost per kilowatt-hour=$0.088
cost per kilowatt-hour=
The cost of the authors’ electricity is about 8.8 cents per kilowatt-hour used.
Locate your electric bill and determine the cost of a kilowatt hour.
(3.15)
Let’s solve for the cost of having a single 100 watt light bulb on for 10 hours per day for 30 days
if electricity costs $.08 per kilowatt hour. We will follow the relationship in (3.14).
E  Pt

 100watt
E 
1000watt

 1kilowatt
E  30kilowatt

  hrs 
 10
  30day 
day




hr
(3.16)
$


cos t   30kilowatt hr   .08

kilowatt hr 

cos t  $2.40
Most electric items in your home have the power listed on them. Sometimes they have the
current listed. For example say a clock states that the current required to operate is 200
milliamp. A milliamp is one-thousandth of an amp. An amp is an abbreviation for Ampere'
therefore 200 milliamps is .2 amps. Most appliances in the home will run on 120 volts, with a
few exceptions like the stove, heater, air conditioner and dryer. We can determine the power
used by the clock and then determine the cost of operation.
P  VI
P  120volts .2amp 
P  24watts


 24 watts 

hr 
E 
30days   24



 day 
 1000 watts 
 1kilowatt 
E  17.28kilowatt hr
$


cos t  17.28kilowatt hr   .08

kilowatt hr 

cos t  $1.38
(3.17)
Find 10 appliances in your home and determine all values either by reading it from the
item or calculating. Different appliances will list different values some may list the power
and others the current, remember you know the voltage on most appliances in the home.
Item
Voltage
Current
Resistance
Power
Hours of
use
Cost