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 total atom. The charges of the electrons and protons are equal 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).

Figure 3.1 Atom (ie model not to scale)

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 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:

lRA

ρ= (3.1)

The A represents the cross sectional area (πr2, r is the radius of the wire), l is the length of the wire and the Greek letter rho (ρ) 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.

Figure 3.3 End View of Electric Wire

'

sec

qIt

CoulombI ampere

=

= = (3.2)

I is the symbol for current. It takes 6.25 x 1018 electrons to have one coulomb of charge.

(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.

WVq

JouleV VoltCoulomb

=

= =

(3.4)

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.

2

V IRVRI

JouleVolt Joule SecondCoulombR ohm CoulombAmpere Coulomb

Second

=

=

⋅= = = =

(3.6)

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 one-quarter 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 EPt t

WVq

W Vqtherefore

VqPt

qIt

givesP VI

= =

=

=

=

=

=

(3.7)

From unit analysis we get the following:

sec

sec

P VIjoule coulombwatt

coulombjoulewatt

=

=

=

(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 wired both in series and parallel. Simply put a series circuit is when the electrical current flows from one item to the next. Any break in the pathway will break the flow of electrons in the entire circuit and all items on this circuit will cease to function. Each 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.

Figure 3.4 Series Circuit

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 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.

Figure 3.7 Sinusoidal

Therefore:

1 2

1 1 2 2

P PV I V I

==

(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.

( )

2

V IRP VIP IR I

P I R

==

=

=

(3.10)

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?

( )( ) ( )

1 1 2 2

2

2

2

10000 6 24060000

240250

V I V Ivolts amp volts I

volts ampIvolts

I amp

=

=

=

=

i (3.11)

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 1Ω 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)

( ) ( )

( ) ( )

21 1 1

21

12

2 2 22

2

2

6 136

250 162,500

P I R

P ampP wattP I R

P ampP watts

=

= Ω

=

=

= Ω

=

(3.12)

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.

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 or the digits are moving. Most electric 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:

EPt

E Pt

=

= (3.13)

Therefore 1 kilowatt hour is equal to

( )( )

( )

(1 )(1 )1000 3600

1000 3600

3,600,000

E PtE kilowatt hrE watts s

JE ss

E J

==

=

=

=

(3.14)

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.

Figure 3.8 Electric Meter Photographed by Emily DiNoto

Home Electrical Audit Let compute the cost of electricity from the following electric bill.

Figure 3.9 Electric Bill

costcost per kilowatt-hour=# of kilowatts$43.63cost per kilowatt-hour=

497cost per kilowatt-hour=$0.088

(3.15)

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. 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).

( )

( )

100 10 3010001

30$cos 30 .08

cos $2.40

E Pt

watt hrsE daywatt daykilowatt

E kilowatt hr

t kilowatt hrkilowatt hr

t

=

=

=

=

=

i

ii

(3.16)

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.

( )( )

( )

( )

120 .224

24 30 2410001

17.28$cos 17.28 .08

cos $1.38

P VIP volts ampP watts

watts hrE dayswatts daykilowatt

E kilowatt hr

t kilowatt hrkilowatt hr

t

=

=

=

=

=

=

=

i

ii

(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