# The Electric Bill Project: An Elementary School Introduction to Energy

This unit was developed by Dr. Lawrence D. Woolf

An electric bill can be used as the focal point for introducing the concept of energy at the elementary school level. A student's home energy bill can be used to discuss concepts in math, science, research and public speaking.
Ask each student to bring in their family's SDG&E energy bill. Discuss that the bill consists of a charge both for natural gas - typically used for the energy to heat your home, hot water, range and oven - and electricity - used for anything that plugs into a wall socket. I would suggest focusing on just the electric portion of the bill.

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### Units Of Electricity Use

The watt (W) is a unit of electrical power, which is the rate at which we use energy. We pay the electric company for the use of energy. A kilowatt (kW) is equal to 1000 watts: kilo is a prefix that means 1000. (Note that k is the normal prefix for kilo, W is the normal abbreviation for Watts and h is the normal abbreviation for hours). A watt-hour (Wh) and a kilowatt-hour (kWh) are units of energy, where 1000 Wh= 1 kWh. The equation relating energy and power is:

Energy = Power x Time

For example, if a 75 W bulb (power) is turned on for 2 hours (time), it will use 150 Wh or 0.15 kWh of energy (energy = power x time).

The cost for each unit of energy we use is measured in cents (c) or dollars (\$) per kWh. The typical cost per unit of energy is 10 c/kWh or \$0.10/kWh. Using the equation below, we can determine the cost of our energy use:

Cost of energy use = Energy used x Cost per unit of energy:

Using our example above, the cost of using a 75 W bulb for 2 hours is:

Cost of energy use = 0.15 kWh x 10 c/kWh = 1.5 c.

### Using the Electric Bill

Make a list of the total cost of monthly electricity use as written on the bill. Discuss/calculate the minimum, maximum and average of the classes' electricity bill. Bar graphs could be made of the number of bills totaling less than \$30, \$30-40, \$40-50, \$50-60, \$60-70, \$70-80, \$80-90, \$90-100 and greater that \$100. Discuss with your class the reasons why some bills are higher than others. Perhaps the difference is related to the size of the home, number of refrigerators, freezers, TVs, computers etc. at the home or whether or not they have a pool or spa.

Consider a typical sample electric bill which contains the following information.

 Total Usage 647 kWh Baseline Allowance 266 kWh Baseline Usage 266 kWh @ \$.10077 Non-Baseline Usage 381 kWh @ \$.12039 Amount \$72.67

Next discuss that electricity use is measured using units of kilowatt-hours, abbreviated as kWh on the bill. Each kWh costs a certain amount of money that is specified on the bill. Up to a certain amount of electricity use, called the baseline usage, the cost of a kWh is one amount, which on the sample bill is \$.10077/kWh or 10.077 c/kWh. This can be used to introduce the concept of less than (<) - for electricity usage less than the baseline allowance of 266 kWh, the cost is \$.10077 per kWh. For amounts greater (>) than the baseline usage, the cost is higher - \$.12039 per kWh. Ask your students why SDG&E makes it cost more for you if you use higher amounts of electricity. Explain that this is a way that higher costs are used to try to discourage people from using excessive amounts of energy.

Next have your students calculate the total electricity used by adding their baseline usage (266 kWh) and their non-baseline usage (381 kWh). This should agree with the amount denoted as total usage (266 kWh + 381 kWh = 647 kWh). Then have them determine their electricity bill amount. First have them multiply their baseline usage (266 kWh) by the baseline rate (\$.10077/kWh) to determine their baseline cost (266 kWh x \$.10077/kWh=\$26.80). Second, have them multiply their non-baseline usage (381 kWh) by the non-baseline rate (\$.12039/kWh) to determine their non-baseline cost (381 kWh x \$.12039/kWh=\$45.87). Now they should add the baseline cost and the non-baseline cost (\$26.80 + \$45.87 = \$72.67) to obtain their total electricity cost for the month.

The gas usage and cost could be similarly determined. Students could also calculate the state surcharge tax and the state regulatory fee, given the rates specified on the bill and teachers could discuss the concept of taxes and how taxes are used. For example, as stated in the SDG&E "A Guide to Understanding Your Gas & Electric Bill, " the state surcharge tax is used for various energy management programs as well as the development of energy resources. The state regulatory fee pays for the operation of the California Public Utilities Commission, which determines the rates that the utilities are allowed to charge their customers.

### THE COST OF OPERATING APPLIANCES

The SDG&E booklet "How Much Are Your Appliances Running" provides a way for students to understand why their electric bill costs as much as it does. Each student should be given a copy of the booklet. They should then go home and make a list of all of the electricity using appliances in their home and how often they are used per month. They can then use the costs stated in the booklet to calculate the monthly use cost of these different appliances. This will require the use and understanding of many different units - such as costs per load of running the washer, dryer, dishwasher, etc., costs per hour, costs per day and costs per month. Their total electricity cost per month should approximate the cost shown on their electric bill.

The students can also be challenged to try to reduce their energy usage. Have them suggest ways that they might affect the energy use of their home. Perhaps they will turn off the pool heater, turn down the thermostat in winter or turn it up in the summer, turn off light bulbs, wash dishes more efficiently, turn off a rarely used second refrigerator, etc. They can do this for a day or more ( if they read and record their meter reading on a daily basis) or for a month and then try to see if they reduced their monthly electric bill.

Another interesting concept can be discussed at this point, namely the cost of buying or purchasing an appliance versus the cost of using or operating an appliance. Ask the students to determine the cost of buying an appliance of their choice (by having them go to a store, look at ads in the newspaper or asking their parents). Then have them determine the hourly, daily, monthly or yearly cost of using the appliance (using the SDG&E booklet). Have them determine how long it takes for the operating cost to equal the purchased price.

For example, suppose a 100 watt regular or incandescent light bulb costs 50c and will last (called the average lifetime or avg. life on the box) for 1000 hours. According to the SDG&E booklet, it costs 1c/hour to operate a 100 watt. Therefore, in 50 hours, the cost of using a light bulb will equal 50c, which was the purchased price of the light bulb. Over the 1000 hour lifetime of the light bulb, it will cost 1000c or \$10 to operate the light bulb, which is 20 times the cost of the light bulb.

A compact fluorescent bulb is more expensive than a regular incandescent light bulb. Have the students determine how much more expensive it is. It also lasts much longer. The compact fluorescent bulb also is less expensive to operate than the incandescent light bulb. Over the course of a lifetime of a fluorescent bulb, have the students determine the total purchase price of the one fluorescent bulb, the price of the many incandescent light bulbs that will last as long as the incandescent bulb, and the price of operating the two types of bulbs. Which is cheaper to use, considering both the purchasing cost as well as the operating cost?

Let's do an example. Suppose the compact fluorescent bulb, that has a light output equivalent to a 100 watt incandescent bulb, lasts for 10,000 hours and costs \$10. It costs about 1/4 c per hour to operate according to the SDG&E booklet. So, over 10,000 hours, the compact fluorescent bulb costs 10,000 hours x 1/4 c/hour = 2,500 c or \$25 to operate. For 10,000 hours of use, the total cost is \$10 to buy one bulb and \$25 to use the bulb, for a total of \$35.

Now, let's determine how much it will cost to buy enough incandescent light bulbs to last 10,000 hours and how much it will cost to use them for that length of time. Since a light bulb lasts for 1000 hours in our example, it will take 10 of them to last for 10,000 hours. Since each light bulb costs 50c, then it will cost 10 x 50 c =500 c or \$5 to buy all 10 of the light bulbs. Since it costs 1c/hour to use a light bulb, over 10,000 hours, it will cost 10,000 c or \$100 to use the light bulb. So, for 10,000 hours of use, the total cost is \$5 to buy the bulbs and \$100 to use the bulbs, for a total cost of \$105.

Therefore, for 10,000 hours of use, the compact fluorescent bulb will save a total of \$105 - \$35 = \$70 compared to the incandescent bulb!

### THE ENVIRONMENTAL COST OF USING ELECTRICITY

Students should "think globally and act locally" in regards to environmental issues. They should understand that using energy results in pollution of our environment. Energy is used by power plants to make electricity. It is also used when we drive cars, take airplanes, mow the lawn and cook our food.

Many types of pollutants are produced by power plants. In San Diego County, both oil and gas are burned during the production of electricity. On average, the following pollutants are produced:

1. 852 pounds of CO2 per megawatt-hour of electricity produced.
CO2 contributes to the global warming of the environment.
(Note that 1000 kilowatt-hours = 1 megawatt-hour, or 1000 kWh = 1 MWh)
(Recall that 1000 watt-hours = 1 kilowatt-hour or 1000 Wh = 1kWh)

2. 0.048 pounds of particulates per megawatt-hour of electricity produced.
Particulates are small particles that can contribute to smog.

3. 0.024 pounds of oxides of sulfur per megawatt-hour of electricity produced.
Oxides of sulfur contribute to acid rain pollution.

The average SDG&E customer uses 5649 kilowatt-hours of electricity per year or 5.649 megawatt-hours of electricity per year. How much electricity does each student's family use each year. They can estimate this amount by multiplying their one month electricity usage by 12. Have them convert their family's usage from kilowatt-hours to megawatt-hours. How does it compare to the average SDG&E customer?

In our example energy bill, the total electricity use was 647 kWh in one month. The average annual usage is therefore about 12 months x 647 kWh/month = 7764 kWh = 7.764 MWh. Therefore, this household will generate 7.764 MWh x 852 pounds of CO2/MWh = 6615 pounds of CO2 per year. It will also generate 7.764 MWh x 0.048 pounds of particulates/MWh = 0.37 pounds of particulates per year. Finally, it will generate 7.764 MWh x 0.024 pounds of oxides of sulfur/MWh = 0.18 pounds of oxides of sulfur per year.

Given their annual usage in megawatt-hours, have the students calculate how much pollution of each type their household causes at the power plant. Have them discuss the tradeoffs between their polluting the environment and the convenience/safety/health/enjoyment of appliances such as refrigerators, freezers, washing machines, TVs, computers, video games, etc.

### HOW ELECTRICITY IS PRODUCED

Electricity is produced at power plants that convert energy from one form into a second form, namely electrical energy. Electricity can be produced by burning coal, oil, natural gas or wood. The flow of wind or water can also be used to produce electricity. Sunlight can be harnessed to produce electricity, either by heating water or by direct conversion to electricity using solar cells. The heat of the earth can be used to produce electricity at geothermal power plants. The energy produced by the heat generated by nuclear fission is used in nuclear power plants to produce electricity.

All of these power plants have advantages and disadvantages. Have your students perform a research project to investigate how these different power plants work. Have them determine:

1. What is the source of energy?
2. How is the energy converted into electricity?
3. What types of pollution are produced by this source of energy?
4. What is the cost of electricity produced by this form of energy?
5. Where does this energy source come from? Is it imported? Is it readily available at all times and in all places?
6. What percentage of our nation's electricity is produced by this form of energy? Why? What about other nations that might have different natural resources?

Break your class into study groups. Have them write a report about their topic and present it to the class. Next, have a debate discussing the relatives advantages and disadvantages of all of the different types of power plants.