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Science project idea

Decoding the home electricity bill: units, slabs and appliance costs

A bill is calculated from units used, in kilowatt hours, at slab rates plus fixed charges. By computing the energy of each appliance and checking it against the bill, you apply percentages, multiplication and a piecewise function.

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What it shows

A bill is calculated from units used, in kilowatt hours, at slab rates plus fixed charges. By computing the energy of each appliance and checking it against the bill, you apply percentages, multiplication and a piecewise function.

The science

Energy in kilowatt hours equals the power in kilowatts multiplied by the time in hours, and one unit on the bill is one kilowatt hour. Many bills charge a low rate for the first slab of units and higher rates for the next slabs, so the cost is a piecewise linear function of units used.

Materials

Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.

  • A recent electricity bill (copy the numbers, not the account details)
  • The power rating labels of home appliances
  • A notebook and a calculator
  • A clock for timing use
  • Graph paper
  • A spreadsheet if available

Safety

For this project: Read ratings from labels only and do not open any appliance or touch wiring or the meter. An adult must handle everything electrical.

Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.

All the safety rules

Step by step

8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.

  1. Copy from the bill the units used, slab rates and fixed charge without writing down account numbers.

  2. List ten appliances at home with their power in watts, such as fan, light and fridge.

  3. Estimate the daily hours of use for each and calculate the daily energy in kilowatt hours.

  4. Multiply by 30 for a monthly estimate and add them up.

  5. Compare the estimate with the units on the bill and calculate the percentage difference.

  6. Calculate the bill cost step by step for each slab and check it against the printed amount.

  7. Draw a graph of cost against units to show the slabs.

  8. Suggest three changes that would cut the units, and work out the saving.

What you should see

Your estimate matches the printed units within about 20 percent, and your graph shows a bent line for the slabs. The saving plan shows how much a family can save.

Viva questions

A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.

1What is one unit of electricity?

One kilowatt hour.

2How much energy does a 60 W fan use in 10 hours?

0.6 kWh.

3What is a slab rate?

A rate that changes as the units used cross set limits.

4Which appliance uses the most energy at home?

It is often the one with high power that runs for many hours, such as an air conditioner or geyser.

Free ebook: Viva Questions for Science Projects

Take it further

Compare an LED bulb with an old filament bulb for yearly cost, including purchase price.

Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.

Free ebooks for this project

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