Mathematics 11–12 · Years 11–12
What an appliance costs to run: measured energy in kilowatt-hours and the household bill
Managing money: Budgeting (Mathematics Standard, Year 11); Ratios and rates: Rates (Mathematics Standard 2, Year 12)
School laboratory, not for home
In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.
This site has no interactive model of its own. Where a step or a material names a Concept Studio model, simulation or tool, it has not been built; an external simulation a step names (for example PhET) is not part of this site.
The idea
Power is a rate of energy use, so kilowatts multiplied by hours gives kilowatt-hours, and a measured kilowatt-hour figure multiplied by the tariff on a bill gives a running cost.
Safety card
Setting: In a school laboratory, with a teacher supervising, under the school's risk assessment. Not for home.
Hazards
- mains electricity
- boiling water from the kettle
Controls
- an adult plugs in and removes the meter with the power switched off at the socket
- use only a meter rated for the socket and never near water
- run through the meter only an appliance whose rated current is well below the meter's rating; never a 2400 W kettle on a 10 A meter, which draws the full 10 A at 240 V and more at a higher supply voltage
- at school, use a meter and kettle with a current electrical test tag under the school's electrical safety procedure
- stand the kettle at the back of the bench and let it cool before emptying
Note
No chemicals: the NSW Department of Education Chemical Safety in Schools package does not apply. Use the school's RiskAssess (riskassess.com.au) assessment for mains-powered equipment and hot liquids.
What you need
- A plug-in energy meter rated for 10 A household sockets that displays power (W) and energy (kWh)
- A kettle whose rated current (watts divided by the voltage on its label) is well below the meter's rated current, for example a 2000 W kettle (8.3 A at 240 V) on a 10 A meter, a desk lamp, a phone charger and, over 24 hours, a refrigerator
- A household or school electricity bill showing the usage rate in cents per kilowatt-hour (amounts only, no account details)
- The Australian Government Energy Rating calculator for comparing appliances
How to do it
- Read each appliance's rated power in watts from its label and convert to kilowatts.
- With the adult plugging in the meter, boil 1 L in the kettle and record the measured energy in kWh, the power the meter displays and the time taken; compare the energy with displayed power x time and with rated power x time.
- Record the refrigerator's energy over 24 hours and scale it to a year.
- Multiply each energy figure by the bill's usage rate to find the running cost; compare a phone charge with a kettle boil.
- Use the Energy Rating calculator to compare the running cost of two refrigerators of different star ratings.
What you should see
Worked check with test values: a 2000 W kettle running for 4 minutes uses 2.0 kW x (4/60) h = 0.133 kWh, which at a test tariff of 35.0 c/kWh costs 4.67 c; a refrigerator measured at 1.2 kWh a day uses 438 kWh a year. A kettle's rated power applies at the voltage on its label, and its element's power changes with the square of the supply voltage, so a supply 10 V below a 240 V rating gives about 8 per cent less power; the measured refrigerator figure replaces any label estimate. The learner knows it worked when the meter's kWh reading agrees within about 10 per cent with the power the meter displays multiplied by the time, and any gap between displayed and rated power is explained by the supply voltage.
What changes
- What you change
- appliance and running time
- What you measure
- energy used (kWh) and cost
- What you keep the same
- same meter
- same volume of water for the kettle
- full 24 hours for the refrigerator
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- A watt is an amount of energy; it is a rate, one joule per second.
- High-power appliances always cost the most; a low-power refrigerator running all day can use more energy than a kettle used briefly.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics Standard 11–12 Syllabus (2024), Year 11 focus area Managing money; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-11-04
- Mathematics Standard 11–12 Syllabus (2024), Year 12 Standard 2 focus area Ratios and rates; Year 11 taught from Term 1 2026, Year 12 from Term 4 2026, first HSC examination 2027 (the 2017 syllabus is still taught to Year 12 until then); page read 2026-09-22MST-12-S2-05
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.