Describe how electrical appliances change electrical energy into useful forms, and calculate the energy used in kilowatt-hours and its cost

What this dot point is asking

This dot point wants you to describe how electrical appliances change electrical energy into useful forms, and to work out how much electrical energy an appliance uses and what it costs. You will use the unit the electricity company uses on a bill, the kilowatt-hour (kWh). The big idea is that the power rating of an appliance tells you how fast it uses energy, and that energy used (in kWh) is just power (in kW) multiplied by the time (in hours). Multiply that by the price per unit and you get the cost.

The answer

Appliances change electrical energy

Every electrical appliance takes in electrical energy and changes it into a useful form, usually with some wasted as heat. For example, a lamp changes electrical energy into light, a kettle changes it into heat, a fan changes it into kinetic energy (movement), and a radio changes it into sound. Knowing the useful change for a common appliance is a frequent exam question.

Power: how fast energy is used

The power of an appliance tells you how fast it uses electrical energy. Power is measured in watts (W) or kilowatts (kW), where one kilowatt is 1000 watts.

A higher power rating means the appliance uses energy faster. A kettle (about 2 kW) uses energy much faster than a phone charger (about 0.005 kW). The power rating is printed on the appliance or its label.

The kilowatt-hour

Electricity companies measure the energy you use in kilowatt-hours (kWh). One kilowatt-hour is the energy used by a 1 kW appliance running for 1 hour. It is sometimes just called a "unit" of electricity.

The formula is:

To use it, make sure the power is in kilowatts and the time is in hours. For example, a 2 kW heater on for 3 hours uses $2 \times 3 = 6$ kWh.

Working out the cost

Once you know the energy in kilowatt-hours, the cost is simple:

If electricity costs 30 cents per kWh, then the 6 kWh used by the heater above costs $6 \times 30 = 180$ cents, which is one dollar and 80 cents.

Why this matters

Appliances with a high power rating, used for a long time, cost the most to run and use the most energy. This is why heaters, kettles and ovens are expensive to use, while a phone charger costs almost nothing. Knowing this helps a family save money and waste less energy.

Examples in context

Example 1. Reading the electricity bill. A home electricity bill lists the number of "units" used, where each unit is one kilowatt-hour. The bill multiplies those units by the price per unit to get the total cost. Understanding kilowatt-hours lets you check the bill and see which appliances are pushing it up.

Example 2. Choosing energy-saving bulbs. An old-style bulb might be rated at 60 W, while a modern LED bulb giving the same light is rated at only 8 W. Over a year of evening use, the LED uses far fewer kilowatt-hours, so it costs much less to run and wastes far less energy as heat. The lower power rating is the reason.

Try this

• Cue. A $0.5\ \text{kW}$ television is on for $4$ hours. Work out the energy it uses in kilowatt-hours. Energy = power $\times$ time = $0.5 \times 4 = 2\ \text{kWh}$.

• Cue. Electricity costs $20$ cents per kWh. Find the cost of using the television above. Cost = energy $\times$ price = $2 \times 20 = 40$ cents.

• Cue. Explain why an electric heater costs much more to run than a phone charger. The heater has a much higher power rating, so it uses energy far faster, and it is often left on for longer, so it uses many more kilowatt-hours.