Domestic Electrical Energy Use

From an energy store to a working appliance

A battery contains energy in a chemical store. When it supplies a current to an appliance, this store decreases and energy is transferred electrically to the appliance. An electric current is a flow of charge; when the current transfers energy to a device, it does electrical work. Work done is another way of describing energy transferred, and is measured in joules (J).

What happens to the energy depends on the device. A battery-powered motor transfers energy to the kinetic store of its moving parts. A heater transfers energy to the thermal store of its heating element. In a kettle, energy then passes by heating from the hot element to the water, increasing the water’s thermal store.

For a mains-powered appliance, the energy may originally come from the chemical store of fuel at a power station. Electricity provides a convenient way to transfer this energy over a distance to homes, where an electric current does work on devices such as motors and heaters. The chemical store is at the source; the wires provide a route for electrical energy transfer.

What a power rating tells you

Power is the rate at which energy is transferred, or the rate at which work is done. It tells you how quickly a transfer happens, rather than the total amount transferred.

One watt (W) means one joule transferred each second. A 1000 W appliance therefore transfers 1000 J every second while operating at that power. One kilowatt (kW) is 1000 W.

An appliance’s power rating tells you its operating power. For the same running time, an appliance with twice the power transfers twice as much energy. For the same power, running an appliance for twice as long also doubles the energy transferred.

This connects the appliance’s operation to changes in energy stores: a heater used for longer transfers more energy to thermal stores, while the energy store supplying it decreases by a greater amount. The total electrical energy supplied need not all produce the intended change in the appliance or the object being heated.

Calculating energy in joules

The energy transferred depends on both power and running time:

$$E = P \times t$$

Here, $E$ is energy transferred, $P$ is power and $t$ is time. Use power in watts and time in seconds to obtain energy in joules.

Suppose a kettle operates at 2000 W for 3 minutes. First convert the running time: $3 \times 60 = 180\text{ s}$. Then:

$$E = 2000 \times 180 = 360\,000\text{ J}$$

This is the total energy transferred electrically to the kettle during that time, not necessarily the energy gained by the water alone.

You can also rearrange the relationship to find an unknown power or time:

$$P = \frac{E}{t} \qquad t = \frac{E}{P}$$

Calculating domestic energy use in kilowatt-hours

A kilowatt-hour (kWh) is the energy transferred by a 1 kW appliance operating for 1 hour. The same equation works with a different matching set of units:

$$\text{energy (kWh)} = \text{power (kW)} \times \text{time (h)}$$

Suppose a 2 kW heater runs for 30 minutes. This is 0.5 hours, so it transfers $2 \times 0.5 = 1\text{ kWh}$. A 1 kW heater running for 1 hour transfers the same amount of energy. The first transfers energy faster, but operates for less time.

Because $1\text{ kW} = 1000\text{ W}$ and $1\text{ h} = 3600\text{ s}$:

$$1\text{ kWh} = 1000 \times 3600 = 3.6 \times 10^6\text{ J}$$

Both joules and kilowatt-hours measure energy. Kilowatt-hours are simply more convenient for the large transfers involved in domestic electricity use.

Electrical transfers

• Chemical stores in batteries or power-station fuels supply energy.
• An electric current transfers energy and does work on an appliance.
• Motors increase kinetic stores; heaters increase thermal stores.

Power and running time

Power is energy transferred per second: .