# Calculate Energy and Cost of Electricity Bills

In this worksheet, students will understand the kilowatt-hour and apply it to calculating the cost of energy bills.

Key stage:  KS 3

Curriculum topic:   Physics: Energy

Curriculum subtopic:   Energy Changes and Transfers

Difficulty level:

#### Worksheet Overview

The equation for power

Power is the rate of energy transfer. If a process transfers a large amount of energy in a small space of time, it is powerful.

For example, a crane in a scrapyard that can lift tonnes of metal is very powerful, as it needs to transfer a lot of energy very quickly.

The equation is:

Power = Energy ÷ time

The units of power are Watts. The equation only works if energy is in Joules and time is in seconds.

What is a kilowatt-hour?

Rearranging the equation gives us:

Energy (in J) = Power (in W) x time (in s)

So, if we multiply a power in Watts by a time in seconds, we get an energy in Joules. However, the Joule is an extremely small unit. If we are dealing with much larger quantities of energy, we use the kilowatt-hour (kWh). This is the amount of energy transferred by a kilowatt (1,000 Watts) in 1 hour. So, you are still multiplying a power by a time - you are just using a much bigger power and a much longer time.

Energy (in kWh) = Power (in W) x time (in h)

There are 1,000 W in a kW and 3,600 seconds in 1 hour, so if we multiply these together, we find that 1 kilowatt-hour equals 3,600,000 Joules!

How do we calculate the cost of electricity?

The amount of energy a household uses on energy bills is given in kilowatt-hours. This is because giving the units in Joules would be far too high and would not make much sense.

Energy is charged by the kWh. So, to work out the cost, we use the equation:

Cost = Energy used (in kWh) x cost per kWh

For example, if a company charges 5p per kWh and a household uses 2,000 kWh of energy, the cost of the energy would be calculated as follows:

Cost = Energy used (in kWh) x cost per kWh

Cost = 2,000 x 5 = 10,000p.

Note that this gives an answer in pence. To turn it into pounds, remember to divide by 100:

10,000p ÷ 100 = £100.

How can we save money on energy bills?

It can cost a lot of money for gas and electricity in a home. There are a number of ways that money can be saved on energy bills. The most obvious method is just to use less energy (for example, switching off the lights when you're not in a room). However, there are other things that can be done around the home to waste less energy. Most of the wasted energy in a house is through heat escaping to the outside, so finding ways of preventing this causes a house to need less energy to keep warm, and therefore saves money on bills.

This includes:

Double-glazed windows

Loft insulation

Cavity wall insulation

Draught excluders

Carpets on all floors

All of these effectively 'trap' the heat in the house, as they are all insulators (such as loft insulation, pictured above).

Ready to have a go at some questions?

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