The kilowatt hour and the cost of electricity
Paying for electricity
The amount of electrical energy transferred to an appliance depends on its power, and on the length of time it is switched on for. The kilowatt hour (kWh) is used as a unit of energy for calculating electricity bills.
This equation shows the relationship between energy transferred, power and time,
\(\text{energy transferred (kilowatt-hour, kWh) =}\)
\(\text{power (kilowatt, kW)}\times{\text{time (hour, h)}}\)
Note that power is measured in kilowatts here, instead of the more usual watts. To convert from W to kW you must divide by 1,000.
For example, 2,000 W = 2,000 ÷ 1,000 = 2 kW.
Also note that time is measured in hours here, instead of the more usual seconds. To convert from seconds to hours you must divide by 3,600.
For example, 1,800 s = 1,800 ÷ 3,600 = 0.5 hours.
The cost
Electricity meters measure the number of units of electricity used in a home or other building. The more units used, the greater the cost. This is how the cost of the electricity used is calculated:
\(\text{units used (kWh)}={\text{power (kW)}}\times{\text{time (h)}}\)
\(\text{cost}={\text{units used}}\times{\text{cost per unit}}\)
Example
An electric fire needs 2 kW. It is switched on for 3 hours. If each kWh costs 15p, how much does it cost to run the fire?
Units used (kWh) = 2 × 3 = 6 kWh
Cost = 6 × 15 = 90p
Make sure that you can convert between pounds (£) and pence (p).
£1 = 100p
Question
A television set needs 250 W. It is switched on for 30 minutes. If each unit (kWh) costs 16p, how much does it cost to run the TV?
Remember, you need to convert the power to kW and the time to hours.
250 W = 0.250 kW
30 minutes = 0.5 hours
Units used = 0.25 kW × 0.5 h = 0.125 kWh
Cost = 0.125 × 16 = 2p
You may also need to convert from days to hours.
Question
A 100 W light is left on for 3 days. If each unit of electricity costs 12p, how much does it cost to run the light?
100W = 0.1 kW
3 days = 3 × 24 hours = 72 hours
Units used = 0.1 × 72 = 7.2 kWh
Cost = 7.2 × 12 = 86.4p
Converting between kilowatt hours and joules
The energy in joules is equal to the power in watts × time in seconds.
\(\text{energy (J)}={\text{power (W)}}\times{\text{time (s)}}\)
Question
1 kWh is equal to how many joules of energy?
Remember – 1 kWh is the electrical energy converted by a 1 kW appliance used for 1 hour.
Converting the kW to W and the hour to seconds and substituting the numbers into this equation below.
\(\text{energy (J)}={\text{power (W)}}\times{\text{time (s)}}\)
= 1,000 × 60 × 60
= 3,600,000 J