Higher tier: The cost of using an appliance
The power rating of electrical appliances can be used to calculate the cost of using them.
The following equation enables the number of units used to be calculated:
Energy in kWh = power rating in kW x time in hours
When using this equation it is important to remember that:
- the power must be in kW (1 kW = 1000 W);
- the time must be in hours.
Example
Calculate the cost of using a 2 kW heater for 6 hours if the price of a unit is 13p.
Energy in kWh = power rating in kW x time in hours
Time = 6 hours
Power rating = 2 kW
Energy in kWh = 2 kWh x 6 h = 12 kWh
Total cost = energy in kWh × cost per unit
= 12 kWh x 13p
= 156p
= £1.56
The cost of using the heater is £1 .56
Question
Calculate the total cost a using a 100 W lamp and a 300 W hair dryer for 10 minutes if a unit of electricity is 14p.
For the lamp:
Energy in kWh = power rating in kW x time in hours
Power rating = 100 W
This must be converted to kW by dividing by 1000.
100 W = \(\frac{\text{100}}{\text{1000}} = {0.1~kW} \)
Time = 10 minutes
This must be converted to hours by dividing by 60.
10 minutes = \(\frac{\text{10}}{\text{60}} = {0.167~hours} \)
Energy in kWh = 0.1 kWh x 0.167 h = 0.0167 kWh
Cost of using the lamp = energy in kWh × cost per unit
= 0.0167 kWh x 14p
= 0.23p
For the hair drier:
Energy in kWh = power rating in kW x time in hours
Power rating = 300 W
This must be converted to kW by dividing by 1000.
300 W = \(\frac{\text{300}}{\text{1000}} = {0.3 kW} \)
Time = 10 minutes.
This must be converted to hours by dividing by 60.
10 minutes = \(\frac{\text{10}}{\text{60}} = {0.167~hours} \)
Energy in kWh = 0.3 kWh x 0.167 h = 0.0501 kWh
Cost of using the hair dryer = energy in kWh × cost per unit
= 0.0501 kWh x 14p
= 0.70p
Total cost = 0.23p + 0.70p = 0.93p
The cost of using the lamp and hair dryer is 0.93p.
Question
A TV needs 250 W. It is switched on for 30 minutes. If each kWh costs 14p, how much does it cost to run the TV?
Energy in kWh = power rating in kW x time in hours.
Power rating = 250 W.
This must be converted to kW by dividing by 1000.
250 W = \(\frac{\text{250}}{\text{1000}} = {0.25~kW} \)
Time = 30 minutes.
This must be converted to hours by dividing by 60.
30 minutes = \(\frac{\text{30}}{\text{60}} = {0.5~hours} \)
Energy in kWh = 0.25 kWh x 0.5 h = 0.125 kWh
Total cost = energy in kWh × cost per unit
= 0.125 kWh x 14p
= 1.75p
The cost of running the TV is 1.75p