Kilowatt Hour

We use electricity for many things in our home - television, kettle, cooker, lighting, fan, computer, heater, and so on. And we have to pay for it. So how do the companies that supply us with electricity charge us?

Usually, somewhere in or near our house, there is a meter that measures the amount of electrical energy that we have used. When we switch on the light or computer or other applicances, the number on the meter increases. A person from the electrical supply company will come each month to take the reading. The company will subtract the reading this month from the reading last month, and calculate how much electrical energy we have used.

The unit of the number on the meter is kilowatt hour (kWh).

electric meter

We have learnt that joule (J) is a unit of energy. If kWh is also a unit of energy, how many joules is it?

To understand this, recall that kW is a unit of power, and hour is a unit of time. Recall also that power = energy / time. Therefore energy = power x time. This tells us that kW x hour must be a unit of energy. One kilowatt hour (kWh) simply means 1 kW x 1 hour.

To relate to J, convert to SI units: 1 kW = 1000 W and 1 hour = 3600 seconds. Then 1 kW x 1 h = 1000 W x 3600 s = 3600000 J. This gives us the relation: 1 kWh = 3600000 J. One kilowatt hour is 3.6 million joules.

Exercise. A light bulb has a power rating of 24 W, 240 V. It is switched on for 8 hours. How many kilowatt hours of energy is used in 30 days?

Answer. 1 kW = 1000 W. In kilowatt, the power of the light bulb is 24/1000 = 0.024 kW. In 30 days, the total time of light bulb use is 30 x 8 = 240 hours. So the energy in kilowatt hour is power x time = 0.024 kW x 240 h = 5.76 kWh.

Exercise. The man from the electric power company came to check my meter today. He took down the reading of 268 kWh. When he came last month, the reading was 215 kWh. If the electricity costs 0.10 dollar per kWh, how much must I pay this month?

Answer. The energy I have used this month is 268 - 215 = 53 kWh. The cost is 53 x 0.10 dollar = 5.30 dollars. This is what I have to pay.