The kilowatt hour and electricity bills

The bill at the end of the month

The electricity bill is not in joules. It is in units. A $100\ \text{W}$ lamp that burns for one hour uses $360\,000\ \text{J}$, and a home uses hundreds of millions of joules in a month. So electricity is sold in a bigger unit of energy.

The kilowatt hour

The kilowatt hour ($\text{kWh}$) is the energy used by a $1\ \text{kW}$ appliance in $1$ hour.

One unit on the bill is one kilowatt hour. Power times time is energy, so the kilowatt hour is a unit of energy, not of power.

Finding the units and the cost

The meter shows a reading at the start and at the end of the month. The units used are the difference of the two readings.

You should find that a $1000\ \text{W}$ heater for half an hour uses as much as a $50\ \text{W}$ fan for ten hours: both use $0.5$ unit. Power and time count together.

Watch out. Use kilowatts with hours: $100\ \text{W}$ is $0.1\ \text{kW}$, and $30\ \text{min}$ is $0.5\ \text{h}$.

A worked example

A home runs three fans of $75\ \text{W}$ for $8\ \text{h}$ a day, and a $2\ \text{kW}$ washing machine for $1\ \text{h}$ a day. One unit costs ₹$6$. Find the units and the cost for $30$ days.

1. Fans. $3 \times 0.075\ \text{kW} \times 8\ \text{h} = 1.8\ \text{kWh}$ a day.
2. Washing machine. $2\ \text{kW} \times 1\ \text{h} = 2\ \text{kWh}$ a day.
3. The month. $(1.8 + 2)\ \text{kWh} \times 30 = 114$ units, costing $114 \times$ ₹$6 =$ ₹$684$.

Using energy wisely

• Switch off lights and fans in empty rooms; do not leave devices on standby.
• An LED bulb gives the same light as an old bulb for much less power.
• What counts is power and time: saving $10\ \text{W}$ on a lamp that burns all night beats saving $100\ \text{W}$ on something used for one minute.

Practise with new numbers

Try it in Python

The program adds up the units of a home's appliances and works out the bill.

Remember these

• $1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$, and one unit is one kWh.
• Units $=$ power in kW $\times$ time in hours.
• Cost $=$ units $\times$ the price of one unit.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. How many units does a $2\ \text{kW}$ heater use in $3$ hours?

2. A $60\ \text{W}$ bulb burns for $5$ hours. How many units is that?

3. A meter reads $3120$ at the start of a month and $3245$ at the end. One unit costs ₹$5$. What is the cost?

4. Someone says: 'My heater uses $2\ \text{kWh}$.' What is wrong with saying it this way?