Electrical energy and the electricity bill

What does the electricity bill count?

At the end of every month, a house gets a bill. The bill does not count the current, and it does not count the power. It counts the energy that the house used. Let us see how.

Energy

The energy used by an appliance is its power multiplied by the time for which it works:

In SI units, the power is in watt and the time in second, so the energy is in joule. A $100\ \text{W}$ bulb that works for one hour uses $100\ \text{W} \times 3600\ \text{s} = 360\,000\ \text{J}$. For an appliance used for hours, the numbers in joule are very large, so we use a bigger unit.

The kilowatt hour

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

The kilowatt hour is the commercial unit of electrical energy, and in a bill one kilowatt hour is called one unit.

To find the units, change the power to kilowatt and the time to hours:

• A $100\ \text{W}$ bulb for $10$ hours: $0.1\ \text{kW} \times 10\ \text{h} = 1$ unit.
• A $1000\ \text{W}$ heater for $2$ hours: $1\ \text{kW} \times 2\ \text{h} = 2$ units.
• A $2000\ \text{W}$ iron for $30$ minutes: $2\ \text{kW} \times 0.5\ \text{h} = 1$ unit.

The bill

You should find that the iron, used for only half an hour a day, can match the fan running all day: the power matters as much as the time.

A worked example

A $60\ \text{W}$ bulb works for $7$ hours a day. What is the energy in a month of $30$ days, and the cost, if one unit costs $6.5$ rupees?

Step 1. The energy in a day is $0.06\ \text{kW} \times 7\ \text{h} = 0.42\ \text{kWh}$.

Step 2. For $30$ days, $0.42\ \text{kWh} \times 30 = 12.6\ \text{kWh}$, that is, $12.6$ units.

Step 3. The cost is $12.6 \times 6.5$ rupees $= 81.9$ rupees.

How to save electricity

• Switch off a light or a fan when you leave a room.
• Use appliances that give the same light for a smaller power. A LED bulb of $9\ \text{W}$ gives about the same light as a filament bulb of $60\ \text{W}$.
• Use the heater, the iron and the kettle only as much as you need.

Practise with new numbers

Try it in Python

The program finds the units used by three appliances in a month, and the bill.

Remember these

• Energy $E = Pt$. The kilowatt hour is the commercial unit: $1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$.
• Units used = power in kW × time in hours. Cost = units × price of one unit.
• An appliance of small power can use a lot of energy if it works for a long time.

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 an $1800\ \text{W}$ heater use in $1.5$ hours?

2. How many joules are in $2\ \text{kWh}$?

3. Which uses more energy: a $2000\ \text{W}$ iron for $15$ minutes, or a $60\ \text{W}$ bulb for $10$ hours?

4. A month's bill shows $120$ units, at $6.5$ rupees a unit. What is the cost?