Define the kilowatt-hour (kWh) and calculate the cost of using electrical appliances where the energy unit is the kWh

4.2.4 Resistance – Energy & Cost

What is a Kilowatt‑Hour (kWh)?

⚡️ A kilowatt‑hour is a unit that measures electrical energy.

One kilowatt (kW) is the power used when a device runs at 1,000 watts.

If that device runs for one hour, it consumes 1 kWh of energy.

Think of it like a bucket of water: a 1‑kW device is a bucket that fills at a rate of 1,000 liters per hour. If you let it run for one hour, you’ve filled the bucket once – that’s 1 kWh.

Energy Formula

The energy used is calculated with the simple formula:

\$E = P \times t\$

where \$P\$ is power in kilowatts and \$t\$ is time in hours.

Example: A 0.75 kW kettle running for 0.5 h uses

\$E = 0.75 \times 0.5 = 0.375 \text{ kWh}\$.

Cost of Electricity

Electricity is usually sold by the kWh.

If the price is £0.15 per kWh, the cost of an appliance is:

\$\text{Cost} = E \times \text{price per kWh}\$.

Step‑by‑Step Cost Calculation

1. Find the power rating of the appliance (in kW).
2. Determine how many hours you use it each day.
3. Multiply power by time to get energy in kWh.
4. Multiply energy by the price per kWh to get the cost.

Example: Using a 1.5 kW Hair Dryer

Suppose you use the hair dryer for 0.2 hours (12 minutes) each day.

• Power: 1.5 kW
• Time: 0.2 h
• Energy: \$E = 1.5 \times 0.2 = 0.30 \text{ kWh}\$
• Cost per day (price £0.15/kWh): \$0.30 \times 0.15 = £0.045\$
• Monthly cost (30 days): \$0.045 \times 30 = £1.35\$

💡 Tip: Turning off the dryer when you’re done saves energy and money.

Cost Comparison Table

Quick Quiz

1️⃣ If a 0.8 kW heater runs for 3 hours a day, how much energy does it use?

2️⃣ If the electricity price is £0.12/kWh, what is the daily cost of that heater?

💬 Write your answers below and check with the teacher!