Comparing Power Ratings of Devices

Every electrical appliance has a power rating (in watts) stamped on it. This tells you the rate at which it transfers energy.

Reading power ratings

$P = \frac{E}{t} \quad \Rightarrow \quad E = Pt$

A 2000 W kettle transfers 2000 J every second.

A 10 W LED bulb transfers 10 J every second.

Energy used over time

To find the total energy used:

$E = P \times t$

Ensure the units are consistent: P in watts and t in seconds gives E in joules.

Example: A 3000 W shower runs for 10 minutes (600 s):

$E = 3000 \times 600 = 1{,}800{,}000 \text{ J} = 1800 \text{ kJ}$

The kilowatt-hour

For household energy bills, energy is measured in kilowatt-hours (kWh):

$E(\text{kWh}) = P(\text{kW}) \times t(\text{h})$

1 kWh = 3{,}600{,}000 J = 3600 kJ.

The 3 kW shower running for 10 minutes (1/6 hour):

$E = 3 \times \frac{1}{6} = 0.5 \text{ kWh}$

Common errors and how to correct them

• Mixing units (watts with hours, or kilowatts with seconds).
• Thinking a higher power rating means the device uses more energy overall. A 2000 W kettle boils water in less time than a 1000 W kettle, so the total energy used may be similar.

How to apply this in an exam

Use $E = Pt$ with consistent units. For kWh calculations, use power in kW and time in hours. Show the unit conversion clearly.