Power

Power is the rate of energy transfer.

What does rate mean?

WHenever we have a rate of something, it means ‘how much happens in a certain time’?

For a ‘unit rate’ of something, it means ‘how much happens in one second’.

It therefore also means that the units area going to be ‘something per second’ (e.g. joules per second, J/s).

Formula

We can calculate power using the formula:

\text{Power} = \frac{\text{Energy transferred}}{\text{Time taken}}

Or, in symbols:

P = \frac{E}{t}

Where:

• P is the power, in watts, W
• E is the energy transferred, in joules, J
• t is the time taken, in seconds, s

Rearranged versions

To calculate energy transferred:

• \text{Energy transferred} = \text{Power} \times \text{Time taken}
• E = Pt

To calculate time taken:

• \text{Time taken} = \frac{\text{Energy transferred}}{\text{Power}}
• t = \frac{E}{P}

Examples

A heater is rated at a power of 2000 W. How much energy does it transfer in 30 minutes?

• P = 2000\,W
• t = 30\,\text{minutes} = 30 \times 60\,s = 1800\,s
• E = Pt
• E = 2000\,W \times 1800\,s
• E = 3,600,000\,J

A machine transfers 5000 J of energy in 10 s. What is the power of the machine?

• E = 5000\,J
• t = 10\,s
• P = \frac{E}{t}
• P = \frac{5000\,J}{10\,s}
• P = 500\,W

A machine has a power of 100 W and transfers 2000 J of energy. How long does it take to transfer the energy?

• P = 100\,W
• E = 2000\,J
• t = \frac{E}{P}
• t = \frac{2000\,J}{100\,W}
• t = 20\,s