# Power

When work is done on an object, energy is transferred. The at which this energy is transferred is called . So the more powerful a device is, the more energy it will transfer each second.

## Calculating power

The equation used to calculate the power is:

$power = \frac {work \\ done}{time \\ taken}$

$P = \frac {E}{t}$

This is when:

• power (P) is measured in watts (W)
• work done (E) is measured in joules (J)
• time (t) is measured in seconds (s)

One watt is equal to one joule per second (J/s). This means that for every extra joule that is transferred per second, the power increases by one watt.

### Example

Two electric motors are used to lift a 2 N weight through a vertical height of 10 m.

Motor one does this in 5 seconds.

Motor two does this in 10 seconds.

For both motors, the energy transferred - the work done - is 20 J.

$E = F \times d = 2 \times 10 = 20 \\ J$

For motor one:

$P = \frac {E}{t} = \frac {20}{5} = 4 \\ W$

For motor two:

$P = \frac {E}{t} = \frac {20}{10} = 2 \\ W$

Since twice as much energy is transferred by motor one each second, it is possible to say that motor one is twice as powerful as motor two.

Question

A hairdryer transfers 48,000 J of energy in one minute. What is the power rating of the hairdryer?

$P = \frac {E}{t}$

$P = \frac {48,000}{60}$

$P = 800 \\ W$

Power is the amount of energy that is transferred per second.