The rate at which energy is transferred is called power and the amount of energy that is usefully transferred is called efficiency. It is important to be able to calculate power and efficiency.

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

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.

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.