Power

Power describes how quickly work is done or energy is transferred. If the same amount of energy is transferred in less time, the power is greater.

For work done over a time interval, average power is the work done divided by the time taken:

P = \frac{W}{t}

Here, $$$P$$$ is average power, $$$W$$$ is work done and $$$t$$$ is the time interval. Work done measures energy transferred, so the same relationship can be written using the energy transferred, $\Delta E$ :

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

Power is measured in watts, with the unit symbol $\text{W}$ . One watt is one joule of energy transferred per second: $1,\text{W} = 1,\text{J/s}$ . The symbol $$$W$$$ in the first equation represents work done; it is not the unit watt.

For example, transferring $100,\text{J}$ in $10,\text{s}$ gives an average power of $10,\text{W}$ . Transferring the same energy in $5,\text{s}$ gives $20,\text{W}$ : halving the time doubles the power.

Rearranging the power equations

The power equations can be rearranged to find work done or energy transferred when power and time are known:

W = Pt \qquad \Delta E = Pt

They can also be rearranged to find the time taken:

t = \frac{W}{P} \qquad t = \frac{\Delta E}{P}