1.1.4 Power as the rate of energy transfer

What is power?

1. Power describes how quickly an energy transfer takes place, and a device is more powerful if it transfers more energy each second.
2. Two devices can transfer the same total energy but have different powers, and the one that finishes in less time has the greater power.
3. The unit of power is the watt, symbol $W$.

Calculating power from energy transferred

1. Calculate power with $P=\frac{E}{t}$.
2. Here $P$ is the power in $W$, $E$ is the energy transferred in $J$, and $t$ is the time in $s$.
3. Dividing the energy transferred by the time gives the number of joules transferred each second.

Calculating power from work done

1. You can also calculate power from the work done with $P=\frac{W}{t}$.
2. Here $W$ is the work done in $J$ and $t$ is the time in $s$.
3. Work done is an energy transfer, so both power equations describe the same idea: the energy transferred each second.
4. Take care with the letter $W$: in an equation it stands for work done, but after a number $W$ is the unit watts.

Comparing the power of two motors

1. Suppose two motors lift the same weight through the same height, so they do the same work.
2. If motor A takes $10s$ and motor B takes $5s$, motor B is more powerful because it does the same work in half the time.
3. A full comparison names both quantities: both motors do the same work, but motor B completes it in less time, so it transfers energy at a greater rate.