4.16-4.17 - Power

What power means

In physics, power is not just a word for strength, and it is not the same as force (measured in newtons) or energy (measured in joules). It is a rate: it tells you how much energy is transferred each second, or how much work is done each second.

The unit of power is the watt, symbol $W$. A power of $1 W$ means that $1 J$ of energy is transferred every second:

A higher power means a faster rate of energy transfer. It does not automatically mean a larger total energy transfer, because the total also depends on how long the transfer lasts.

[DIAGRAM: asset_name: Power - diagram 01; asset_slug: p40_power__diagram_01; recommended_method: matplotlib; description: NovaLearn pale-palette energy/J against time/s plot with exact constant-power lines from the origin to 1000 J and 500 J at 10 s, external 100 W and 50 W labels and a leader showing greater slope means greater power.]

In the chart, both lines start at zero because no energy has been transferred at $t = 0 s$. The $100 W$ line is steeper than the $50 W$ line, so it transfers energy twice as fast. The gradient of each line is its power: the $100 W$ line rises by $1000 J$ in $10 s$, and $1000 / 10 = 100 W$.

Reading the chart in both directions shows what a greater power means. At the same time, $10 s$, the $100 W$ line has reached $1000 J$ but the $50 W$ line only $500 J$: more energy in the same time. For the same energy, $500 J$, the $100 W$ line takes $5 s$ but the $50 W$ line takes $10 s$: the same energy in less time.

Using the equation

The required relationship is:

In this equation:

• $P$ is power in watts, $W$
• $W$ is work done or energy transferred in joules, $J$
• $t$ is time taken in seconds, $s$

This relationship is not on Edexcel's list of equations you must recall, so it is given in the exam. You still need to choose it and rearrange it yourself.

The symbol $W$ can be confusing because it is used in two different ways. In the equation, italic $W$ means work done. After a number, $W$ is the unit watt. For example, $W = 600 J$ is work done, while $P = 60 W$ is power.

Worked example: a winch transfers $2400 J$ of energy in $12 s$. Calculate its power.

So the winch transfers energy at a rate of $200 J$ every second.