Power Equation: Joules per Second Explained

Power is the rate at which energy is transferred. The power equation is $P=\frac{E}{t}$, where $P$ is power in watts ($\mathrm{W}$), $E$ is energy transferred in joules ($\mathrm{J}$), and $t$ is time in seconds ($\mathrm{s}$). Therefore, $1\mathrm{W}=1J/s$. A device has a power of one watt when it transfers one joule of energy every second.

How to use the equation

To calculate power, divide the total energy transferred by the time taken:

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

First check that the energy is measured in joules and the time is measured in seconds. Then substitute the values, calculate the answer, and give the unit as watts.

For example, a motor transfers $600\mathrm{J}$ of energy in $30\mathrm{s}$. Its power is:

$$P=\frac{600\mathrm{J}}{30\mathrm{s}}=20\mathrm{W}.$$

This means the motor transfers energy at a rate of $20\mathrm{J}$ each second. It does not mean that the motor transfers only $20\mathrm{J}$ altogether; the total energy transferred is $600\mathrm{J}$.

Power is useful for comparing devices that do the same job at different speeds. If another motor transfers the same $600\mathrm{J}$ in $60\mathrm{s}$, its power is $10\mathrm{W}$. Both motors transfer the same amount of energy, but the first transfers it in half the time, so its power is twice as great. Faster energy transfer means greater power.

Rearranging the equation

If power and time are known, you can calculate energy by rearranging the equation:

$$E=Pt.$$

For example, a $50\mathrm{W}$ appliance switched on for $10\mathrm{s}$ transfers:

$$E=50\mathrm{W}\times 10\mathrm{s}=500\mathrm{J}.$$

You can also calculate power from work done using $P=\frac{W}{t}$, where $W$ represents work done in joules. Work done is energy transferred by a force.

Common exam mistake: using minutes instead of seconds. If a question gives $2$ minutes, convert it to $120\mathrm{s}$ before substituting. Also, do not confuse energy with power: joules measure the amount transferred, while watts measure how quickly it is transferred. This explanation uses the AQA GCSE separate Physics Energy topic and applies at both Foundation and Higher tier.