Power as a Rate

In physics, a rate tells you how much happens each second. Power is a rate: it measures how many joules of energy are transferred each second, or how many joules of work are done each second.

A high-power device does not magically create more energy. It transfers energy more quickly. For example, if two motors lift the same load through the same height, they do the same task. If motor A finishes in 4 s and motor B finishes in 8 s, motor A has the greater power because the same energy transfer happens in less time.

One watt means one joule transferred each second:

So a 50 W device transfers 50 J every second, while a 200 W device transfers 200 J every second.

Recall Equations and Units

There are two official power equations in this lesson. They have the same structure because both energy transferred and work done are measured in joules.

Use $P = \frac{E}{t}$ when the question gives an energy transferred. Use $P = \frac{W}{t}$ when the question gives work done. The symbols and units are:

Be careful with the letter $W$. In $P = \frac{W}{t}$, $W$ means work done. In the unit column, W means watts, the unit of power. GCSE questions usually make the meaning clear from the context.

If time is given in minutes, convert it to seconds before substituting:

Calculating Power

A calculation is usually safest if you write the equation first, substitute with units, then calculate the answer.

Worked example: a motor transfers 1200 J of energy in 6 s. Calculate the power of the motor.

The motor transfers 200 J every second.

Now compare that with a motor that transfers the same 1200 J in 3 s:

The same energy transfer in half the time gives twice the power.

Rearranging for Energy, Work, or Time

The power equations can be rearranged when power is not the unknown. Multiplying both sides by time gives:

and

This means the total energy transferred or work done depends on both power and time. A higher-power device used briefly might transfer less total energy than a lower-power device used for a long time.

Worked example: a 75 W motor runs for 20 s. Calculate the work done.

To find time, rearrange to $t = \frac{E}{P}$ or $t = \frac{W}{P}$.

Example: a device transfers 2400 J at a power of 300 W.

Comparing Power

Power comparisons are about rate, not just total energy. Read the comparison carefully:

The official motor example is a useful model. Suppose two electric motors both lift the same weight through the same height. The work done is the same for both motors because the lifting task is the same. The motor that lifts the weight faster has the greater power because it does the same work in a shorter time.

For a numerical comparison, calculate the power for each machine using the same equation, then compare the answers.

Example:

• Motor A does 600 J of work in 5 s: $P = 600 \div 5 = 120\text{ W}$
• Motor B does 600 J of work in 10 s: $P = 600 \div 10 = 60\text{ W}$

Motor A is twice as powerful as motor B because it does the same work in half the time.

Exam Habits and Misconceptions

For power calculations, keep the method tidy:

1. Choose $P = \frac{E}{t}$ or $P = \frac{W}{t}$.
2. Convert time into seconds if needed.
3. Substitute numbers in joules and seconds.
4. Give the answer with the correct unit.

Common mistakes usually come from mixing up symbols or rates:

• Do not use minutes directly unless the equation has been adapted; GCSE power equations use seconds.
• Do not confuse power with total energy. Power is a rate.
• Do not confuse $W$ for work done with W for watts.
• Do not assume the higher-power device always transfers more total energy; time matters too.
• Do not bring in unrelated equations unless the question explicitly supplies them.