Power

Two cranes might both lift the same load to the same height, transferring the same amount of energy. If one does it in half the time, it is doing so at a greater rate. That rate is power.

Power is the rate of energy transfer, or the rate of doing work. It is measured in watts (W).

Power tells you how fast energy is being transferred, not how much. A 60 W bulb and a 2000 W kettle both transfer energy electrically, but the kettle does so more than thirty times faster. A more powerful device transfers the same energy in less time.

The word work here means energy transferred by a force moving an object. Doing work at a fast rate and transferring energy at a fast rate are the same thing, which is why power can be defined in either way.

The watt links power directly to energy and time.

An energy transfer of 1 joule per second (1 J/s) equals a power of 1 watt (1 W).

So a device with a power of 100 W transfers 100 J of energy every second. A 2 kW (2000 W) heater transfers 2000 J each second.

Larger powers are written with prefixes:

Prefix	Symbol	Meaning	Example
kilo	kW	1000 W	Electric kettle
mega	MW	1 000 000 W	Power station generator

To convert a power in kilowatts to watts, multiply by 1000. Always work in watts, joules and seconds when substituting into the equations, converting any kilowatts or minutes first.

Power can be calculated from energy transferred or from work done, over the time taken.

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

In the first, $P$ is power in watts (W), $E$ is energy transferred in joules (J), and $t$ is time in seconds (s). In the second, $W$ is work done in joules (J). Since work done is simply energy transferred, the two equations are really the same relationship written with different symbols.

You must recall and apply both $P=E/t$ and $P=W/t$. Neither is given on the equation sheet.

Rearranging gives the energy transferred in a time $t$ as $E=Pt$, and the time for a transfer as $t=E/P$. Being fluent with all three forms saves time in the exam.

Worked example 1 — a device transfers 30 000 J of energy in 20 s. Find its power.

$P=\frac{E}{t}=\frac{30000}{20}=1500\text{W}$

Worked example 2 — a 2 kW microwave runs for 30 s. How much energy does it transfer?

First convert the power to watts: $2\text{kW}=2000\text{W}$. Then rearrange to $E=Pt$:

$E=Pt=2000\times 30=60000\text{J}=60\text{kJ}$

Worked example 3 — a crane does 2000 J of work lifting a load in 8 s. Find its power.

$P=\frac{W}{t}=\frac{2000}{8}=250\text{W}$

Convert kilowatts to watts and minutes to seconds before substituting. A power in kW or a time in minutes left unconverted is a common source of wrong answers.

The specification asks you to explain, with an example, that the same energy transfer at a faster rate means a greater power. Two motors lifting the same weight the same height make this concrete.

Both motors lift a load, doing the same work against gravity. Suppose each raises a 200 N weight through 5 m, so each does:

$W=Fs=200\times 5=1000\text{J}$

Motor A takes 10 s:

$P=\frac{W}{t}=\frac{1000}{10}=100\text{W}$

Motor B takes 5 s:

$P=\frac{W}{t}=\frac{1000}{5}=200\text{W}$

Motor B transfers the same 1000 J but in half the time, so its power is twice as large. This is the key idea: power depends on the rate of transfer, not just the total energy.

1. Confusing energy and power

Energy (joules) is the total transferred; power (watts) is how fast it is transferred. Read the question to see which is asked for, and check your unit matches.

2. Not converting kilowatts to watts

A 2 kW device is 2000 W. Substituting 2 instead of 2000 gives an answer a thousand times too small.

3. Leaving time in minutes

Time in $P=E/t$ must be in seconds. Multiply minutes by 60 first: 3 minutes is 180 s.

4. Thinking the equations are given

$P=E/t$ and $P=W/t$ must both be recalled from memory. They are not printed on the equation sheet.

5. Assuming more energy means more power

A device can transfer a large amount of energy at a low power if it takes a long time. Power compares energy against time, so always divide by the time taken.