Power is the energy transferred each second: P = E ÷ t. It appears whenever a question gives a device rating in watts, a time and an amount of energy, and asks you to find the missing one.
This lesson is the base of power and energy resources. It builds on energy and efficiency from work, energy and efficiency.
What does the equation say?
Power (W) = energy transferred (J) ÷ time taken (s). One watt is one joule per second. A 60 W lamp transfers 60 J of electrical energy every second, to light and thermal energy.
Rearranged, the equation gives two more forms: E = P × t and t = E ÷ P. A triangle with E on top and P and t below is enough to keep these straight, as long as you write the unit with every number.
Which units should I use?
Pick one set and keep to it.
| Set | Power | Energy | Time |
|---|---|---|---|
| SI | watt (W) | joule (J) | second (s) |
| Household | kilowatt (kW) | kilowatt-hour (kWh) | hour (h) |
Conversions to remember: 1 kW = 1000 W, 1 kWh = 3.6 MJ, 1 min = 60 s, 1 h = 3600 s. To decide how many significant figures your final answer deserves, the bounds and rounding explainer shows how rounded readings limit precision.
Worked example
A small electric motor transfers 4500 J of energy in 30 s. A student also asks how long a 150 W motor needs to transfer 9000 J. (Invented example data.)
Part (a), power: P = E ÷ t = 4500 ÷ 30 = 150 W.
Part (b), time: t = E ÷ P = 9000 ÷ 150 = 60 s.
Check: 150 W for 60 s gives 150 × 60 = 9000 J, which matches the question.
Now a kilowatt example. A 2.4 kW oven element transfers 7.2 MJ.
Convert: 7.2 MJ = 7 200 000 J and 2.4 kW = 2400 W. Then t = 7 200 000 ÷ 2400 = 3000 s, which is 50 minutes.
The mistake to watch for
A common slip is to use minutes directly. Suppose a heater transfers 360 kJ in 2.5 minutes.
Mistaken answer: P = 360 000 ÷ 2.5 = 144 000 W
The time was left in minutes, so the answer is joules per minute, not watts.
The correction is to convert first: 2.5 min = 150 s, so P = 360 000 ÷ 150 = 2400 W, or 2.4 kW. A quick sense check helps: a heater of 144 kW would be far larger than a household kettle, so the first answer cannot be realistic.
Check yourself
Try these, then open each answer.
1. A pump transfers 12 000 J in 40 s. What is its power?
Show answer
P = 12 000 ÷ 40 = 300 W.
2. A 60 W lamp is on for 5.0 minutes. How much energy does it transfer, in joules?
Show answer
5.0 min = 300 s. E = 60 × 300 = 18 000 J (18 kJ).
3. A 0.50 kW device runs for 3.0 hours. How much energy does it transfer, in kWh and in MJ?
Show answer
E = 0.50 × 3.0 = 1.5 kWh. Then 1.5 × 3.6 = 5.4 MJ.
Where this leads next
Next, compare two devices over an equal task, where a higher power rating does not always mean more energy used. The whole set is tested in the power and energy resources practice set.
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