Energy and power
Two workers can lift identical loads to the same height and do exactly the same amount of work — yet if one finishes in half the time, everyone calls that worker "more powerful." That everyday word hides a precise physics idea: power is not how much work gets done, but how fast it gets done. A tiny motor left running for hours can move as much total energy as a big motor running for a minute; only their power ratings, and hence their speed of working, differ. This article builds power from the definition up: the formula , its SI unit the watt, and the sharp distinction between energy (a total amount) and power (a rate). We reuse and extend the two worked examples from the syllabus — a 6000 J motor and the Amit-versus-Sonal comparison — so every number here matches what you have already checked once. By the end you should be able to move confidently between work, time and power in either direction, and explain in one line why a higher wattage does not automatically mean more total energy used.
Power is the rate of doing work, , measured in watts (one watt equals one joule per second), and it is a completely different quantity from energy itself — the total amount transferred.
The core idea
Power tells you speed, not size. Work and energy answer "how much?"; power answers "how fast?" A person, machine or appliance doing a fixed amount of work in less time is developing more power, even though the total work done has not changed at all. Formally, power is defined as work done per unit time:
where: is power (watts, W), is the work done or energy transferred (joules, J), and is the time taken (seconds, s).
The SI unit is the watt. One watt is the power developed when one joule of work is done in one second:
Rearranging the same relation gives two other useful forms. If you know power and time, the work done is ; if you know power and work, the time taken is . All three are the same equation written three ways — memorising one and rearranging is safer than memorising three.
Why "more powerful" does not mean "does more work." Two agents can do identical total work (identical energy) while having very different power, simply because they take different times. Equally, a low-power device left running long enough can transfer more total energy than a high-power device that runs only briefly. Power compares rates; only work (or energy) compares totals. Keeping this straight is the single most exam-relevant idea in this chapter.
Reading appliance labels. Every household appliance carries a power rating in watts — a small table fan might be rated near 60 W, a large water pump several hundred watts. A higher wattage means the appliance can transfer energy faster, but the rating alone does not tell you the total energy it will use — for that you also need the running time, via . A 60 W fan run for a long evening can easily use more total energy than a 300 W kettle boiled for a minute.
The goal is to show that the one relation can always be rearranged to find whichever quantity — power, work, or time — is missing from a question, and then to use that rearranged form to find how long a differently-rated motor takes to do the same 6000 J of work that the syllabus example already checked, so the new number stays anchored to a value you have seen before.
Step 1. Start from the definition of power as work done per unit time, . This says power is found by dividing the total work by the total time it took — a single division, provided the work is done at a steady rate (which is all this chapter asks you to assume).
Step 2. Multiply both sides by to isolate work: , which simplifies to . This form is the one to use when power and time are known and work is the unknown — for instance, finding how much work a labelled appliance does if left running for a stated time.
Step 3. Divide both sides of by instead, to isolate time: . This form answers "how long will it take a machine of known power to do a given amount of work?" — exactly the question an exam asks when it gives you a power rating and a work target.
Step 4. Apply Step 3 to a new but related situation. The syllabus example already established that a motor doing of work in has power . Suppose instead a more powerful motor, rated at , must do the same 6000 J of work. Using : the more powerful motor finishes the identical job in 24 seconds instead of 30 — six seconds faster, exactly what a higher power rating should buy you.
Worked example
Question: A 250 W motor is used to do 6000 J of work (the same work as the syllabus motor example). How long does it take, and how does this compare with the original 200 W motor that did the same work in 30 s?
Step 1. Write down what is known: , . The unknown is time, so use the rearranged formula .
Step 2. Substitute: .
Step 3. Compare with the original motor: the 200 W motor took 30 s to do the same 6000 J, while the 250 W motor takes only 24 s. Both motors do exactly the same total work (6000 J, the same energy transferred), but the more powerful motor finishes 6 seconds sooner.
The 250 W motor takes 24 seconds — 6 seconds less than the 200 W motor — to do the same 6000 J of work.
Competitive stretch
If the same 250 W motor is instead run for the original 30 s (the time the 200 W motor needed), how much work does it do? Using — 1500 J more than the 200 W motor managed in that same time, because the extra power does extra work every second it runs.
Common traps
- Confusing energy or work, a total quantity in joules, with power, a rate in watts — always ask whether the question wants "how much" or "how fast."
- Assuming more total work automatically means more power; power also depends on the time taken, so less time for the same work means greater power.
- Forgetting to convert time into seconds before substituting into if a problem states time in minutes.
- Assuming a higher power rating on an appliance always means more total energy used — total energy also needs the running time, via .
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If two machines do the same work, does the faster one always use more energy?
No. Doing work faster changes the power, not the total energy. Both machines transfer exactly the same energy, , because the job done is identical; only the time taken differs, so their powers differ. The faster machine simply reaches that same energy total sooner. Total energy used depends on how much work was done, not on how quickly it was done.
Why does a small appliance sometimes use more total energy than a powerful one?
Because total energy is , and it depends on both power and time, not power alone. A 60 W fan left running for several hours transfers more total energy than a 2000 W kettle boiled for two minutes, since the fan's much longer running time outweighs its lower wattage. The power rating alone tells you the rate, never the total, unless you also know how long the device runs.
Do I ever need to bring force, distance or kinetic energy into a power question at this level?
Not in this chapter. Here, power questions are single-step substitutions into (or its rearrangements and ), using a work value already given in joules. Multi-step numericals that first compute work from force and distance, or that combine power with kinetic or potential energy, go beyond the ICSE Class 8 syllabus and belong to later, more advanced physics.