Power and Efficiency KS3 Physics

Two machines can do the same job, but one might do it ten times faster and waste far less energy. Power measures how quickly energy is transferred; efficiency tells you what fraction of that energy is actually useful. These two quantities are among the most practical in all of physics.

What is power and how is it measured?

Power is the rate at which energy is transferred — how much energy is transferred per second.

Equation:

Power (W) = Energy transferred (J) ÷ Time (s) P = E ÷ t

The unit of power is the watt (W), named after James Watt. One watt means one joule of energy is transferred every second.

Larger units used in practice:

• Kilowatt (kW): 1 kW = 1,000 W (used for household appliances)
• Megawatt (MW): 1 MW = 1,000,000 W (used for power stations)
• Gigawatt (GW): 1 GW = 1,000,000,000 W (used for national electricity demand)

Typical power values to know:

How do you calculate power?

Worked example 1: A motor transfers 12,000 J of energy in 40 seconds. What is its power?

P = E ÷ t = 12,000 ÷ 40 = 300 W

Worked example 2: A weightlifter lifts a barbell, doing 2,500 J of work in 5 seconds. What is their power output?

P = E ÷ t = 2,500 ÷ 5 = 500 W

Rearranging the equation: If you know power and time and want the energy transferred: E = P × t

If you know power and energy and want the time: t = E ÷ P

Always check your units — if energy is in joules and time in seconds, power comes out in watts. If time is in hours and power is in kilowatts, energy comes out in kilowatt-hours (kWh).

What is a kilowatt-hour and how is it used?

A kilowatt-hour (kWh) is the unit used on electricity bills. It is the energy transferred by a 1 kW device running for 1 hour:

Energy (kWh) = Power (kW) × Time (h)

Worked example: A 2 kW electric kettle runs for 3 minutes (= 0.05 hours). How much energy does it use in kWh?

Energy = 2 × 0.05 = 0.1 kWh

If electricity costs 25p per kWh (typical in the UK in 2026): Cost = 0.1 × 25p = 2.5p to boil the kettle once.

Converting to joules: 1 kWh = 3,600,000 J = 3.6 MJ

What is efficiency and why is no device 100% efficient?

Efficiency is the proportion of total energy input that is transferred usefully. No real device is 100% efficient because some energy is always transferred to the surroundings in a less useful form — usually as heat (thermal energy) due to friction or electrical resistance, and sometimes as sound.

Equation:

Efficiency = (Useful energy output ÷ Total energy input) × 100%

Or equivalently:

Efficiency = (Useful power output ÷ Total power input) × 100%

Efficiency is a ratio and has no unit. It is expressed as a percentage (if you multiply by 100) or as a decimal between 0 and 1.

How do you calculate efficiency?

Worked example 1: An electric motor receives 5,000 J of electrical energy. It transfers 3,500 J as kinetic energy (useful) and 1,500 J as heat (wasted).

Efficiency = (3,500 ÷ 5,000) × 100 = 70%

Worked example 2: A petrol car engine receives 1,000 J from burning fuel. Only 250 J drives the wheels.

Efficiency = (250 ÷ 1,000) × 100 = 25%

The remaining 750 J is wasted, mostly as heat in the engine and exhaust gases.

Worked example 3 — given efficiency, find useful output: A pump is 60% efficient. Its motor inputs 800 W. What is the useful power output?

0.60 = Useful power ÷ 800 Useful power = 0.60 × 800 = 480 W

What is a Sankey diagram?

A Sankey diagram is a visual representation of energy transfers. The width of each arrow is proportional to the amount of energy it represents.

• Energy always flows left to right.
• The main arrow (energy input) enters from the left.
• Useful energy output arrow continues to the right.
• Wasted energy arrows branch off — usually downwards.
• The total width of all output arrows equals the width of the input arrow (energy is conserved).

Example — LED bulb (10 W input):

• 9 W useful light energy (thick arrow continuing right)
• 1 W wasted heat energy (thin arrow downwards)
• Efficiency = 9/10 × 100% = 90%

Example — incandescent bulb (60 W input):

• 6 W useful light energy (thin arrow right)
• 54 W wasted heat energy (thick arrow down)
• Efficiency = 6/60 × 100% = 10%

This comparison explains why LED bulbs have replaced incandescent bulbs for energy saving.

How can efficiency be improved?

Efficiency is improved by reducing energy wasted in non-useful forms:

No improvement can ever make efficiency 100% — some energy is always lost to the surroundings as heat due to the second law of thermodynamics (not required at KS3, but worth knowing).

Frequently asked questions

What is the difference between energy and power?

Energy is the total amount transferred — measured in joules (J) or kilowatt-hours (kWh). Power is the rate at which energy is transferred — measured in watts (W). A 100 W light bulb running for 10 hours transfers 1 kWh of energy. A 200 W motor running for 5 hours also transfers 1 kWh — the same total energy, but at twice the power (twice as fast). Think of energy as the total amount of "work done" and power as how quickly it is being done.

Why can't a machine ever be 100% efficient?

In any real machine, some energy is always transferred to the surroundings as heat due to friction between moving parts or electrical resistance in wires. This is an unavoidable consequence of the second law of thermodynamics: thermal energy always spreads from hot to cold regions and cannot be completely recaptured. Even the most advanced electric motors reach efficiencies of 95–97% — impressive but never 100%. The wasted energy is not destroyed (energy is always conserved); it is simply spread out as low-grade heat that is difficult or impossible to use for anything useful.

How do you read a Sankey diagram in an exam?

First check the units (joules or watts). Find the input arrow on the left — this is the total. Find the useful output arrow (often labelled or the one continuing straight). Wasted outputs are usually the other arrows, often angled downwards. To find efficiency: divide useful output by the total input and multiply by 100. To find the missing wasted energy: total input − useful output = wasted. Remember, the widths of all output arrows must add up to the width of the input arrow.

Why are kettles almost always rated at around 2,000–3,000 W?

A kettle boils water using an electrical heating element. The higher the power, the faster the water heats up. 2–3 kW is the practical sweet spot: enough power to boil a litre of water in about 2–3 minutes (convenient for the user) without drawing so much current that it would trip a standard 13-amp household fuse (which limits UK kettle power to a maximum of about 3,120 W at 240 V). Running at lower power (e.g. 500 W) would mean waiting 10–12 minutes to boil the same water — inconvenient but no less energy-efficient overall, since the same energy (2 × 60 × 60 × 500 = 3.6 MJ) is still used.

Professor Newton at aitutors.me can walk you through power and efficiency calculations step by step, help you draw and read Sankey diagrams, and quiz you until both equations feel automatic.