Power and Efficiency

This lesson covers power — the rate of energy transfer — and efficiency — the proportion of energy that is usefully transferred. Both are fundamental concepts in the AQA GCSE Physics specification (Section 4.1) and are tested with both calculation and explanation questions.

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What Is Power?

Power is the rate at which energy is transferred or the rate at which work is done. It tells you how quickly a device converts energy from one form to another.

An appliance with a high power rating transfers energy quickly. An appliance with a low power rating transfers energy slowly.

Power Equations

There are two key equations for power:

P = E / t

Where:

• P = power in watts (W)
• E = energy transferred in joules (J)
• t = time in seconds (s)

P = W / t

Where:

• W = work done in joules (J)

Quantity	Symbol	Unit
Power	P	watts (W)
Energy transferred	E	joules (J)
Work done	W	joules (J)
Time	t	seconds (s)

1 watt = 1 joule per second (1 W = 1 J/s)

For larger values:

• 1 kilowatt (kW) = 1000 W
• 1 megawatt (MW) = 1 000 000 W

Exam Tip: Power is energy transferred per second. If a question asks "how much energy is transferred in 5 minutes," remember to convert to seconds first (5 minutes = 300 seconds). This is a very common source of lost marks.

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Worked Examples — Power

Example 1: A kettle transfers 460 000 J of energy in 200 seconds. Calculate its power.

P = E / t P = 460 000 / 200 P = 2300 W (or 2.3 kW)

Example 2: A 60 W light bulb is left on for 2 hours. How much energy does it transfer?

First convert time: 2 hours = 2 x 3600 = 7200 seconds

E = P x t E = 60 x 7200 E = 432 000 J (or 432 kJ)

Example 3: An electric motor has a power of 500 W. It does 15 000 J of useful work lifting a load. How long does this take?

t = E / P t = 15 000 / 500 t = 30 seconds

Exam Tip: You should be able to rearrange the power equation for E or t. Use the formula triangle if it helps: E is on top, P and t are on the bottom.

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Comparing Power Ratings

Appliance	Typical Power Rating	Energy Transfer
LED light bulb	10 W	Electrical to light and some internal energy
Filament light bulb	60 W	Electrical to light and a lot of internal energy
Laptop	50 W	Electrical to light, sound, and internal energy
Kettle	2000-3000 W	Electrical to internal (thermal) energy of water
Electric shower	7000-10 000 W	Electrical to internal (thermal) energy of water
Washing machine	500-2000 W	Electrical to kinetic and internal energy

A higher power rating means the appliance uses energy faster. This does not necessarily mean it wastes more energy — that depends on its efficiency.

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What Is Efficiency?

Efficiency is a measure of how much of the input energy is usefully transferred. No device is 100% efficient because some energy is always dissipated (wasted).

Efficiency Equations

Efficiency = useful output energy transfer / total input energy transfer

Efficiency = useful output power / total input power

Efficiency can be expressed as a decimal (e.g., 0.75) or as a percentage (e.g., 75%).

To convert from decimal to percentage: multiply by 100. To convert from percentage to decimal: divide by 100.

Expression	Decimal	Percentage
3/4 of energy is useful	0.75	75%
1/2 of energy is useful	0.50	50%
9/10 of energy is useful	0.90	90%

Exam Tip: Efficiency can NEVER be greater than 1 (or 100%). If your calculated efficiency is greater than 1, you have made an error — check that you used useful OUTPUT in the numerator and total INPUT in the denominator.

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Worked Examples — Efficiency

Example 1: A motor uses 500 J of electrical energy and does 400 J of useful work. Calculate its efficiency.

Efficiency = useful output / total input Efficiency = 400 / 500 Efficiency = 0.80 (or 80%)

Example 2: An LED bulb has an input power of 10 W and a useful light output of 8.5 W. Calculate its efficiency.

Efficiency = useful output power / total input power Efficiency = 8.5 / 10 Efficiency = 0.85 (or 85%)

Example 3: A car engine is 30% efficient. If it receives 50 000 J of chemical energy from fuel, how much useful kinetic energy is produced?

Useful output = efficiency x total input Useful output = 0.30 x 50 000 Useful output = 15 000 J

How much energy is wasted? Wasted = total input - useful output = 50 000 - 15 000 = 35 000 J

graph LR
    A["Total input energy: 50 000 J (Chemical)"] --> B["Useful output: 15 000 J (Kinetic)"]
    A --> C["Wasted: 35 000 J (Internal energy of engine, exhaust, friction)"]
    style B fill:#aaffaa,stroke:#006600
    style C fill:#ffcccc,stroke:#cc0000

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Sankey Diagrams

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

Key Features

Feature	Meaning
Total width of input arrow	Total energy input
Width of useful output arrow	Useful energy transferred
Width of wasted arrow(s)	Wasted (dissipated) energy
Arrows drawn to scale	Widths are proportional to energy values

Reading a Sankey Diagram

For a light bulb with 100 J input, 10 J useful light, and 90 J wasted heat:

graph LR
    A["100 J Electrical energy input"] --> B["10 J Light output (useful)"]
    A --> C["90 J Internal energy (wasted)"]
    style B fill:#aaffaa,stroke:#006600
    style C fill:#ffcccc,stroke:#cc0000

From a Sankey diagram, you can calculate efficiency: Efficiency = useful output / total input = 10 / 100 = 0.10 (or 10%)

Exam Tip: When drawing Sankey diagrams, the arrows MUST be drawn to scale. If the total input is 200 J, the useful output is 150 J, and waste is 50 J, then the useful arrow should be three times wider than the waste arrow. Use a ruler and label all values.

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Increasing Efficiency

Devices can be made more efficient by reducing wasted energy transfers.