Efficiency
Master Efficiency for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Efficiency is the fraction of input energy transferred usefully, found by dividing useful output energy by total input energy.
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Topic overview
Efficiency measures how much of the energy supplied to a device is transferred usefully. It is calculated as useful output energy transfer divided by total input energy transfer.
It can also be calculated using power: useful power output divided by total power input. Multiplying by 100 gives the answer as a percentage.
Efficiency can never exceed 1, or 100 per cent, because a device cannot transfer more useful energy than it is supplied with. A value above 100 per cent means an arithmetic error. No device is perfectly efficient, because some energy is always dissipated, usually to thermal stores.
Revision notes
The equations
Efficiency = useful output energy transfer ÷ total input energy transfer.
Efficiency = useful power output ÷ total power input. Multiply by 100 for a percentage. Efficiency has no units because it is a ratio.
The limit
Efficiency can never be greater than 1, or 100 per cent.
A device cannot transfer more useful energy than it receives, because energy is conserved. A calculated value above 100 per cent means a mistake has been made.
Improving efficiency
Reducing unwanted energy transfers increases efficiency.
Lubricating moving parts reduces friction. Insulating reduces thermal transfer. Streamlining reduces air resistance. Each means a greater proportion of the input energy is transferred usefully.
Key points
- Efficiency = useful output ÷ total input.
- It can be calculated with energy or with power.
- Multiply by 100 for a percentage.
- Efficiency has no units.
- Efficiency can never exceed 100 per cent.
- Reducing dissipation increases efficiency.
Worked examples
Example 1
A device is supplied with 500 J and usefully transfers 300 J. Calculate its efficiency as a percentage. [2 marks]
Model answer
Efficiency = useful output ÷ total input × 100 = 300 ÷ 500 × 100 (1 mark) = 60 per cent (1 mark).
Example 2
A motor has a useful power output of 40 W and a total power input of 50 W. Calculate its efficiency. [2 marks]
Model answer
Efficiency = useful power output ÷ total power input = 40 ÷ 50 (1 mark) = 0.8, or 80 per cent (1 mark).
Example 3
Explain why no device can be 100 per cent efficient. [2 marks]
Model answer
Some energy is always dissipated to the surroundings, usually to thermal energy stores (1 mark), so not all of the input energy can be transferred usefully (1 mark).
Common mistakes
Getting the fraction upside down.
It is useful output ÷ total input, so the answer is 1 or less.
Giving an efficiency above 100 per cent.
This is impossible and indicates an arithmetic error.
Giving efficiency a unit.
It is a ratio, so it has no units, though it may be written as a percentage.
Forgetting to multiply by 100.
If the question asks for a percentage, the ratio must be multiplied by 100.
Exam tips
- Put useful output on top of the fraction.
- Check the answer is 100 per cent or below.
- Multiply by 100 only if a percentage is asked for.
- Explain imperfect efficiency through dissipation.
Key terms
- Efficiency
- The proportion of input energy transferred usefully.
- Useful output
- The energy transferred in the way intended.
- Total input
- All the energy supplied to a device.
- Dissipation
- Energy transferred to the surroundings unusefully.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.