Energy and particles · GCSE Physics
Efficiency
Teacher-written GCSE Physics revision on efficiency: useful energy or power divided by total input, then × 100 for a percentage, with Sankey diagrams and why values cannot exceed 100%.
Efficiency = useful output ÷ total input. Multiply by 100 for a percentage. It has no unit and cannot be greater than 100%.
The important bits
What you need to know
- 1
Efficiency = useful energy output / total energy input, or useful power output / total power input. Keep joules with joules, or watts with watts.
- 2
As a percentage: efficiency = (useful / total) × 100. A 0.60 ratio is 60%. Write the ratio first, then convert if the question asks for a percentage.
- 3
Efficiency has no unit. It cannot exceed 1, or 100%, because you cannot get more useful energy out than you put in.
- 4
Wasted energy = total input − useful output. In a kettle the wasted store is usually thermal energy heating the kettle body and the kitchen air.
- 5
Sankey diagrams: the useful arrow’s width divided by the input arrow’s width is the efficiency. Measure or read the values; do not guess from the picture.
- 6
Reducing friction, lubricating, insulating, and matching the device to the job all raise efficiency by cutting dissipation to unwanted thermal stores.
- 7
A more efficient device still conserves energy. The “missing” percentage has not vanished; it has been dissipated.
- 8
Power form is often easier in electrical questions: efficiency = useful power / total power, with P in watts (W).
Quotations worth analysing
Short evidence. Real method.
“Efficiency = useful energy output / total energy input.”
The useful quantity must match the job: light from a lamp, kinetic store of a motor, thermal store of the water in a kettle — not the heating of the room.
“(useful / total) × 100”
Multiply only after the ratio is correct. Swapping useful and total gives a number bigger than 100%, which is an instant giveaway that the fraction is upside down.
“Energy is conserved even when a device is inefficient.”
Inefficiency is about usefulness, not about destruction. Examiners credit the sentence that names the wasted thermal store in the surroundings.
Go deeper
Useful is a judgement about the job, not about the joules
A 60% efficient kettle still conserves energy: 40% has gone to heating the kitchen. Those joules are real; they are just not the job you wanted. Decide what “useful” means before you divide. For a lamp, useful output is the light. For an electric motor lifting a load, useful output is the gain in gravitational potential store, mgh, not the humming and the warm casing. For a loudspeaker, useful output is the sound. If you put the wasted heating in the numerator you will invent an efficiency above 100% or a meaningless ratio. Write “useful = …” and “total = …” as two short lines, then divide, then × 100 if the question asked for a percentage.
Go deeper
Sankey diagrams are efficiency drawn as widths
The incoming arrow is the total. Split arrows are the useful and wasted outputs. If the input is drawn 10 cm wide and the useful output is 7 cm wide, efficiency is 0.70 or 70%. Students often read the wasted arrow as the useful one because it is labelled “heat” and heat feels like the point of a kettle. Read the question: heating the water is useful; heating the air is wasted. In six-mark evaluations, say how you would increase efficiency: reduce friction, add insulation, or stop the device wasting energy on a job it was not designed for. Do not write “make it more efficient” without a physical change.
See the idea in action
A motor is supplied with 5000 J electrically. It lifts a 20 kg load through 8.0 m. g = 10 N/kg. Useful output = mgh = 20 × 10 × 8.0 = 1600 J. Efficiency = useful / total = 1600 / 5000 = 0.32. As a percentage: (1600 / 5000) × 100 = 32%. Wasted energy = 5000 − 1600 = 3400 J, dissipated to thermal stores in the motor and the air. Energy is conserved; 32% is the useful fraction, not the fraction that “survived”.
Exam technique
Turn knowledge into marks
Write useful ÷ total, then × 100 if a percentage is required. Keep the units the same on top and bottom. If the answer is greater than 100%, you have inverted the fraction.
Common mistakes
Do not give these marks away
- 01
Calculating efficiency as total ÷ useful, or quoting a value over 100%.
- 02
Mixing joules on top with watts on the bottom.
- 03
Calling dissipated energy “destroyed”, or treating heating of the surroundings as useful for a lamp or a motor.
A lamp transfers 200 J electrically. 40 J is usefully transferred as light. What is its percentage efficiency?
A20%
B40%
C80%
D500%
Show the answer
20%. Efficiency = (useful / total) × 100 = (40 / 200) × 100 = 20%. The other 160 J is dissipated, usually as thermal energy.
Quick questions
If this is the bit you searched
How do you calculate efficiency?
Useful energy (or power) output divided by total energy (or power) input. Multiply by 100 for a percentage. It cannot be greater than 1, or 100%.
Can efficiency be greater than 100%?
Not for an ordinary device. That result means the fraction is upside down, or you have counted wasted energy as useful.
Should I use energy or power in the efficiency formula?
Either, as long as both the top and the bottom are the same type of quantity. Useful power over total power is often quicker in electrical questions.
How is efficiency shown on a Sankey diagram?
Compare arrow widths: useful output width divided by input width. The wasted arrows make up the rest, so the diagram still conserves energy.