AQA · GCSE · Physics
Course version: 8463 · Version from Sept 2016
Efficiency: efficiency = useful power output / total power input
This equation defines efficiency as the fraction of the total power supplied to a device that is transferred usefully.
Checked against the AQA 8463 specification (opens in a new tab) on .
- Point 4 of 7
Study notes
From the checked teaching notes for this specification point.
The idea
This equation defines efficiency as the fraction of the total power supplied to a device that is transferred usefully. Power is measured in watts, so if a lamp takes 60 W from the supply and radiates 12 W as useful light, its efficiency is 12 ÷ 60 = 0.20, which is 20%. The other 48 W is wasted, mostly heating the lamp and surroundings. Because energy is conserved, the useful power output cannot exceed the total power input, so efficiency lies between 0 and 1, or between 0% and 100%. A device with efficiency 0.20 converts one fifth of the supplied power into the intended form; the rest is dissipated. The same numerical value is obtained whether you use power or energy, because power is energy transferred each second.
What earns the marks
- Quote or select the equation efficiency = useful power output ÷ total power input.
- Identify the useful power output and total power input with correct values and units.
- Substitute the values into the equation and calculate the efficiency as a decimal or percentage.
- Interpret the result, for example stating that 20% of the input power is transferred usefully.
- Use conservation of energy to explain why efficiency cannot exceed 1 or 100%.
Common mistakes and how to put them right
Using energy values in joules in place of power values in watts without converting.
Put it right by ensuring both quantities in the fraction are powers, or by using the energy version of the equation consistently.
Mixing units, such as kilowatts on top and watts underneath.
Put it right by converting both quantities to the same unit before dividing.
Reporting efficiency as a whole number of watts.
Put it right by recognising that efficiency is a ratio with no unit, expressed as a decimal or percentage.
Exam tips
- Write the equation exactly as given, then substitute numbers beneath it so the examiner can follow your working.
- If the answer is a recurring decimal, give it to a sensible number of significant figures, usually two or three, unless told otherwise.
- When asked to improve efficiency, link your suggestion to reducing the wasted power transfer rather than simply repeating the equation.
Try the lesson
The start of the Efficiency: efficiency = useful power output / total power input lesson, made from checked teaching notes for this specification point.
Have a go first
A heater has a useful power output of 400 W and a total power input of 500 W. What is its efficiency?
Listen
This equation defines efficiency as the fraction of the total power supplied to a device that is transferred usefully. Power is measured in watts, so if a lamp takes 60 W from the supply and radiates 12 W as useful light, its efficiency is 12 ÷ 60 = 0.20, which is 20%. The other 48 W is wasted, mostly heating the lamp and surroundings. Because energy is conserved, the useful power output cannot exceed the total power input, so efficiency lies between 0 and 1, or between 0% and 100%. A device with efficiency 0.20 converts one fifth of the supplied power into the intended form; the rest is dissipated. The same numerical value is obtained whether you use power or energy, because power is energy transferred each second. A strong answer earns marks for these points. Quote or select the equation efficiency = useful power output ÷ total power input. Identify the useful power output and total power input with correct values and units. Substitute the values into the equation and calculate the efficiency as a decimal or percentage. Interpret the result, for example stating that 20% of the input power is transferred usefully. A common slip: Using energy values in joules in place of power values in watts without converting. Instead, ensuring both quantities in the fraction are powers, or by using the energy version of the equation consistently. Exam tip: Write the equation exactly as given, then substitute numbers beneath it so the examiner can follow your working.
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