Efficiency: Efficiency may also be calculated using the equation:

The idea

Efficiency compares the useful energy or power transferred by a device with the total energy or power supplied to it. The word 'also' signals that this is an alternative route: you may already know efficiency = useful output / total input using energy in joules, and the same idea applies using power in watts. Because power is energy transferred each second, dividing useful power output by total power input gives the same fraction as dividing useful energy by total energy over the same time. For example, a motor drawing 500 W and delivering 350 W usefully has efficiency 350 / 500 = 0.70, or 70%. The remaining 150 W is wasted, often as heating of surroundings. Always identify which value is useful and which is total before substituting, and remember efficiency has no unit.

What earns the marks

• State that efficiency compares useful output with total input and can be found from either energy or power values.
• Identify the useful power output and the total power input from the information given, in watts.
• Substitute correctly into efficiency = useful power output / total power input.
• Evaluate the fraction and express the result either as a decimal or as a percentage.
• Recognise that wasted power is the difference between total power input and useful power output, and that efficiency has no unit.

Common mistakes and how to put them right

• Dividing total power input by useful power output instead of the other way round.

  Put it right by checking that the fraction is less than 1 for any real device.

• Mixing units, such as using useful energy in joules with total power in watts.

  Put it right by converting both quantities to the same type, either both energies or both powers.

• Forgetting to convert a decimal to a percentage when the question asks for a percentage.

  Put it right by multiplying the decimal by 100 and adding the % sign.

Exam tips

• Underline the words useful and total in the question before choosing numbers, because the total is often the larger value.
• Show the substitution line, not just the final answer, so that a correct method can be followed even if the arithmetic slips.
• Check whether the answer should be a decimal or a percentage, and give the unit only when the quantity has one; efficiency itself has no unit.