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Extended · Practice questions · Efficiency

Useful out, total in.

Six original Cambridge-style questions on calculating efficiency from energy or power, finding wasted energy, reading a Sankey diagram, and matching the right quantities.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Match the quantities

Efficiency = useful ÷ total.

01
[2 marks]

Write the two equivalent equations for efficiency, one using energy and one using power.

  • efficiency = useful energy output ÷ total energy input (× 100%). ✓
  • efficiency = useful power output ÷ total power input (× 100%). ✓
02
Calculation
[2 marks]

A machine is given 400 J of energy and usefully transfers 240 J. Calculate its efficiency as a percentage.

efficiency = 240 ÷ 400 = 0.60

60 %

03
Calculation
[2 marks]

A lamp has a power input of 60 W and produces 9.0 W of light. Calculate its efficiency.

efficiency = useful power ÷ total power = 9.0 ÷ 60

15 %

power over power, not power over energy

04
Calculation
[3 marks]

A device is supplied with 800 J of energy and is 25% efficient. Calculate the useful energy output and the energy wasted.

useful = 0.25 × 800 = 200 J wasted = 800 − 200 = 600 J

useful 200 J, wasted 600 J

05
Analysis
[2 marks]

A Sankey diagram for a motor shows 1000 J flowing in and 400 J of useful output. State the energy wasted and describe how the widths of the useful and input arrows compare.

  • Wasted energy = 1000 − 400 = 600 J. ✓
  • The useful arrow is narrower than the input arrow, with its width 400/1000 of the input, since width is proportional to energy. ✓
06
Analysis
[2 marks]

Explain why no real device can be 100% efficient.

  • Some energy is always transferred to a non-useful store, usually the thermal store, by friction, resistance or sound. ✓
  • So the useful output is always less than the total input, giving an efficiency below 100%. ✓