Power and efficiency

Power

P = E / t and P = W / t, where E is the energy transferred and W the work done, in time t. Power is measured in watts: 1 W = 1 J/s. 1 kW = 1000 W.

Efficiency

efficiency = useful energy output / total energy input

efficiency = useful power output / total power input

Multiply by 100 for a percentage. Efficiency can never be more than 1 (100%), because energy cannot be created.

Lifting problems

For a motor or person lifting a load, the useful energy is the GPE gained, mgΔh. Useful power = mgΔh / t.

Worked example

A motor lifts a 50 kg load through 6.0 m in 12 s. Its input power is 400 W. Find its efficiency.

1. Useful energy = 50 x 9.81 x 6.0 = 2943 J
2. Useful power = 2943 / 12 = 245 W
3. Efficiency = 245 / 400 = 0.613

Answer: Efficiency = 61%

Check yourself

1. A machine does 1200 J of work in 4.0 s. Find its power in W.
   Show answer

   300 W. P = W / t = 1200 / 4.0 = 300 W.

2. A 1.5 kW kettle is switched on for 3.0 minutes. How much energy does it transfer, in kJ?
   Show answer

   270 kJ. E = Pt = 1500 x 180 = 270000 J = 270 kJ.

3. A lamp takes in 60 W and gives out 9.0 W as light. Find its efficiency as a percentage.
   Show answer

   15 %. Efficiency = 9.0 / 60 = 0.15 = 15%.

4. A motor has an efficiency of 0.80 and a useful output power of 400 W. Find its input power in W.
   Show answer

   500 W. Input = output / efficiency = 400 / 0.80 = 500 W.

5. A 70 kg student runs up stairs of vertical height 3.0 m in 4.0 s. Find her useful power output in W, to 3 s.f.
   Show answer

   515 W. P = mgΔh / t = 70 x 9.81 x 3.0 / 4.0 = 515 W.

6. Why can the efficiency of a machine never be greater than 100%?
   • Energy cannot be created
   • Power is always lost as sound
   • Machines always have friction
   • Efficiency has no units
   Show answer

   Energy cannot be created. Useful output can never exceed total input, by conservation of energy.

7. What is 1 watt equal to?
   • 1 newton per metre
   • 1 joule per metre
   • 1 joule per second
   • 1 newton second
   Show answer

   1 joule per second. Power = energy / time.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson Edexcel IAL Physics Unit 1 (WPH11) question paper, January 2023: list of data (g = 9.81 m/s²)

Last updated 7 November 2026. Spotted a mistake? Tell us.