Efficiency (AQA GCSE Physics: Combined Science)

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Efficiency

  • The efficiency of a system is a measure of the amount of wasted energy in an energy transfer
  • Efficiency is defined as:

The ratio of the useful energy output from a system to its total energy input

  • If a system has high efficiency, this means most of the energy transferred is useful
  • If a system has low efficiency, this means most of the energy transferred is wasted
  • Efficiency can be represented as a decimal or as a percentage
  • The equations for efficiency are: 

efficiency space equals space fraction numerator useful space output space energy space transfer over denominator total space input space energy space transfer end fraction

 

efficiency space equals fraction numerator space useful space power space output over denominator total space power space input end fraction

  • Since power is the energy transferred per unit time, power can also be used to calculate efficiency

Worked example

An electric motor has an efficiency of 35%. It lifts a 7.2 kg load through a height of 5 m in 3 s.

Calculate the power of the motor.

Answer:

Step 1: Write down the efficiency equation 

Efficiency space equals space fraction numerator useful space power space output over denominator total space power space input end fraction cross times 100 percent sign

Step 2: Rearrange to make power input the subject

power space input space equals fraction numerator space power space output over denominator efficiency space divided by space 100 end fraction  OR  power space input space equals space fraction numerator power space output space cross times space 100 over denominator efficiency end fraction

Step 3: Calculate the power output

power space output space equals space E over t

  • ΔE is equal to the change in gravitational potential energy as the load is lifted

increment E subscript P space equals space m g increment h

increment E subscript P space equals space 7.2 space cross times space 9.8 space cross times space 5

increment E subscript P space equals space 352.8 space straight J

Therefore, power space output space equals space fraction numerator 352.8 over denominator 3 end fraction

power space output space equals space 117.6 space straight W

Step 4: Substitute the values into the power input equation 

power space input space equals space fraction numerator 117.6 space over denominator 0.35 end fraction  OR  power space input space equals space fraction numerator 117.6 space cross times space 100 over denominator 35 end fraction

power space input space equals space 336 space straight W

Examiner Tip

Efficiency can be given in a ratio (between 0 and 1) or percentage format (between 0 and 100 %)

If the answer is required as a percentage, remember to multiply the ratio by 100 to convert it: if the ratio = 0.25, percentage = 0.25 × 100 = 25 %

Remember that efficiency has no units

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Leander

Author: Leander

Expertise: Physics

Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.