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Efficiency (Oxford AQA IGCSE Combined Science Double Award)

Revision Note

Leander Oates
Oxford AQA Combined Science Double Award: PhysicsOxford AQA Physics

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 power or energy output from a system to its total power or 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 is represented as a percentage, and can be calculated using the following equations:

efficiency space equals fraction numerator space useful space energy space out over denominator total space energy space in end fraction space cross times space 100 percent sign

efficiency space equals fraction numerator space useful space power space out over denominator total space power space in end fraction space cross times space 100 percent sign

Worked Example

An electric motor turns the blades of a fan. In one second, 300 J of energy is transferred electrically from the mains power supply. 85 J of energy is wasted due to friction and sound.

Calculate the efficiency of the motor.

 Answer:

Step 1: List the known quantities

  • Total energy in = 300 J

  • Total wasted energy = 85 J

Step 2: State the equation

efficiency space equals fraction numerator space useful space energy space out over denominator total space energy space in end fraction space cross times space 100 percent sign 

Step 3: Determine the total energy out

  • Due to the conservation of energy:

total space energy space in space equals space total space energy space out

total space energy space out space equals space 300 space straight J space

Step 4: Calculate the useful energy out

  • Due to the conservation of energy

total space energy space out space equals space useful space energy space out space plus space wasted space energy

useful space energy space out space equals space total space energy space out space minus space wasted space energy

useful space energy space out space equals space 300 space minus space 85

useful space energy space out space equals space 215 space straight J 

Step 5: Substitute these values into the efficiency equation 

efficiency space equals fraction numerator space useful space energy space out over denominator total space energy space in end fraction space cross times space 100 percent sign

efficiency space equals fraction numerator space 215 space over denominator 300 end fraction space cross times space 100 percent sign

efficiency space equals space 0.72

efficiency space equals space 72 percent sign

Examiner Tip

Efficiency can be given as a ratio (between 0 and 1) or as a percentage (between 0 and 100%). If the question asks for efficiency as a ratio, give your answer as a fraction or decimal.

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 (only %)

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    Leander Oates

    Author: Leander Oates

    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.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.