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GCSEPhysicsEdexcelRevision Notes3. Conservation of EnergyEfficiency & Energy ResourcesEfficiency

Efficiency (Edexcel GCSE Physics)

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Leander Oates

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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 output

  • 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 equation for efficiency is: 

    efficiency space equals space fraction numerator useful space energy space transferred space by space the space device over denominator total space energy space supplied space to space the space device end fraction  

Worked Example

The blades of a fan are turned by an electric motor. In one second, 300 J of energy is transferred electrically from the mains supply to the fan. 85 J is wasted due to friction and sound.

Calculate the percentage efficiency of the motor.

Answer:

Step 1: List the known quantities

  • Total energy supplied to the device (input) = 300 J

  • Total wasted energy = 85 J

Step 2: State the equation

efficiency space equals fraction numerator space useful space energy space transferred space by space the space device space open parentheses output close parentheses over denominator total space energy space supplied space to space the space device space open parentheses input close parentheses end fraction space cross times space 100 percent sign

Step 3: Determine total energy transferred by the device (output)

  • Due to the conservation of energy:

total space energy space transferred space by space the space device space open parentheses output close parentheses equals space total space energy space supplied space to space the space device space open parentheses input close parentheses

  • Therefore, total energy transferred by the device (output) = 300 J

Step 4: Calculate the useful energy transferred by the device (output)

  • Due to conservation of energy

total space energy space transferred space by space the space device space equals space useful space energy space transferred space by space the space device space plus space wasted space energy

useful space energy space transferred space by space the space device space equals space total space energy space transferred space by space the space device space minus space wasted space energy

useful space energy space transferred space by space the space device space equals space 300 space minus space 85

useful space energy space transferred space by space the space device 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 transferred space by space the space device space open parentheses output close parentheses over denominator total space energy space supplied space to space the space device space open parentheses input close parentheses 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 72 percent sign

Examiner Tips and Tricks

Efficiency can be in a ratio (between 0 and 1) or percentage format (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.