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:

$efficiency = \frac{useful energy transferred by the device}{total energy supplied to the device}$

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.

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

$efficiency = \frac{useful energy transferred by the device (output)}{total energy supplied to the device (input)} \times 100 %$

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

- Due to the conservation of energy:

$total energy transferred by the device (output) = total energy supplied to the device (input)$

- 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

$total energy transferred by the device = useful energy transferred by the device + wasted energy$

$useful energy transferred by the device = total energy transferred by the device - wasted energy$

$useful energy transferred by the device = 300 - 85$

$useful energy transferred by the device = 215 J$

Step 5: Substitute these values into the efficiency equation

$efficiency = \frac{useful energy transferred by the device (output)}{total energy supplied to the device (input)} \times 100 %$

$efficiency = \frac{215}{300} \times 100 %$

$efficiency = 72 %$

Examiner Tip

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 %)

Efficiency (Edexcel GCSE Physics: Combined Science)

Revision Note

Efficiency

Worked example

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Author: Leander