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:

$efficiency = \frac{useful output energy transfer}{total input energy transfer}$

$efficiency = \frac{useful power output}{total power input}$

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

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. 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 input = 300 J
Total wasted energy = 85 J

Step 2: State the equation

$efficiency = \frac{useful energy output}{total energy output} \times 100 %$

Step 3: Determine total energy output

Due to the conservation of energy:

total energy input = total energy output

Therefore, total energy output = 300 J

Step 4: Calculate the useful energy output

Due to the conservation of energy:

Total energy output = useful energy output + wasted energy

Useful energy output = total energy output − wasted energy

Useful energy output = 300 − 85

Useful energy output = 215 J

Step 5: Substitute these values into the efficiency equation

$efficiency = \frac{useful energy output}{total energy output} \times 100 %$

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

$efficiency = 72 %$

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
the percentage = 0.25 × 100 = 25 %

Remember that efficiency has no units

Efficiency (OCR Gateway GCSE Physics: Combined Science)

Revision Note

Efficiency

Worked example

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Author: Leander