Efficiency (OCR GCSE Combined Science A (Gateway): Physics): Revision Note

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

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

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 

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

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

$\mathrm{efficiency}=72\%$

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