Efficiency

Efficiency

• A device usually transfers only part of its input into the output we want. The rest is dissipated, often as heating or sound.
• Efficiency asks: what fraction of the total inputbecomes the useful output?

Useful output divided by total input

total inputdissipated heating + sounduseful output

Definition

1 mark

What is meant by the efficiency of a system?

Model answer: The ratio of useful energy output to total energy input, or the ratio of useful power output to total power input.

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

Symbols

• $\text{useful output}$= useful energy or useful power (J or W)
• $\text{total input}$= input energy or input power of the same type (J or W)

• Use energy with energy, or power with power. Do not mix them.
• Efficiency has no unit. Write it as a decimal from 0 to 1, or multiply by 100 to give a percentage.
• Energy or power dissipated = total input − useful output.
• For a real machine, total input is at least as large as useful output. If your answer is above 100%, recheck the ratio.

Worked example

From input power to efficiency

A motor takes 900 W and delivers 600 W of useful power.

1. $\eta=600/900=0.667$.
2. As a percentage, the efficiency is 66.7%.

Answer

$$0.667\text{ or }66.7\%$$

Your turn9702/21/O/N/24 Q3(c)(iii)

A motor has total input power 900 W and useful output power 600 W. Determine its efficiency. (9702/21/O/N/24 Q3(c)(iii))

Show worked answer

Worked answer: $\eta=600/900=0.67$, or 67%.

Common mistake

If useful output and efficiency are known, divide by efficiency to find the input. The input must not come out smaller than the useful output.