# 5.1.3 Efficiency

### Efficiency of a System

• The efficiency of a system is the ratio of the useful energy output from the system to the 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
• Multiplying this ratio by 100 gives the efficiency as a percentage

Efficiency equation in terms of energy

• Efficiency can also be written in terms of power (the energy per second):

Efficiency equation in terms of power

#### Exam Tip

Efficiency can be in a ratio or percentage format. If the question asks for an 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, e.g. Ratio = 0.25, Percentage = 0.25 × 100 = 25 %

### Solving Problems Involving Efficiency

• Recall the two equations for calculating efficiency are:

• Which to use will depend on whether you’re given a system calculating energies or power as shown in the examples below

#### Worked example

• The pump is what converts the water’s kinetic energy into gravitational potential energy. Since its efficiency is 20%, you would multiply the kinetic energy by 0.2 since only 20% of the kinetic energy will be converted (not 20% of the gravitational potential energy)

#### Exam Tip

Equations for kinetic and potential energies are important for these types of questions. Also familiarise yourself with the different equations for power depending on what quantities are given.

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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