# 4.6.3 Efficiency

### Efficiency

• The efficiency of a system is a measure of how well energy is transferred in a system
• Efficiency is defined as the ratio of the useful power output from a system to its total power 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
• What type of energy is useful or wasted depends on the system
• When electrical energy is converted to light in a lightbulb, the light energy is useful and the heat energy produced is wasted
• When electrical energy is converted to heat for a heater, the heat energy is useful and the sound energy produced is wasted
• Where power is defined as the energy transferred per unit of time • The energy can be of any form e.g. gravitational potential energy, kinetic energy

#### Worked Example

An electric motor has an efficiency of 35 %. It lifts a 7.2 kg load through a height of 5 m in 3 s.

Calculate the power of the motor.

Step 1: Write down the efficiency equation Step 2: Rearrange for the power input Step 3: Calculate the power out

• The power output is the energy ÷ time
• The electric motor transferred electric energy into gravitational potential energy to lift the load

Gravitational potential energy = mgh = 7.2 × 9.81 × 5 = 353.16 J

Power = 353.16 ÷ 3 = 117.72 W

Step 4: Substitute values into power input equation #### Exam Tip

Efficiency can be in a ratio or percentage format.

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 % ### 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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