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

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.

Answer:

Step 1: Write down the efficiency equation

$Efficiency = \frac{useful power output}{total power input} \times 100 %$

Step 2: Rearrange to make power input the subject

$power input = \frac{power output}{efficiency \div 100}$ OR $power input = \frac{power output \times 100}{efficiency}$

Step 3: Calculate the power output

$power output = \frac{E}{t}$

ΔE is equal to the change in gravitational potential energy as the load is lifted

$∆ E_{P} = m g ∆ h$

$∆ E_{P} = 7.2 \times 9.8 \times 5$

$∆ E_{P} = 352.8 J$

Therefore, $power output = \frac{352.8}{3}$

$power output = 117.6 W$

Step 4: Substitute the values into the power input equation

$power input = \frac{117.6}{0.35}$ OR $power input = \frac{117.6 \times 100}{35}$

$power input = 336 W$

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, percentage = 0.25 × 100 = 25 %

Remember that efficiency has no units

Efficiency (AQA GCSE Physics: Combined Science)

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1. Energy

1.1 Energy Changes in a System

1.1.1 Energy Stores & Transfers

1.1.2 Examples of Energy Transfer

1.1.3 Kinetic Energy

1.1.4 Gravitational Potential Energy

1.1.5 Elastic Potential Energy

1.1.6 KE, GPE & EPE

1.1.7 Thermal Energy

1.1.8 Required Practical: Investigating Specific Heat Capacity

1.1.9 Changes in Energy

1.1.10 Power

1.1.11 Conservation & Dissipation of Energy

1.1.12 Wasted Energy

1.1.13 Conduction of Heat

1.1.14 Efficiency

1.1.15 Improving Efficiency

1.2 National & Global Energy Resources

1.2.1 Energy Resources

1.2.2 Comparing Energy Resources

1.2.3 Environmental Issues

2. Electricity

2.1 Current, Potential Difference & Resistance

2.1.1 Circuit Diagrams

2.1.2 Charge & Current

2.1.3 Current, Resistance & Potential Difference

2.1.4 Required Practical: Investigating Resistance

2.1.5 Resistors

2.1.6 I–V Graphs

2.1.7 Thermistors

2.1.8 LDRs

2.1.9 Investigating Resistance in Thermistors & LDRs

2.1.10 Required Practical: Investigating I–V Characteristics

2.2 Series & Parallel Circuits

2.2.1 Series & Parallel Circuits

2.2.2 Resistors in Series & Parallel

2.2.3 Comparing Series & Parallel Circuits

2.2.4 AC & DC

2.2.5 Mains Electricity

2.2.6 Dangers of Mains Electricity

2.3 Energy Transfers

2.3.1 Electrical Power

2.3.2 Electrical Energy

2.3.3 Calculating Energy Transfers

2.3.4 Power Ratings

2.3.5 The National Grid

2.3.6 Use of Transformers

3. Particle Model of Matter

3.1 Changes of State & the Particle Model

3.1.1 Density

3.1.2 Solids, Liquids & Gases

3.1.3 Required Practical: Determining Density

3.1.4 Changes of State

3.2 Internal Energy & Energy Transfers

3.2.1 Internal Energy

3.2.2 Specific Heat Capacity

3.2.3 Latent Heat

3.2.4 Specific Latent Heat

3.2.5 Heating & Cooling Graphs

3.2.6 Specific Heat Capacity v Specific Latent Heat

3.3 Particle Model & Pressure

3.3.1 Kinetic Theory

4. Atomic Structure

4.1 Atoms & Isotopes

4.1.1 Atomic Structure

4.1.2 The Absorption & Emission of EM Radiation

4.1.3 Atomic & Mass Number

4.1.4 Isotopes

4.1.5 Positive Ions

4.1.6 The Plum Pudding Model

4.1.7 Rutherford Scattering

4.1.8 Bohr's Model of the Atom

4.1.9 Discovery of the Proton & Neutron

4.1.10 Changes in the Atomic Model

4.2 Atoms & Nuclear Radiation