Efficiency
- The efficiency of a system is a measure of how successfully 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
- Determining which 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 thermal energy in a heater, the heat energy is useful, and the sound energy produced is wasted
- Efficiency is represented as a percentage, and can be calculated using the equation:
- Where power is defined as the energy transferred per unit of time
- The efficiency equation can also be written in terms of energy:
- 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 
Examiner Tip
Efficiency can be in a ratio (between 0 and 1) or percentage format (between 0% and 100%).
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 %.
Remember that efficiency has no units. It is a ratio with both the numerator and denominator with the same units.
