4.1.22

# Power & Efficiency

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## Power

The "energy transferred per second" is equivalent to saying "the rate of energy transfer". Both are definitions for power.

### Rate of energy transfer

• The rate at which energy is transferred from one form to another is called power.
• This is equivalent to saying the energy transferred per second.
• The energy transferred is also known as the work done, W.
• So, power can also be described as the work done per second (or the rate of doing work).

### Equation

• Power is the rate of doing work.
• Power = work done ÷ time taken
• $P = \frac{\Delta W}{\Delta t}$

### Units

• Power is measured in Watts (W).
• 1 Watt is defined as 1 Joule transferred per second.

### Force × velocity

• Power is also equal to the force applied times the velocity of the object the force is applied to.
• $P = F v$
• This equation can be more useful if you're given the speed and not the distance travelled.

## Efficiency

When energy is transferred, there are some losses. For example, some energy may be dissipated as heat or sound.

### Useful energy

• Efficiency is the fraction of energy that is used for something useful.
• The higher the efficiency, the better.
• Efficiency is calculated by:
• Efficiency = $\frac{useful\space output\space power}{input \space power}$
• A kettle supplied with 50 W of power and converts 40 W to heat water has an efficiency of $\frac{40}{50} = 0.8$.

### Percentage

• Efficiency can also be expressed as a percentage:
• Efficiency (%) = $\frac{useful\space output\space power}{input \space power} \times 100$
• A kettle supplied with 50 W of power and converts 40 W to heat water has an efficiency of 80%.

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