# 1.1.10 Power

### Power

• Machines, such as car engines, transfer energy from one type to another every second
• The rate of this energy transfer, or the rate of work done, is called power

Two identical cars accelerating to the same final speed will both gain the same amount of energy. But if one of them reaches that speed sooner, it will have a greater power

• Power is defined as the energy transferred per unit time:

• Power can also be defined as the work done per unit time:

• The energy transferred, or work done, is always in units of joules (J)
• Time is measured in seconds (s)
• Power, P is measured in the units watts (W)
• This equation can be rearranged with the help of a formula triangle:

Work, power and time formula triangle

#### How to Use Formula Triangles

• Formula triangles are really useful for knowing how to rearrange physics equations
• To use them:
1. Cover up the quantity to be calculated, this is known as the ‘subject’ of the equation
2. Look at the position of the other two quantities
• If they are on the same line, this means they are multiplied
• If one quantity is above the other, this means they are divided – make sure to keep the order of which is on the top and bottom of the fraction!
• In the example below, to calculate speed, cover-up ‘speed’ and only distance and time are left
• This means it is equal to distance (on the top) ÷ time (on the bottom)

How to use formula triangles

• Common power ratings are shown in the table below:

Power Ratings Table

#### Worked Example

Calculate the energy transferred if an iron of power 2000 W is used for 5 minutes

Step 1: List the known values

• Power, P = 2000 W
• Time, t = 5 minutes = 5 × 60 = 300 s

Step 2: Write down the relevant equation

Step 3: Rearrange for energy transferred, E

Energy transferred = power × time

E = Pt

Step 4: Substitute in the values

E = 2000 × 300 = 600 000 J

#### Exam Tip

Think of power as “energy per second”. Thinking of it this way will help you to remember the relationship between power and energy

### The Watt

• The watt is the unit of power
• Since power is energy transferred per second, the watt can also be defined as 1 joule per second

1 W = 1 J / s

• 1 kilowatt (1 kW) is equal to 1000 watts, or 1000 joules of energy transferred per second (1 kJ / s)

#### Exam Tip

One way to remember this unit is it remember the saying “Watt is the unit of power?”

### Comparing Power Outputs

• An example that illustrates the definition of power is by comparing two electric motors if:
• They lift the same weight
• They are lifted by the same height
• One lifts it faster than the other
• The motor that lifts the weight faster is said to have more power
• This is because the work done does not depend on time, only the force (weight) and the distance lifted

Two motors with different powers

#### Maths Tip

• GCSE physics equations will mostly require fractions
• These are made up of the numerator (the top number) and the denominator (the bottom number)
• If the denominator decreases and the numerator stays the same, the whole fraction increases
• If the denominator increases and the numerator stays the same, the whole fraction decreases
• This is known as inverse proportionality
• If the denominator stays the same and the numerator increases, the whole fraction increases
• If the denominator stays the same and the numerator decreases, the whole fraction decreases
• This is known as direct proportionality

How to know whether the value of a fraction increases or decreases

#### Worked Example

Two electric motors transfer 40 J of energy to lift a load. Motor A does this in 10 seconds, motor B does this is in 20 seconds.

Determine which motor is more powerful, and by how much.

Step 1: List the known quantities

• Energy transferred for both motors, E = 40 J
• Time for motor AtA = 10 s
• Time for motor B, tB = 20 s

Step 2: Write down the equation for power

Step 3: Calculate the power for both motors by substituting values into the power equation

Power for motor A = 40 ÷ 10 = 4 W

Power for motor B = 40 ÷ 20 = 2 W

Step 4: Determine which motor is more powerful

• Motor A is twice (4 ÷ 2 = 2) as powerful as motor B

### 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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