Power

In this lesson you will learn what power means in physics, how to calculate it, and how to apply it to compare different devices and situations. Power is part of AQA GCSE Combined Science Trilogy (8464), Section 6.1.

What Is Power?

Power is the rate of energy transfer — how quickly energy is transferred from one store to another. A more powerful device transfers the same amount of energy in less time.

The Equation

$P = \frac{E}{t}$

Where:

$P$ = power in watts (W)
$E$ = energy transferred in joules (J)
$t$ = time in seconds (s)

The Watt

$1 \text{ W} = 1 \text{ J/s}$

A device with a power of 1 W transfers 1 joule of energy every second.

Unit	Equivalent
1 kW	1000 W
1 MW	1,000,000 W

Exam Tip: Always convert kilowatts to watts and minutes to seconds before substituting into the equation.

Rearranging the Equation

$E = P \times t \qquad t = \frac{E}{P}$

Worked Example 1

A 2000 W kettle is used for 3 minutes. How much energy does it transfer?

Convert time: $3 \text{ min} = 180 \text{ s}$

$E = 2000 \times 180 = 360{,}000 \text{ J} = 360 \text{ kJ}$

Worked Example 2

A motor transfers 45,000 J of energy in 90 seconds. What is its power?

$P = \frac{45{,}000}{90} = 500 \text{ W}$

Worked Example 3

A 60 W light bulb transfers 18,000 J of energy. How long was it on for?

$t = \frac{18{,}000}{60} = 300 \text{ s} = 5 \text{ minutes}$

Power and Work Done

Power can also be expressed in terms of work done:

$P = \frac{W}{t}$

Where $W$ is work done in joules. This is because work done is equal to energy transferred.

Worked Example 4

A crane lifts a 500 kg load 12 m in 20 seconds. What is the useful power output? (Use $g = 10$ N/kg.)

Step 1: Work done = GPE gained. $W = mgh = 500 \times 10 \times 12 = 60{,}000 \text{ J}$

Step 2: Power. $P = \frac{60{,}000}{20} = 3000 \text{ W} = 3 \text{ kW}$

Comparing Power Ratings

Device	Typical Power
LED bulb	5–10 W
Laptop	30–65 W
Filament bulb	60–100 W
Kettle	2000–3000 W
Electric shower	7000–10,000 W
Electric car motor	50,000–150,000 W

A higher power rating means the device transfers energy more quickly. Two devices can transfer the same total energy, but the more powerful one does it in less time.

graph LR
    A["More powerful device"] --> B["Transfers energy faster"]
    C["Less powerful device"] --> D["Transfers same energy but more slowly"]
    B --> E["Same total energy transferred"]
    D --> E

Exam Tip: AQA questions may ask you to compare two devices that do the same job. The more powerful one completes the job in less time, but the total energy transferred is the same.

Linking Power to Other Energy Equations

You can combine the power equation with other energy equations:

Power from Kinetic Energy

If an object accelerates from rest:

$P = \frac{E_k}{t} = \frac{\frac{1}{2}mv^2}{t}$

Power from GPE

$P = \frac{mgh}{t}$

Exam Tip: If a question asks for power and gives you mass, height, and time, use $P = mgh/t$ directly. There is no need to calculate energy as a separate step — though you can for clarity.

Common Mistakes

Mistake	Correction
Using minutes instead of seconds	Always convert time to seconds
Confusing power and energy	Power is the rate of transfer; energy is the total amount transferred
Using kW without converting	1 kW = 1000 W; convert before calculating
Forgetting the unit	Power is measured in watts (W)

Summary

Power is the rate of energy transfer: $P = E/t$ .
1 watt = 1 joule per second.
A more powerful device transfers energy more quickly.
Power can also be calculated as $P = W/t$ (work done per unit time).
Combine with energy equations: $P = mgh/t$ or $P = \frac{1}{2}mv^2/t$ .
This topic is assessed in AQA GCSE Combined Science Trilogy (8464), Section 6.1.

Extended Worked Examples

Worked Example 5 — Athlete Climbing Stairs

A 60 kg athlete runs up a flight of stairs with a vertical height of 4 m in 5 s. Calculate the useful power output. ( $g = 10$ N/kg.)

$E_p = mgh = 60 \times 10 \times 4 = 2400 \text{ J}$

$P = \frac{E_p}{t} = \frac{2400}{5} = 480 \text{ W}$

Worked Example 6 — Accelerating Car

A 1,000 kg car accelerates from rest to 20 m/s in 8 s. Calculate the useful power output (ignore friction and air resistance).

$E_k = \tfrac{1}{2} \times 1000 \times 20^2 = 200{,}000 \text{ J}$

$P = \frac{200{,}000}{8} = 25{,}000 \text{ W} = 25 \text{ kW}$

Worked Example 7 — Comparing Electric Kettles

Kettle A: 2.2 kW, takes 120 s to boil water. Kettle B: 3.0 kW, takes 90 s to boil the same water. Compare the total energy they each use.

Kettle A: $E = 2200 \times 120 = 264{,}000$ J.

Kettle B: $E = 3000 \times 90 = 270{,}000$ J.

Kettle B is more powerful and finishes faster, but uses slightly more total energy — probably because at higher power it loses slightly more energy to its surroundings per unit water boiled. Not all "more powerful" devices are more efficient.

Worked Example 8 — Finding Time

A 1.5 kW motor must transfer 90 kJ of energy. How long must it run?

$t = \frac{E}{P} = \frac{90{,}000}{1500} = 60 \text{ s} = 1 \text{ minute}$

Power

Power

What Is Power?

The Equation

The Watt

Rearranging the Equation

Worked Example 1

Worked Example 2

Worked Example 3

Power and Work Done

Worked Example 4

Comparing Power Ratings

Linking Power to Other Energy Equations

Power from Kinetic Energy

Power from GPE

Common Mistakes

Summary

Extended Worked Examples

Worked Example 5 — Athlete Climbing Stairs

Worked Example 6 — Accelerating Car

Worked Example 7 — Comparing Electric Kettles

Worked Example 8 — Finding Time

Comparison Table — Units of Power

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