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1.9 Energy and Power

GCSE Physics · AQA · Chapter 1: Conservation and Dissipation of Energy

A free GCSE Physics lesson for AQA (8463) from OBA School: power as the rate of energy transfer: P = E/t and P = W/t, power ratings, personal power, efficiency and wasted power. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define power and use P = E ÷ t and P = W ÷ t, including rearranging
  • Convert between W, kW and MW, and between minutes and seconds
  • Use orders of magnitude and standard form for power ratings
  • Measure and compare the power output of people
  • Calculate efficiency and wasted power using power values

Key words

  • Power: The rate at which energy is transferred, or the rate at which work is done.
  • Watt (W): The unit of power. 1 W = 1 J/s (one joule transferred each second).
  • Kilowatt (kW): 1 kW = 1000 W. Megawatt: 1 MW = 1 000 000 W = 10⁶ W.
  • Power rating: The input power of an appliance, usually printed on it.
  • Order of magnitude: A value given to the nearest power of ten, shown with the symbol ~.
  • Wasted power: Total power in − useful power out.

What is power?

A powerful lift motor raises a lift faster than a weak one, even though both transfer the same energy to the lift’s GPE store. Power is how quickly energy is transferred – the energy transferred per second.

  • P = E ÷ t P = W ÷ t E = P t t = E ÷ P; Symbols and units P = power, in watts (W) E = energy transferred, in joules (J) W = work done, in joules (J) t = time, in seconds (s)

Worked example: power of a food mixer

A food mixer transfers 18 000 J in 1.5 minutes.
t = 1.5 × 60 = 90 s; P = E ÷ t = 18 000 J ÷ 90 s

Answer: P = 200 W

Worked example: energy from a power rating

A 2.2 kW hairdryer is used for 5 minutes.
P = 2200 W, t = 300 s; E = P t = 2200 × 300

Answer: E = 660 000 J (6.6 × 10⁵ J)

Exam tip: Convert to SI units first: kW → W (× 1000), MW → W (× 10⁶), minutes → s (× 60), hours → s (× 3600), kJ → J (× 1000).

Power ratings and orders of magnitude

Powers cover a huge range, so we often give them as an order of magnitude – to the nearest power of ten – using the symbol ~. A kettle is ~10³ W; a large power station is ~10⁹ W. Standard form keeps big numbers tidy: 2 GW = 2 × 10⁹ W.

Worked example: an estimate

During a TV ad break, 5 million people switch on a 3 kW kettle at the same time.
extra power = 5 × 10⁶ × 3 × 10³ W = 1.5 × 10¹⁰ W

Answer: ~10¹⁰ W – about five or six large power stations’ worth

Measuring your own power

  • Measure your mass m with bathroom scales.
  • Measure the height of one step and count the steps to find the vertical height h.
  • Time the run up the stairs with a stopwatch.
  • Power output = increase in GPE store ÷ time = m g h ÷ t.

Worked example: stair run

A 55 kg student runs up stairs 3.6 m high in 4.2 s.
ΔEp = 55 × 9.8 × 3.6 = 1940.4 J
P = 1940.4 J ÷ 4.2 s = 462 W

Answer: about 460 W

Key fact: If two people do the same work (same weight, same height), the one who takes less time has the greater power. Your real power output is larger, because your muscles also warm up.

Efficiency and wasted power

Because power is energy per second, efficiency can be calculated from powers too:

efficiency = useful power output ÷ total power input (× 100 for a percentage)

power wasted = total power input − useful power output

Worked example: a lift motor

A lift motor has an input power of 5.0 kW. It transfers energy to the GPE store of the lift at a rate of 3.5 kW.
efficiency = 3.5 ÷ 5.0 = 0.70 = 70%
power wasted = 5.0 kW − 3.5 kW = 1.5 kW = 1500 W

Answer: 70%; 1.5 kW wasted

Common mistakes

  • Using minutes instead of seconds in P = E ÷ t.
  • Mixing up power (W) and energy (J). A 2 kW heater does not “use 2 kW of energy”.
  • Forgetting to convert kW to W (or leaving one value in kW and the other in W).
  • Saying the more powerful person is the one who does more work. Power depends on how fast the work is done.

Revision questions

Try these, then check your answers below each one.

Question 1. A motor transfers 36 000 J in 60 s. Calculate its power.

Answer: 600 W

Working: P = 36 000 ÷ 60 = 600 W.

Question 2. A 1.5 kW microwave oven runs for 2 minutes. Calculate the energy transferred.

Answer: 180000 J

Working: E = 1500 W × 120 s = 180 000 J.

Question 3. One watt is equal to … (Choose from: one joule per second, one newton per metre, one joule per kilogram, one second per joule.)

Answer: one joule per second

Working: 1 W = 1 J/s.

Related lessons

Continue in the full course

This lesson is section 1.9 (AGCPH0109) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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