What you'll learn
This revision guide covers power and efficiency as tested in AQA GCSE Physics. You'll learn how to calculate the rate of energy transfer, understand what makes devices and systems efficient, and apply these concepts to real-world contexts. These topics appear frequently in both paper-based calculations and practical assessments.
Key terms and definitions
Power — the rate of energy transfer or the rate of doing work, measured in watts (W)
Watt — the unit of power; one watt equals one joule of energy transferred per second (1 W = 1 J/s)
Efficiency — the proportion of energy supplied to a system that is usefully transferred, expressed as a percentage or decimal
Input energy — the total energy supplied to a device or system
Useful output energy — the energy transferred by a device or system in the desired form
Wasted energy — energy that is transferred to unwanted forms, typically thermal energy dissipated to surroundings
Sankey diagram — a visual representation showing energy transfers in a system, with arrow width proportional to energy quantity
Dissipation — the spreading out of energy to the surroundings, usually as thermal energy, making it less useful
Core concepts
Understanding power
Power measures how quickly energy is transferred or work is done. A device with high power transfers more energy per second than one with low power doing the same task.
The equation for power is:
Power (W) = Energy transferred (J) ÷ Time (s)
or in symbols:
P = E ÷ t
An alternative equation when considering work done:
Power (W) = Work done (J) ÷ Time (s)
or:
P = W ÷ t
Since work done equals energy transferred, these equations are equivalent.
Key points about power:
- A 100 W light bulb transfers 100 J of energy every second
- More powerful devices transfer energy faster but may be less economical
- Power ratings tell you the rate of energy transfer when operating normally
- Domestic appliances have power ratings from a few watts (LED bulbs) to several kilowatts (electric showers, kettles)
Common power values you should recognise:
- LED bulb: 5-10 W
- Laptop computer: 50-100 W
- Microwave oven: 700-1000 W
- Electric kettle: 2000-3000 W (2-3 kW)
- Electric shower: 7000-10,500 W (7-10.5 kW)
Calculating energy from power
You can rearrange the power equation to find energy transferred:
Energy transferred (J) = Power (W) × Time (s)
or:
E = P × t
This equation is essential for calculating:
- How much energy an appliance uses
- Running costs of electrical devices
- Energy consumption over time
When time is measured in hours rather than seconds, energy may be expressed in kilowatt-hours (kWh), particularly for domestic electricity billing.
Energy (kWh) = Power (kW) × Time (h)
One kilowatt-hour is the energy transferred by a 1 kW device operating for 1 hour:
1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ
Understanding efficiency
No device or system is 100% efficient. Some input energy is always wasted, usually dissipated as thermal energy to the surroundings due to friction, air resistance, or electrical resistance.
Efficiency can be calculated using energy values:
Efficiency = Useful output energy transfer ÷ Input energy transfer
or using power values:
Efficiency = Useful power output ÷ Total power input
Efficiency can be expressed as:
- A decimal between 0 and 1 (e.g., 0.75)
- A percentage between 0% and 100% (e.g., 75%)
To convert decimal to percentage: multiply by 100
The relationship between input, useful output and wasted energy:
Input energy = Useful output energy + Wasted energy
The same relationship applies to power:
Total power input = Useful power output + Wasted power
Efficiency in different devices
Different devices have characteristic efficiency values:
Electric heaters: 100% efficient at transferring electrical energy to thermal energy (though not always useful if heating is unwanted)
Filament light bulbs: approximately 5% efficient — most energy wasted as heat rather than light
LED bulbs: approximately 70-80% efficient — much more of the electrical energy becomes light
Electric motors: typically 70-90% efficient — energy wasted due to friction and electrical resistance causing heating
Petrol/diesel cars: approximately 20-30% efficient — most chemical energy from fuel becomes waste heat rather than kinetic energy
Electric vehicles: approximately 60-70% efficient — much better than combustion engines
Representing efficiency with Sankey diagrams
Sankey diagrams provide a visual way to show energy transfers. The width of each arrow represents the amount of energy.
Key features:
- Input energy shown on the left
- Useful output energy continues to the right
- Wasted energy branches off (usually upward or downward)
- Arrow widths are proportional to energy quantities
- Total width of outputs equals width of input
Example: A Sankey diagram for a filament bulb with 100 J input might show:
- Input arrow: 100 J wide
- Useful light output: 5 J wide (to the right)
- Wasted thermal energy: 95 J wide (branching upward)
Improving efficiency
Methods to reduce wasted energy and improve efficiency:
Lubrication: reduces friction between moving parts, reducing thermal energy dissipation
Thermal insulation: reduces unwanted thermal energy transfers (cavity walls, loft insulation, double glazing in homes)
Streamlining: reduces air resistance for moving vehicles
Making components from materials with lower resistance: reduces electrical energy wasted as heat in circuits
Using more efficient technologies: LED bulbs instead of filament bulbs, electric motors instead of combustion engines
The importance of efficiency:
- Reduces fuel consumption and running costs
- Conserves limited energy resources
- Reduces environmental impact and carbon emissions
- Can improve performance of devices
Worked examples
Example 1: Calculating power
Question: A crane lifts a 500 kg load through a vertical height of 20 m in 25 seconds. The gravitational field strength is 10 N/kg. Calculate the power output of the crane. [4 marks]
Solution:
Step 1: Calculate the weight of the load
- Weight = mass × gravitational field strength
- Weight = 500 kg × 10 N/kg = 5000 N ✓
Step 2: Calculate work done lifting the load
- Work done = force × distance
- Work done = 5000 N × 20 m = 100,000 J ✓
Step 3: Calculate power
- Power = work done ÷ time
- Power = 100,000 J ÷ 25 s ✓
- Power = 4000 W (or 4 kW) ✓
Example 2: Calculating efficiency
Question: An electric motor is supplied with 2400 J of electrical energy. It lifts a weight, doing 1800 J of useful work. Calculate: (a) The efficiency of the motor [2 marks] (b) The energy wasted [1 mark]
Solution:
(a) Efficiency = useful output energy ÷ input energy ✓
- Efficiency = 1800 J ÷ 2400 J = 0.75 or 75% ✓
(b) Wasted energy = input energy − useful output energy
- Wasted energy = 2400 J − 1800 J = 600 J ✓
Alternative method for (b): Wasted energy = 25% of 2400 J = 600 J
Example 3: Using kilowatt-hours
Question: A 2.5 kW electric kettle is used for 15 minutes each day. Electricity costs 15p per kWh. Calculate: (a) The energy used by the kettle in one day in kWh [2 marks] (b) The cost of running the kettle for 30 days [2 marks]
Solution:
(a) Convert time to hours: 15 minutes = 15/60 = 0.25 hours ✓
- Energy = power × time
- Energy = 2.5 kW × 0.25 h = 0.625 kWh ✓
(b) Energy for 30 days = 0.625 kWh × 30 = 18.75 kWh ✓
- Cost = 18.75 kWh × 15p = 281.25p = £2.81 ✓
Common mistakes and how to avoid them
Confusing energy and power: Power is the rate of energy transfer, not the total energy. Always check units — joules for energy, watts for power. Don't use the terms interchangeably.
Forgetting to convert units: When using E = P × t, time must be in seconds if power is in watts and you want energy in joules. For kWh calculations, power must be in kW and time in hours. Always write your units and check conversions.
Calculating efficiency greater than 100%: This violates the conservation of energy. If your answer exceeds 100%, you've likely divided input by output instead of output by input. Useful output can never exceed total input.
Not converting efficiency to percentage when asked: If the question asks for efficiency "as a percentage", multiply your decimal answer by 100 and include the % symbol. An answer of 0.85 should be written as 85%.
Mixing up useful and wasted energy: Read questions carefully. "Useful output" is energy in the desired form; "wasted" is energy transferred to unwanted forms. The sum of these equals the input energy.
Incorrect Sankey diagram proportions: Arrow widths must be proportional to energy values. A 75% efficient device should show an output arrow 3/4 the width of the input arrow and waste arrow 1/4 the width. Use a ruler and calculate proportions.
Exam technique for "Power and efficiency"
Show your working clearly: Even if your final answer is wrong, you can gain method marks. Write out the equation, substitute values with units, then calculate. For a 3-mark calculation, expect: 1 mark for correct equation, 1 mark for correct substitution, 1 mark for correct answer with unit.
Understand command words: "Calculate" requires numerical working and an answer with units. "Describe" needs you to state what happens without calculations. "Explain" requires reasons — use "because" or "this causes" to link statements. "State" needs a brief answer without explanation.
Check your answer is reasonable: A domestic appliance shouldn't have a power of millions of watts. Efficiency shouldn't exceed 100%. A kettle shouldn't cost £500 per month to run. If your answer seems unrealistic, check your working and unit conversions.
Use standard form for very large or small numbers: For values like 3,600,000 J, you can write 3.6 × 10⁶ J. This reduces errors and saves time. Make sure you're comfortable converting between standard form and ordinary numbers.
Quick revision summary
Power is the rate of energy transfer, measured in watts (W). Calculate using P = E/t. Efficiency shows what proportion of input energy is usefully transferred, calculated as useful output divided by total input, expressed as a decimal or percentage. All real devices waste some energy, usually as dissipated thermal energy. Sankey diagrams visually represent energy transfers with proportional arrow widths. Remember: input energy equals useful output plus wasted energy. Converting between joules and kilowatt-hours is essential for electricity cost calculations.