What you'll learn
This revision guide covers energy and power as tested in WJEC GCSE Physics exams. You'll master the relationship between work done, energy transfer and power, understand efficiency calculations, and apply these concepts to real-world scenarios. These fundamentals underpin many topics across the specification, making them essential for exam success.
Key terms and definitions
Work done — the energy transferred when a force moves an object through a distance, measured in joules (J)
Power — the rate at which energy is transferred or work is done, measured in watts (W)
Efficiency — the ratio of useful energy output to total energy input, expressed as a percentage or decimal
Joule — the SI unit of energy and work, equivalent to one newton-metre (1 J = 1 N·m)
Watt — the SI unit of power, equivalent to one joule per second (1 W = 1 J/s)
Kilowatt-hour (kWh) — a unit of energy equal to 3.6 million joules, commonly used for measuring electrical energy consumption
Core concepts
Work done and energy transfer
When a force causes an object to move, work is done and energy is transferred. The amount of work done depends on both the size of the force and the distance moved in the direction of the force.
The equation for work done is:
Work done (J) = Force (N) × Distance moved in direction of force (m)
W = F × d
Key points about work done:
- Work is only done when the force causes movement
- If the force acts at an angle, only the component of force in the direction of movement counts
- No movement means no work done, regardless of force applied
- Pushing against a stationary wall transfers no energy (no work done)
- Lifting an object against gravity transfers energy to its gravitational potential energy store
When work is done against frictional forces, energy is transferred to the thermal energy store of the objects, causing temperature increases. This is why rubbing your hands together warms them.
Power calculations
Power measures how quickly energy is transferred or work is done. A more powerful device transfers the same amount of energy in less time, or transfers more energy in the same time period.
The two key power equations are:
Power (W) = Work done (J) ÷ Time (s)
P = W ÷ t
Power (W) = Energy transferred (J) ÷ Time (s)
P = E ÷ t
These equations are interchangeable because work done equals energy transferred.
Common power ratings you should recognise:
- Light bulb: 5-100 W
- Kettle: 2000-3000 W (2-3 kW)
- Car engine: 50,000-200,000 W (50-200 kW)
- Power station: 500,000,000-2,000,000,000 W (500 MW-2 GW)
Energy and power units
Understanding unit conversions is essential for calculations:
Energy units:
- 1 kJ (kilojoule) = 1,000 J
- 1 MJ (megajoule) = 1,000,000 J
- 1 kWh (kilowatt-hour) = 3.6 MJ = 3,600,000 J
Power units:
- 1 kW (kilowatt) = 1,000 W
- 1 MW (megawatt) = 1,000,000 W
- 1 GW (gigawatt) = 1,000,000,000 W
The kilowatt-hour is particularly important for electricity billing. Energy suppliers charge per kWh of energy used. To calculate energy in kilowatt-hours:
Energy (kWh) = Power (kW) × Time (h)
For example, a 2 kW heater running for 3 hours uses 6 kWh of energy.
To convert kWh to joules, multiply by 3,600,000 (or 3.6 × 10⁶).
Efficiency
No energy transfer is perfectly efficient. Some energy is always dissipated (spread out) into less useful forms, typically as thermal energy to the surroundings.
Efficiency = Useful energy output ÷ Total energy input
or
Efficiency = Useful power output ÷ Total power input
Efficiency can be expressed as:
- A decimal (0 to 1)
- A percentage (0% to 100%)
To convert from decimal to percentage, multiply by 100.
Examples of typical efficiencies:
- Filament light bulb: 5% (most energy wasted as heat)
- LED light bulb: 40-50%
- Electric motor: 80-90%
- Petrol car engine: 25-30%
- Power station: 35-40%
Ways to improve efficiency:
- Reduce friction (lubrication, streamlining)
- Prevent heat loss (insulation)
- Use more efficient components
- Reduce air resistance
- Use regenerative braking systems
Power and energy in mechanical systems
When objects are lifted, work is done against gravity. The energy transferred equals the gain in gravitational potential energy:
Work done = Force × Distance = Weight × Height = mgh
When a car accelerates, the engine does work to increase the kinetic energy of the vehicle. Power output determines how quickly this happens:
- High power = rapid acceleration
- Low power = slow acceleration
Braking systems must dissipate kinetic energy. In traditional brakes, this energy is transferred to thermal energy in the brake pads and discs. The power dissipated during braking can be very large:
If a 1000 kg car travelling at 20 m/s stops in 4 seconds, the kinetic energy (200,000 J) must be dissipated, requiring an average power of 50,000 W (50 kW).
Electrical power
For electrical devices, power can be calculated using additional equations involving voltage and current:
Power (W) = Voltage (V) × Current (A)
P = V × I
Power (W) = Current² (A²) × Resistance (Ω)
P = I²R
Power (W) = Voltage² (V²) ÷ Resistance (Ω)
P = V²/R
The energy transferred by an electrical device can be calculated:
Energy transferred (J) = Power (W) × Time (s)
E = P × t
or
Energy transferred (J) = Voltage (V) × Current (A) × Time (s)
E = V × I × t
Worked examples
Example 1: Work done and power
Question: A student with a weight of 500 N runs up a flight of stairs with a vertical height of 3 m in 2.5 seconds. Calculate: (a) the work done [2 marks] (b) the power developed [2 marks]
Solution:
(a) Work done = Force × Distance W = 500 N × 3 m [1 mark] W = 1500 J [1 mark]
(b) Power = Work done ÷ Time P = 1500 J ÷ 2.5 s [1 mark] P = 600 W [1 mark]
Example 2: Efficiency calculation
Question: An electric motor has a total power input of 2000 W. It lifts a 150 N load through a height of 8 m in 1.2 seconds. (a) Calculate the useful power output [3 marks] (b) Calculate the efficiency of the motor [2 marks]
Solution:
(a) Work done = Force × Distance W = 150 N × 8 m = 1200 J [1 mark]
Power output = Work done ÷ Time P = 1200 J ÷ 1.2 s [1 mark] P = 1000 W [1 mark]
(b) Efficiency = Useful power output ÷ Total power input Efficiency = 1000 W ÷ 2000 W [1 mark] Efficiency = 0.5 or 50% [1 mark]
Example 3: Energy and cost calculation
Question: A Caribbean household uses a 3 kW air conditioning unit for 6 hours per day. Electricity costs 40 cents per kWh. (a) Calculate the energy used per day in kWh [2 marks] (b) Calculate the daily cost of running the air conditioner [2 marks]
Solution:
(a) Energy = Power × Time E = 3 kW × 6 h [1 mark] E = 18 kWh [1 mark]
(b) Cost = Energy × Cost per kWh Cost = 18 kWh × 40 cents [1 mark] Cost = 720 cents or $7.20 [1 mark]
Common mistakes and how to avoid them
Using inconsistent units — Always convert to standard SI units before calculating. Convert kW to W, hours to seconds, and km to m where necessary. Check the units given in the question carefully.
Confusing work and power — Work is energy transferred (measured in joules), while power is the rate of energy transfer (measured in watts). They're related but fundamentally different quantities.
Forgetting to convert kWh to joules — When a question requires an answer in joules but gives energy in kWh, multiply by 3,600,000. Many students lose marks by forgetting this conversion.
Mixing up efficiency formulas — Efficiency always equals useful output ÷ total input. Never divide input by output or subtract one from the other.
Rounding too early — Keep at least 3-4 significant figures during multi-step calculations. Only round your final answer to an appropriate number of significant figures (usually 2-3 for GCSE).
Not showing working — Even if you use a calculator, write down the equation you're using and substitute values before calculating. This earns method marks even if your final answer is wrong.
Exam technique for "Energy and Power"
Master command words — "Calculate" requires numerical working and units. "State" or "Give" needs a brief answer without explanation. "Explain" requires reasoning using physics principles.
Use equation format consistently — Always write: equation in symbols, equation with numbers substituted (including units), final answer with correct unit. This structure maximises method marks.
Check magnitude — Does your answer make sense? A domestic appliance with a power of 5,000,000 W or efficiency of 250% indicates an error. Develop a feel for realistic values.
Unit marks matter — One mark is often allocated specifically for the correct unit. Include units in every final answer, even if the question doesn't explicitly ask for them.
Quick revision summary
Work done equals force multiplied by distance moved, transferring energy measured in joules. Power is the rate of energy transfer, measured in watts (joules per second). Efficiency compares useful output to total input, always less than 100% due to wasted energy. Energy bills use kilowatt-hours, where 1 kWh equals 3.6 MJ. Higher power means faster energy transfer—crucial in mechanical and electrical systems. Always show working, use correct units, and check your answers make physical sense.