PowerCambridge IGCSE Physics: Revision notes
Section 1
What is power?
Power is a measure of how quickly work is done or energy is transferred. It tells us the rate at which energy is being used or supplied.
Power is defined in two equivalent ways:
- Power as work done per unit time: the amount of work completed divided by the time taken
- Power as energy transferred per unit time: the amount of energy supplied or converted divided by the time taken
Both definitions are equally valid and are used depending on the context of the problem.
Think of power like the flow rate of water from a tap: two taps may transfer the same total volume of water (energy), but one tap open for 10 seconds transfers it much faster, so it has higher power.
Section 2
How do we calculate power from work done?
The equation for power in terms of work is:
P = W/t
Where:
- P = power (measured in watts, W)
- W = work done (measured in joules, J)
- t = time taken (measured in seconds, s)
This equation shows that power is directly proportional to the work done and inversely proportional to the time taken. More work done in less time means higher power.
A student lifts a 5 kg mass vertically by 2 m in 4 seconds. Work done = mgh = 5 × 10 × 2 = 100 J. Power = W/t = 100/4 = 25 W. The student is working at a power of 25 watts.
Always rearrange the formula if needed: W = Pt or t = W/P. Show the formula, substitute values with units, and state your final answer in watts.
Section 3
How do we calculate power from energy transferred?
The equation for power in terms of energy transfer is:
P = ΔE/t
Where:
- P = power (measured in watts, W)
- ΔE = change in energy or energy transferred (measured in joules, J)
- t = time taken (measured in seconds, s)
The Greek letter Δ (delta) represents 'change in', so ΔE means the energy transferred. This could be electrical energy in a circuit, thermal energy dissipated as heat, kinetic energy gained by an object, or any other form of energy.
A heater dissipates 6000 J of thermal energy in 30 seconds. Power = ΔE/t = 6000/30 = 200 W. The heater operates at 200 watts.
Students often forget to include the Δ symbol or confuse it with just 'E'. Remember: ΔE means the energy changed or transferred, not the total energy in the system.
Section 4
What are the units and conversions for power?
The SI unit of power is the watt (W).
One watt is defined as:
- 1 W = 1 J/s (one joule per second)
- This means 1 watt of power transfers 1 joule of energy every second
Larger units of power are commonly used:
- 1 kilowatt (kW) = 1000 W
- 1 megawatt (MW) = 1,000,000 W
When calculating power, always ensure that energy is in joules and time is in seconds to obtain the answer directly in watts. If energy is given in kilowatt-hours (kWh), convert to joules first (1 kWh = 3.6 × 10⁶ J).
When answering exam questions, always state the unit 'watts' (or W) with your power answer. If the question asks for power in kW, divide your answer in watts by 1000.
Section 5
How do the two power equations relate to each other?
The two equations P = W/t and P = ΔE/t are fundamentally equivalent because:
- Work done is a form of energy transfer. When work is done on an object, energy is transferred to it.
- The work-energy theorem states that the work done on an object equals the change in its energy.
- Therefore, W = ΔE in most contexts.
This means:
- If you're calculating power from work done by a force, use P = W/t
- If you're calculating power from electrical energy supplied or thermal energy dissipated, use P = ΔE/t
- Both give the same answer when applied correctly
The choice of equation depends on which quantity (work or energy) is given in the problem.
Read the question carefully to identify whether you're given work done or energy transferred. Both lead to the same power formula structure, but recognising which one applies shows understanding.
Must Know
- Power is the rate of doing work or transferring energy: it measures how fast energy is being used or supplied
- Two equivalent equations: P = W/t (power from work) and P = ΔE/t (power from energy transferred)
- SI unit is the watt (W), where 1 W = 1 J/s; larger units include kW (1000 W) and MW (1,000,000 W)
- Rearrange formulas as needed: W = Pt, ΔE = Pt, t = W/P, or t = ΔE/P depending on what you're solving for
- Always include units in your working and final answer; ensure energy is in joules and time is in seconds when using these formulas
- The two equations are equivalent because work done equals energy transferred; choose which one to use based on whether the problem gives work or energy information
That's the notes covered.
Carry on to the next subtopic.