Edexcel IGCSE Physics · Spec 2.13-2.16
Power & Energy: Using the Equations
Worked examples using the electrical power and energy equations.
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Power & Energy: Using the Equations
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Explained
Two equations, and knowing which one a question wants
Power equals current multiplied by potential difference, P equals I times V. Watts, amperes, volts.
Energy transferred equals power multiplied by time, E equals P times t. Joules, watts, seconds.
They connect at power. The first gives you a power from an electrical circuit; the second turns a power into an energy over a period. So a question that gives a current, a voltage and a time is asking you to use both, in that order.
Rearranging without losing marks
From P equals I times V you get current equals power divided by voltage, and voltage equals power divided by current.
From E equals P times t you get power equals energy divided by time, and time equals energy divided by power.
The safe habit is to write the equation as it stands, substitute the numbers you have, and only then solve for the missing quantity. Rearranging in your head before the numbers appear is where mistakes happen, and mark schemes for these questions award the substitution separately from the evaluation, so a visible substitution is worth a mark even if the arithmetic afterwards goes wrong.
Units, and the two traps
Time must be in seconds for E equals P times t. A question quoting minutes or hours is testing the conversion, and it is a mark of its own on many mark schemes.
Power must be in watts. Kilowatts appear on appliance labels, so 2 kW means 2000 W, and a factor of a thousand left in place produces an answer that is wrong by exactly that factor.
The exception is kilowatt hours, used for electricity bills. There you deliberately keep the power in kilowatts and the time in hours, because a kilowatt hour is defined that way. Every other energy calculation on the course uses joules and seconds, and mixing the two conventions is the standard error.
Worked examples
A hairdryer draws 5 A from a 230 V supply. Its power is 5 multiplied by 230, which is 1150 W.
Run for 3 minutes, that is 180 seconds, so the energy transferred is 1150 multiplied by 180, which is 207 000 J, or 207 kJ.
Going the other way: a 60 W lamp transfers 18 000 J. Time equals energy divided by power, so 18 000 divided by 60 gives 300 seconds, which is 5 minutes.
What the mark scheme accepts and rejects
An Edexcel International GCSE Physics mark scheme sets a practical where students calculate their own power output by climbing stairs, working through the gravitational potential energy gained, a mean of three timings, and then power equals energy divided by time. All three parts allow an error carried forward from the ones before.
What is worth studying is the part that follows the calculation. Four marks are available for evaluating whether the results support a conclusion, and the mark scheme lists six ways to earn them.
There are not enough data points to make a valid conclusion, allowing the idea that more students or readings are needed. A greater range of masses should be tested. Masses in between the values used should be tested. There is a general, weak positive correlation, allowing that power increases with mass for the first two data points. One of the data points could be anomalous, allowing any named point. And it goes on to consider what follows if the first point is treated as anomalous.
Its instruction at the top is the surprising one: ignore students are correct or incorrect.
So the verdict earns nothing. Only the reasoning does. An answer beginning the students are wrong has spent its first sentence on the one thing the mark scheme has already said it will pass over, and an answer that never states a verdict at all can still collect all four marks.
Notice how specific the credited criticisms are. Not enough data, too narrow a range, gaps between the values, a possible anomaly. Each names something you could point at in the table.
Where these equations turn up
Choosing a fuse: rearrange to current equals power divided by voltage, then pick the next standard rating above the answer.
Comparing running costs: find the energy in kilowatt hours, then multiply by the price per unit.
Efficiency: find the input power and the output power, each with P equals I times V, then divide the useful output by the total input and multiply by 100.
In each case the first move is the same. Identify which quantities you have been given, and which of the two equations contains all of them.
Spec 2.13-2.16
What you need to know
- Use power equals I times V
- Use energy equals power times time
- Rearrange both equations
Active recall
Quick check
Answer each question before opening the answer.
What is the power of a device drawing 3 A at 230 V?
P = I × V = 3 × 230 = 690 W.
How much energy does a 2000 W kettle use in 60 s?
E = P × t = 2000 × 60 = 120 000 J (120 kJ).
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