Electrical Energy, Power and Cost
Three equations for power, one for energy, and a unit — the kilowatt-hour — that trips people up because it is not a joule.
1. Electrical power
Power is the rate of energy transfer — energy transferred per second.
Unit: the watt (W). 1 W = 1 J/s.
The three power equations:
P = V I P = I² R P = V² / R
The last two follow from the first by substituting V = IR.
Example: a lamp carries 0.5 A at 12 V.
- P = VI = 12 × 0.5 = 6 W
Example: a 3 A current through a 20 Ω resistor.
- P = I²R = 3² × 20 = 9 × 20 = 180 W
Square the current in P = I²R — not the resistance.
Choose the equation that matches what you’re given. Confusing the power formulae with each other, and with the energy formula, were both recorded errors. If you have V and I, use P = VI; if you have I and R, use P = I²R.
2. Electrical energy
E = P t — energy (J) = power (W) × time (s) E = V I t E = Q V — energy = charge × potential difference
Example: a 2000 W heater running for 5 minutes.
- t = 5 × 60 = 300 s
- E = 2000 × 300 = 600 000 J (600 kJ)
Time must be in SECONDS when power is in watts. Failing to convert minutes or hours to seconds was recorded repeatedly and is the most common error here.
E = QV lets you find energy from charge — useful when a question gives coulombs rather than current and time. Not knowing this route was recorded.
Power is energy DIVIDED by time; energy is power MULTIPLIED by time. Getting these the wrong way round was recorded — check the units: watts are joules per second.
3. The kilowatt-hour and cost
Domestic electricity is billed in kilowatt-hours, not joules.
1 kilowatt-hour (kWh) is the energy used by a 1 kW appliance in 1 hour.
Energy (kWh) = power (kW) × time (HOURS)
For kWh, power must be in KILOWATTS and time in HOURS. This is the one place where you do not convert to seconds — and mixing the two conventions is the classic error.
Converting: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J
Calculating cost:
Cost = energy (kWh) × price per kWh
Worked example. A 2 kW heater runs for 3 hours at 15p per kWh.
- Energy = 2 × 3 = 6 kWh
- Cost = 6 × 15 = 90p (£0.90)
Worked example with watts and minutes. A 500 W appliance for 90 minutes at 20p/kWh.
- Power = 500 W = 0.5 kW
- Time = 90 min = 1.5 hours
- Energy = 0.5 × 1.5 = 0.75 kWh
- Cost = 0.75 × 20 = 15p
Convert watts to kilowatts (÷1000) and minutes to hours (÷60) first. Both conversions are needed, and missing either was recorded.
4. Power ratings and multiple appliances
An appliance’s power rating tells you the energy it transfers per second at its normal operating voltage.
For several identical heating elements, the total power is the SUM. Two 1 kW elements switched on together give 2 kW. Misunderstanding how the number of heating elements affects total power was recorded.
Choosing a fuse: find the normal operating current from I = P/V, then pick the next fuse value above it.
5. Efficiency and conservation
Efficiency = (useful energy output ÷ total energy input) × 100% or equivalently with power.
Efficiency can never exceed 100%, and the output must always be less than the input. If your calculation gives more out than in, something is wrong — this check was flagged in lessons.
Never say energy is “created” or “destroyed” — say it is transferred or wasted. Tutors flagged this exact wording, and a recorded error described energy as being created. Conservation of energy is absolute: the “missing” energy has been dissipated, usually as thermal energy.
6. Accuracy
Give answers to a sensible number of significant figures — usually 2 or 3 — and always include the unit: W, J, kWh, or a currency.
Not every formula is on the formula sheet. Tutors warned that some must be memorised — check your own sheet so you know which.
7. Mistakes that cost marks
Not converting time to seconds for joules.
Converting to seconds when the question wants kWh.
Leaving power in watts for a kWh calculation.
Confusing P = VI with P = I²R or with the energy equation.
Squaring the resistance instead of the current.
Multiplying when you should divide for power.
Efficiency over 100%, or output greater than input.
Saying energy is created or destroyed.
Omitting units or using the wrong ones.
Frequently asked questions
What is electrical power? The rate of energy transfer, in watts.
What are the power equations? P = VI, P = I²R, and P = V²/R.
How do I calculate electrical energy in joules? E = Pt (or E = VIt), with time in seconds.
What is a kilowatt-hour? The energy used by a 1 kW appliance in 1 hour — equal to 3.6 × 10⁶ J.
How do I calculate energy in kWh? Power in kilowatts × time in hours.
How do I calculate the cost of electricity? Energy in kWh × price per kWh.
How do I convert watts to kilowatts? Divide by 1000.
What is efficiency? Useful output ÷ total input × 100% — never more than 100%.
Can energy be created? No — it is transferred or wasted, never created or destroyed.
How do I choose a fuse? Find I = P/V, then choose the next fuse rating above it.
Quick revision checklist
- I know power is the rate of energy transfer, in watts
- I know all three power equations and when to use each
- I square the current in P = I²R
- I know E = Pt = VIt = QV
- I convert time to seconds for joules
- I know what a kilowatt-hour is
- I use kW and hours for kWh calculations
- I can convert kWh to joules
- I can calculate the cost of running an appliance
- I can add power ratings for multiple appliances
- I can calculate efficiency and check it is under 100%
- I say energy is transferred or wasted, never created
- I give units and sensible significant figures
These notes cover electrical energy, power and cost in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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