Electrical power measures the rate at which energy is transferred in a circuit, measured in watts. The three key equations are P = IV, P = I²R, and P = V²/R. Choosing the right equation depends on which quantities are given: current and voltage, current and resistance, or voltage and resistance.
What is electrical power?
Electrical power is the rate at which electrical energy is converted into other forms of energy — heat, light, sound, kinetic energy — within a device or circuit. It is measured in watts (W), where 1 watt equals 1 joule per second (1 W = 1 J/s).
A 100 W lamp transfers 100 joules of energy every second. A phone charger rated at 20 W transfers 20 joules every second. Power tells you how quickly energy moves, not how much in total — that is the job of the energy equation E = Pt.
What are the three equations for electrical power?
| Equation | When to use | Quantities needed |
|---|---|---|
| P = IV | Voltage and current are both known | P in W, I in A, V in V |
| P = I²R | Current and resistance are both known | P in W, I in A, R in Ω |
| P = V²/R | Voltage and resistance are both known | P in W, V in V, R in Ω |
All three equations are derived from combining P = IV with Ohm's law (V = IR):
- Substituting V = IR into P = IV gives P = I × (IR) = I²R
- Substituting I = V/R into P = IV gives P = (V/R) × V = V²/R
So you only ever need to remember P = IV and V = IR; the other two follow automatically.
How do you choose the right power equation?
Before you pick an equation, list the quantities you have been given and the one you want to find. Then choose the form that contains exactly those quantities:
- Given I and V, but not R: use P = IV
- Given I and R, but not V: use P = I²R
- Given V and R, but not I: use P = V²/R
Exam questions sometimes give you more information than you need (e.g. current, voltage, and resistance), to let you cross-check your answer. If two equations give different answers for P, you have made an arithmetic error in one of them.
How do you calculate electrical power — worked examples?
Example 1 — using P = IV:
A kettle draws a current of 9.5 A from a 230 V mains supply. Calculate its power.
- Equation: P = IV
- Substitute: P = 9.5 × 230
- P = 2,185 W (≈ 2.2 kW)
This matches the typical rating on a household kettle label.
Example 2 — using P = I²R:
A resistor carries a current of 3.0 A and has a resistance of 8.0 Ω. Calculate the power dissipated.
- Equation: P = I²R
- Substitute: P = (3.0)² × 8.0 = 9 × 8.0
- P = 72 W
Example 3 — using P = V²/R:
A 12 V lamp has a resistance of 4.0 Ω. Calculate its power.
- Equation: P = V²/R
- Substitute: P = (12)² ÷ 4.0 = 144 ÷ 4.0
- P = 36 W
How does electrical energy relate to power?
Energy and power are linked by:
$$E = Pt$$
Where E is energy transferred (joules, J), P is power (watts, W), and t is time (seconds, s).
Example: How much energy does a 2,000 W microwave transfer in 3 minutes?
- Convert time: t = 3 × 60 = 180 s
- E = Pt = 2,000 × 180
- E = 360,000 J (360 kJ)
Energy is also measured in kilowatt-hours (kWh) on electricity bills: 1 kWh = 3,600,000 J. A 2 kW microwave running for 0.5 h uses 1 kWh of energy — and that unit appears in both GCSE physics and everyday life.
How does power relate to heating effects in wires?
The P = I²R equation is particularly important for understanding why high-voltage transmission lines carry electricity at very high voltage and very low current. For a fixed resistance in a cable:
- Doubling the current quadruples the power dissipated as heat (P ∝ I²)
- Halving the current reduces heating losses to one quarter
Transformers step voltage up to hundreds of kilovolts before transmission, keeping current tiny and therefore cable heating losses very small. This is the direct physical reason the National Grid uses high-voltage, low-current transmission rather than the reverse.
Frequently asked questions
What are the three formulas for electrical power in GCSE physics?
The three power equations are P = IV (power = current × voltage), P = I²R (power = current² × resistance), and P = V²/R (power = voltage² ÷ resistance). All three give power in watts. You derive P = I²R and P = V²/R by combining P = IV with Ohm's law (V = IR). Choose whichever equation contains the two quantities you have been given.
What is the unit of electrical power?
Electrical power is measured in watts (W), where 1 W = 1 J/s. Larger appliances are often rated in kilowatts (kW): 1 kW = 1,000 W. On exam papers, read the rating carefully — a 2 kW appliance must be converted to 2,000 W before using it in P = IV or E = Pt unless the question explicitly works in kW and kWh.
How do you calculate electrical energy from power?
Multiply power by time: E = Pt. Power must be in watts and time in seconds to get energy in joules. If you prefer kilowatt-hours, keep power in kilowatts and time in hours: a 3 kW shower running for 2 hours uses 6 kWh. Exam questions may ask for energy in joules (use seconds) or in kWh (use hours) — always check the expected unit.
Why does doubling the current more than double the heating in a wire?
Because power dissipated as heat follows P = I²R: power is proportional to the square of the current, not just the current itself. Doubling I multiplies P by 2² = 4 — the wire produces four times as much heat. This squared relationship is why overloaded circuits heat up dangerously fast and why fuses and circuit breakers are sized to interrupt current before wires overheat.
For Socratic GCSE physics with Professor Newton — predict whether a higher current or a higher resistance causes more heating before reaching for P = I²R, then check whether the squared relationship matched your intuition — visit aitutors.me.