A phone charger sips energy; a kettle gulps it. The difference is power — how fast a component turns electrical energy into something else, like heat, light or motion. In circuits, power has one main equation and two handy spin-offs, and a neat surprise hiding inside them: doubling the current does far more than double the heat. Let’s unpack it.
📘 What you need to know
Power is the rate of transferring energy — energy per second, measured in watts (W)
The main equation for electrical power is P = IV
Using Ohm’s law it becomes P = I2R and P = V2 / R
A resistor turns electrical energy into heat (thermal energy) — that’s dissipation
Because P depends on I2, doubling the current gives four times the power
Energy transferred is E = Pt = VIt, measured in joules (J)
What is power?
In physics, power is the rate of transferring energy — how many joules a device shifts each second. It’s measured in watts (W), where 1 watt = 1 joule per second.
Power — the general ideaP = energy transferred ÷ time = E / t
A 60 W light bulb transfers 60 joules of energy every second. A 2000 W kettle shifts 2000 joules a second — which is why it heats water so fast. Higher power just means energy moved faster.
The main equation: P = IV
For an electrical component, there’s a lovely shortcut. Remember two facts we’ve already met:
Potential difference is the energy given to each coulomb of charge (V = energy per charge).
Current is the number of coulombs per second flowing (I = charge per second).
Multiply them together — energy-per-charge times charge-per-second — and the charge cancels, leaving energy per second, which is power:
Electrical powerP = IV
where P is in watts (W), I in amperes (A) and V in volts (V). This is your go-to power equation.
WE 1
A motor draws a current of 2.0 A when connected to a 12 V supply. Calculate its power.
Step 1 — use P = IVP = IVStep 2 — substituteP = 2.0 × 12P = 24 WThe motor transfers 24 joules of energy every second.
Two more versions, from Ohm’s law
Sometimes a question gives you the resistance instead of both I and V. No problem — just swap in Ohm’s law (V = IR) and you get two more forms of the same equation:
The power familyP = IVP = I2R (replace V with IR)P = V2 / R (replace I with V/R)
All three power equations come from P = IV plus Ohm’s law. Pick whichever fits the quantities you’re given.
You don’t have to memorise three separate equations — and they’re all in your data booklet anyway. Just remember P = IV, then let the question tell you which version to use. Got current and resistance? Use I2R. Got voltage and resistance? Use V2/R. A handy memory jingle: “Twinkle twinkle little star, power equals I squared R.”
WE 2
A current of 0.50 A flows through a resistor of 8.0 Ω. Calculate the power dissipated.
Step 1 — we have I and R, so use P = I²RP = I2RStep 2 — substitute (square the current first!)P = (0.50)² × 8.0 = 0.25 × 8.0P = 2.0 WSquare the current before multiplying — a very common slip.
WE 3
A potential difference of 6.0 V is applied across a 12 Ω resistor. Calculate the power dissipated.
Step 1 — we have V and R, so use P = V²/RP = V2 / RStep 2 — substituteP = (6.0)² ÷ 12 = 36 ÷ 12P = 3.0 WChoosing the right form saved us from working out the current first.
Power as heat — dissipation
When current flows through a resistor, the electrons collide with the metal ions (just like on the resistance page) and hand over energy. That energy shows up as heat. We say the resistor dissipates power — it turns electrical energy into thermal energy that spreads into the surroundings.
Electrical energy in, heat out. A kettle or toaster uses a high-resistance element on purpose to dissipate lots of power as heat.
Now the surprise. Look at P = I2R — the current is squared. So if you double the current, the power doesn’t just double, it goes up four times (22 = 4). Triple the current and the power is nine times greater. That squared relationship is why big currents produce so much heat, and why thick wires (low resistance, so lower currents for the same job) waste less energy.
This is the whole reason power companies send electricity across the country at very high voltage. High voltage lets them use a low current for the same power (since P = IV). And because heat loss goes as I2R, a small current wastes far less energy heating up the cables. Same idea, huge real-world payoff.
Energy transferred over time
Power tells you the rate of energy transfer. To get the total energy transferred, just multiply the power by how long it runs:
Energy transferredE = Pt = VIt
with energy E in joules (J), power P in watts (W) and time t in seconds (s).
WE 4
A 60 W light bulb is left on for 5.0 minutes. Calculate the electrical energy it transfers.
Step 1 — convert time to secondst = 5.0 × 60 = 300 sStep 2 — use E = PtE = 60 × 300E = 18 000 J (18 kJ)Always turn minutes into seconds first — the watt is joules per second.
Power P = IV (W)
× time (seconds)
Energy E = Pt (J)
💡 Top tips
P = IV is the master equation; I2R and V2/R come from it via Ohm’s law.
Match the equation to your data: I & R → I2R; V & R → V2/R; I & V → IV.
Square the right quantity — and do the squaring before multiplying or dividing.
Double the current → four times the power (it’s the I2 effect).
For energy, convert time to seconds first, then use E = Pt.
⚠ Common mistakes
Forgetting to square in I2R or V2/R
Squaring after multiplying by R instead of before
Thinking doubling the current only doubles the power — it quadruples it
Leaving time in minutes or hours when using E = Pt
Picking a power equation that needs a quantity you weren’t given — choose the one that fits
Quick recap: Power is the rate of energy transfer, in watts. The master equation is P = IV, which becomes P = I2R and P = V2/R using Ohm’s law. Resistors dissipate power as heat, and because power depends on I2, doubling the current quadruples the power. Total energy is E = Pt = VIt.
We’ve treated the cell as a perfect, tireless energy source — but real batteries aren’t quite so generous. Some of their energy gets wasted inside the battery itself, so the voltage you actually get is a little less than the battery’s full “push”. Next up in Sources of Electrical Energy we’ll look at the different ways we generate that push, before diving into what really goes on inside a cell.
Want power calculations to feel automatic?
Book a free meeting and we’ll drill the three equations until picking the right one is second nature.
