Flick on a phone charger and it stays cool for hours. Flick on an electric kettle and it roars through nearly two litres of boiling water in barely a minute. Both are just "electricity" — so why is one a gentle trickle and the other a firehose? The difference is power: how fast each device turns electrical energy into something useful.

The power of an electrical device is the energy it transfers every second. A big number means energy is being shifted quickly — a bright lamp, a fierce heater, a fast motor. A small number means a slow dribble — a night-light, a clock, a charging phone. In this lesson we'll pin that idea down to two short formulas you can carry into any exam, and see exactly why the kettle is a monster and the charger a mouse.

Power is volts times amps

Two things decide how much energy an electrical device shifts each second. The potential difference V (in volts) is the energy handed to each unit of charge as it passes through. The current I (in amps) is how much charge flows past every second. Multiply "energy per charge" by "charge per second" and you get "energy per second" — which is exactly power:

Power comes out in watts (symbol \text{W}), and one watt is one joule of energy transferred per second. So a device rated 1500\ \text{W} is pouring out 1500 joules every single second it runs.

There is a second, equally useful form. Because Ohm's law tells us V = I\,R, we can swap V for I\,R in P = V\,I:

This P = I^2 R version is the one you reach for whenever you care about the heat made in a resistor or a wire — because a wire's resistance R is fixed, so the heat it wastes depends on the square of the current running through it. That single squared term explains most of this lesson.

Worked examples

Example 1 — a kettle's power from its volts and amps. A kettle runs on the mains at 230\ \text{V} and draws a current of 10\ \text{A}. What is its power?

Just as advertised on the box — a couple of kilowatts, which is why it boils so fast.

Example 2 — a light bulb. A car headlight bulb runs on a 12\ \text{V} battery and draws 5\ \text{A}. Its power is

A bright bulb — sixty joules of light and heat every second.

Example 3 — heat made in a resistor, using P = I^2 R. A current of 3\ \text{A} flows through a heating element of resistance 8\ \Omega. How much power does it turn into heat?

Notice the current is squared first: doubling the current to 6\ \text{A} would give 6^2 \times 8 = 288\ \text{W} — four times the heat, not twice.

Example 4 — energy used over time. That 2300\ \text{W} kettle from Example 1 boils for 80\ \text{s}. How much energy does it transfer? Use E = P\,t:

The units keep you right: watts (joules per second) times seconds gives joules back. If your units don't cancel to joules, a rearrangement has slipped.

See it: build your own appliance

Below is an appliance fed through a cable. Set its voltage V and the current I it draws, and the top bar shows the useful power P = V\,I it delivers. The lower bar is the power wasted as heat in the cable, which has a small fixed resistance — and that waste follows I^2 R. Watch what happens:

• turn either control up and the useful power grows — power is volts times amps;
• but the cable-heat bar reacts to the current alone, and grows far faster, because it depends on I^2. Double the current and it quadruples.

Why power cables are thick and made of copper

Every wire has a little resistance, so every wire wastes some power as heat — P_{\text{waste}} = I^2 R. Engineers can't change the current a house or a city needs, but they can change R. A thick cable of a good conductor like copper has a very low resistance, so I^2 R is small and hardly any energy leaks away as heat.

This is also the secret behind the tall pylons that march across the countryside carrying electricity at hundreds of thousands of volts. For a fixed power P = V\,I, pushing the voltage up lets the current I come down for the same power delivered — and since waste is I^2 R, a smaller current means dramatically less energy lost heating up hundreds of kilometres of wire. High voltage, low current, thick copper: three ways to keep I^2 R tiny.

Power ratings and the energy bill

Every appliance carries a power rating stamped on its label — the power it draws at normal mains voltage. It's a quick guide to how hungry a device is:

• a phone charger: about 5\ \text{W};
• an LED lamp: about 10\ \text{W};
• a laptop: roughly 50\ \text{W};
• a toaster: about 1000\ \text{W} = 1\ \text{kW};
• a kettle or an electric heater: about 2{-}3\ \text{kW}.

The rating also tells you the current the device needs, since I = P/V — a 3\ \text{kW} appliance on 230\ \text{V} pulls about 13\ \text{A}, which is exactly why UK plugs top out at a 13\ \text{A} fuse.

Your electricity bill, though, is charged for energy, not power — and energy is power multiplied by time, E = P\,t. To avoid gigantic numbers of joules, energy companies measure in kilowatt-hours (\text{kWh}): one kilowatt-hour is a 1\ \text{kW} device left on for one hour. So a 2\ \text{kW} heater running for 3 hours uses

At, say, 30\text{p} per unit, that's 6 \times 30\text{p} = \pounds1.80 of electricity — the same E = P\,t idea, just in bill-friendly units.