Electrical Power and Energy

The energy behind every switch

Every time you boil a kettle, charge a phone or switch on a lamp, electrical energy is being transferred into heat, light or sound. Some devices gulp that energy quickly; others sip it. The quantity that tells us how fast energy is moving is power.

This lesson links three big ideas — current, voltage and power — and shows you how to work out exactly how much energy a device uses, and what it costs.

What power really means

Power is the rate of transferring energy: how many joules of energy a device moves every second.

Power (watts) = energy transferred (joules) ÷ time (seconds) P = E / t

The unit is the watt (W), where 1 watt = 1 joule per second. A 60 W lamp transfers 60 joules of electrical energy into light and heat every second. A 2000 W kettle transfers 2000 joules every second — over 30 times faster — which is why it boils water so quickly.

The key equation: P = IV

In an electric circuit there is a beautifully simple way to find power without measuring energy directly. Power equals current times voltage:

P = I × V

where I is the current in amperes (A) and V is the potential difference in volts (V).

Why does this work? Voltage tells you how much energy each unit of charge carries (joules per coulomb), and current tells you how much charge flows each second (coulombs per second). Multiply them and the coulombs cancel, leaving joules per second — power.

Because voltage, current and resistance are linked by V = IR, you can rewrite the power equation in two other handy forms:

• Substitute V = IR: P = I²R
• Substitute I = V/R: P = V²/R

All three give the same answer; you simply pick the one that matches the quantities you already know.

Worked example: a hairdryer

A hairdryer runs on a 230 V mains supply and draws a current of 5 A. What is its power, and how much energy does it use in 4 minutes?

Step 1 — find the power:

P = IV = 5 × 230 = 1150 W (1.15 kW)

Step 2 — find the energy. Energy is power times time, with time in seconds:

t = 4 min = 240 s E = P × t = 1150 × 240 = 276,000 J (276 kJ)

So in four minutes the hairdryer transfers over a quarter of a million joules of energy — mostly into warm, fast-moving air.

Worked example: heat in a resistor

A resistor of 20 Ω carries a current of 2 A. How much power does it dissipate as heat?

Here we know current and resistance but not voltage, so the neatest form is P = I²R:

P = I²R = (2)² × 20 = 4 × 20 = 80 W

This is exactly the effect used in household electricity and safety: a fuse is a thin wire that gets hot when too much current flows, and the P = I²R heating melts it to break the circuit.

Paying for energy: the kilowatt-hour

Your electricity bill does not charge you for power — it charges for energy used. But joules are inconveniently small, so suppliers use the kilowatt-hour (kWh):

Energy (kWh) = power (kW) × time (hours)

One kilowatt-hour is the energy a 1 kW device uses in 1 hour, equal to 3,600,000 joules.

Example: if a 2 kW heater runs for 3 hours:

E = 2 × 3 = 6 kWh

If each kWh costs 30 cents, that heater costs 6 × 30 = 180 cents ($1.80) to run. This is why leaving high-power appliances on is far more expensive than leaving a low-power LED lamp glowing.

Try it yourself! 🧪 (safe version)

You can compare power ratings safely without opening anything or touching mains wiring — never poke around inside plugs or sockets.

1. Walk around your home and read the small label or moulded text on several appliances. Most show a power rating in watts (e.g. "1200 W") or volts and amps.
2. Make a table from lowest to highest power: phone charger, LED lamp, TV, microwave, kettle.
3. For any two devices, estimate which uses more energy in 10 minutes by multiplying power × time. A 1000 W microwave for 10 minutes uses far more than a 5 W charger.
4. Notice the pattern: things that heat or move (kettles, heaters, motors) are high power; things that only light up or process information are low power.

You have just ranked your home's energy users using nothing but P = IV and a bit of arithmetic. To see where all this energy comes from in the first place, visit how we generate electricity.