Heating Effect of Current (Joule's Law)

1. Introduction: Why Does the Wire Get Hot?

Touch the back of a working electric iron. It is hot. Hold your hand near a glowing bulb. You feel warmth. Both run on the same current that flows quietly through the wires in your wall — yet the wall wire stays cool and the iron burns.

So here is the question this whole topic answers: when current flows through something, how much heat does it make, and what decides that amount?

You already know two things from before. You know current — the flow of charge through a wire, measured in ampere ($A$). And you know resistance ($R$) — how strongly a material opposes that flow, measured in ohm ($\Omega$). When charge is pushed through a resistance, it has to do work, and that work turns into heat. That heat is the "heating effect of current."

By the end, you will be able to write the exact rule for that heat — it is called Joule's Law — derive it from scratch, and use it to explain why a heater glows but the connecting wire does not.

Stop scrolling. Try it in your head before reading on: a heater and the wire feeding it carry the same current. Why does only one get hot?