physics//electromagnetism//electric circuit//electrical resistance//Joule heating

Joule heating is the conversion of electrical energy into heat when a current flows through a resistance, and it is at once the working principle of every kettle, toaster and fuse and the main loss in every cable, motor and transformer. The electrons pushed through a conductor keep colliding with the atoms of its crystal, and each collision hands their energy to the crystal as vibration, which is heat.

Joule heating is the conversion of electrical energy into heat when a current flows through a resistance, and it is at once the working principle of every kettle, toaster and fuse and the main loss in every cable, motor and transformer. The electrons pushed through a conductor keep colliding with the atoms of its crystal, and each collision hands their energy to the crystal as vibration, which is heat.

The power turned into heat is

P=I2R,P = I^2 R ,P=I2R,

the current squared times the resistance. The square is the part to remember: double the current and the heat quadruples. A kettle heats water with a few tens of ohms of element and about 10 A; a fuse is a short thin wire chosen to melt at a set current; a power line is designed to carry as little current as possible for the power it delivers.

Heat goes with the current squared.

That one exponent is why the grid transmits at hundreds of kilovolts, why wires are sized by amperes, and why a short circuit melts things before anything else happens.

In the body, heat is the injury of large currents. Burns along the path of a current dominate from about an ampere upwards; at the milliamperes of most household shocks the heart's rhythm fails long before any tissue heats (electric shock).

Chips are limited by it. The switching current of billions of transistors becomes heat that has to be carried away, which is why cooling sets the power budget of a processor.