Why does electric current heat a conducting wire?

Electric current heats a conducting wire due to a phenomenon known as Joule heating.1

When an electric current flows through a conductor, the free electrons responsible for the current are accelerated by an electric field. As these electrons move, they frequently collide with the fixed ions that make up the material's structure. During these collisions, the electrons transfer some of their kinetic energy to the ions, causing the ions to vibrate more vigorously. This increase in atomic motion is observed macroscopically as a rise in the wire's temperature.2

This process is fundamentally linked to the material's electrical resistance, which is the measure of how much a conductor opposes the flow of current. Quantitatively, the rate at which electrical energy is converted into heat—known as power loss (P)—is proportional to the resistance (R) and the square of the current (I), expressed by the formula:32

$$P=I^{2}R$$

In this equation, power is measured in watts, current in amperes, and resistance in ohms.1