The heating effect

1. Whenever there is a current in a conductor, the conductor becomes warmer than its surroundings. This is the heating effect of an electric current.
2. The effect occurs in every metal conductor: in connecting leads, in a resistor, in the element of a kettle and in the filament of a lamp. Even a thick copper lead carrying a small current warms up by a small amount.
3. The energy that appears in the thermal store of the conductor is transferred from the chemical store of the cell, or from the mains supply, along the electrical working pathway.
4. The heating effect is not a fault and not a special case. It is the unavoidable consequence of driving charge through a material that has resistance.
5. The effect is easy to observe. A resistor in a circuit feels warm after a minute or two, the filament of a lamp reaches about $2500{}^{\circ }C$ and glows white hot, and the wire inside a fuse can become hot enough to melt.
6. Two quantities travel through the wire and they must be kept apart. The charge passes through the conductor and out the other side, while the energy carried by that charge is left behind in the metal.

Inside a metal conductor

1. A metal consists of positive ions arranged in a regular repeating pattern called a lattice. Each ion has a fixed average position in that pattern.
2. Each metal atom has released one or more of its outer electrons. Those electrons are no longer attached to any one atom, so they are described as delocalised or free electrons.
3. The delocalised electrons are free to move throughout the whole piece of metal. This sea of mobile electrons is what makes a metal a good conductor of electricity.
4. The lattice ions are not free to move through the metal. They vibrate about their fixed positions, and the higher the temperature of the metal, the larger the amplitude of that vibration.
5. With no potential difference across the metal the free electrons still move, and move fast, but their directions are random. As much charge moves one way as the other, so there is no net flow of charge and no current.
6. The random speed of the electrons is very high, but the extra drift that a potential difference adds is slow, typically less than $1{mm\; s}^{-1}$. The heating effect comes from that slow drift, not from the random motion.

The collision mechanism

1. A potential difference applied across the ends of the wire sets up an electric field along the wire, and that field exerts a force on every free electron inside it.
2. The force gives each electron a steady drift in one direction along the wire, added on top of its fast random motion. This net drift of charge in one direction is the current.
3. A drifting electron does not travel freely from one end of the wire to the other. It repeatedly collides with the vibrating positive ions of the lattice.
4. In each collision the electron transfers some of its kinetic energy to the ion it strikes. Energy passes from the electrons to the lattice.
5. The ion that receives the energy then vibrates with a larger amplitude about its fixed position, so the kinetic energy of the lattice has increased.
6. The internal energy of the metal is the total kinetic and potential energy of all of its particles. More vigorous lattice vibration therefore means the internal energy of the metal has risen.
7. A rise in the internal energy of the lattice appears as a rise in the temperature of the wire, so the wire becomes hotter than its surroundings.
8. Because the wire is now hotter than its surroundings, energy is transferred out of it by heating: by conduction into whatever the wire touches, by convection in the air around it, and by radiation from its surface.
9. The electrons lose energy at every collision, yet the current does not die away. Between collisions the potential difference does work on each electron again and accelerates it again, so the supply keeps replacing the energy the electrons hand to the lattice.
10. The temperature of the wire stops rising when it reaches a steady state, in which the wire transfers energy to the surroundings at the same rate as the supply transfers energy to the wire.
11. Every link in this chain depends on the one before it. No potential difference means no drift, no drift means no collisions, and no collisions means no rise in the internal energy of the lattice.

Resistance and dissipation

1. The collisions that heat the wire are the same collisions that obstruct the flow of charge through it. Resistance and the heating effect are two views of one mechanism, not two separate pieces of physics.
2. Energy transferred out of the electrical pathway into the internal energy of the lattice, and then spread into the surroundings, is said to be dissipated.
3. Dissipated energy is not destroyed. It becomes shared between an enormous number of particles in the surroundings, spread so thinly that it can no longer be gathered up and used for the same job again.
4. A conductor of higher resistance takes more energy from each coulomb of charge that passes through it, because that charge meets greater obstruction on its way through.
5. The more strongly the lattice ions vibrate, the larger the volume they sweep out and the more often the drifting electrons run into them. This is why the resistance of a metal wire is greater when the wire is hot than when it is cold.
6. A perfect conductor, one of resistance $0\Omega$, would dissipate no energy at all. No ordinary metal at everyday temperatures behaves like that, so every real conductor warms up at least a little.

What makes the effect larger

1. For a given wire, a larger current means more charge passes every second, so there are more electron collisions with the lattice every second and the wire heats up faster.
2. For a given current, a larger resistance means each electron gives up more energy to the lattice on its journey through, so more energy is dissipated every second.
3. Current has the stronger influence of the two. Doubling the current in a fixed resistance raises the rate at which energy is dissipated by considerably more than double.
4. The time for which the current flows matters as well. The longer the current continues, the more energy in total is dissipated in the conductor.
5. A conductor of very low resistance, such as a short thick copper lead, still dissipates energy, but so little that the temperature rise is hard to detect by touch.
6. A conductor of high resistance carrying a large current can reach a very high temperature, which is why the thin filament of a lamp glows white hot while the thick leads feeding it stay cool.