Drift Velocity of Electrons through a conductor.

The "average speed" at which the "free" charges are moving in the wire is called the drift velocity.

In a wire, collisions of the conduction charges with impurities, imperfections, and vibrations of the atomic lattice causes the motion of the conduction charges to be slowed down. This represents a loss of energy which is dissipated as heat.

Although your light turns on very quickly when you flip the switch, he actual drift velocity of electrons through copper wires is very slow. It is the change or "signal" which propagates along wires at essentially the speed of light. in other words, electricity propogates at the speed of light, but not the individual electrons through the conductor. Electrcity is a signal.

A Specific Example:

The total volume of the cylinder is A x l (cross section x length).

Within that volume there is some average density, n of free electrons.

Each electron carries with it a charge of q.

So the total charge Q = density of electrons x volume x charge per electron =

nAlq

We can now replace the length of the cylinder by velocity x time where velocity is the drift velocity of the electrons as they move over a length l and time is how long it takes to move that length.

so l = v x t

Remember that current is the amount of charge that flows passed a fixed point per unit time

so,

current = charge/time = Q/t = nAqvt/t = nAvq

Resistivity of material and charge density:

A material with a lot of free electrons (a high value of n) can carry a current more easily than one with a smaller charge density.

To carry a given current, the electrons don't have to move very fast because there are so many of them to carry the charge.

This means that they rarely collide with atoms or impurities in the metal, and so it is a good conductor.

A semiconductor is a material with perhaps a free electron density about 1 million times smaller than a good conductor (e.g. cooper).

Therefore, the (fewer) free electons in a semiconductor have to have significantly higher drift velocities to carry the same current.

As a result, the collide with atoms much more often. These collisions are the basic source of resistance in a material. Each collision also heats up the material.

A numerical example:

Drift velocity in Cooper.

n = 8.5 x 10²⁸ per cubic meter (yeah, that's a lot of electrons)

q = 1.6 x 10^-19 C (coloumbs)

assume a 5 amp current and a cross section of copper wire of area = 0.5 mm² (=0.5 x 10^-6m²)

plug these numbers into I =nAvq

5 = 8.5 x 10²⁸ x 0.5 x 10^-6 x v x 1.6 x 10^-19

5 = 27200v

v = 7.35 x 10^-4 m/s = about 0.1 mm per second! extremely slow because the electron mobility is so good.

For a semi-conductor, the velocity would be about 1 million times higher. This means the kinetic energy (1/2mv²) of the electrons is large which means when they have collisions with other atoms a lot of heat can be dissipated.

This is the main physical reason why your laptop gets hot and in general, why switching information by using electrons generates heat as a by product.