How fast must free electrons move in a wire to produce a decent current?

‘Current’ means the rate at which electric charge flows past a point in a circuit. Imagine standing at point X with a stopwatch and timing the charge flowing past. (We have to imagine that all the electrons move at the same speed, v.) We'll watch what happens to the electron highlighted in red.

Suppose you start your watch and let it run for a time, t. The highlighted electron electron will have travelled a distance . In fact, in time t, all of the electrons in the cylinder of length have flowed past you.

So what current has flowed? We need to work out how much charge has passed point A.
We start by thinking of the volume of the cylinder.

Volume of cylinder = A ×		where A is the cross-sectional area of the wire
	If concentration of electrons in the metal is n per cubic metre then:
Number of electrons in cylinder = n × A ×
	If each electron carries charge Q then:
Charge carried by electrons in cylinder = n × A × × Q
	But the length of the cylinder is v * t	where v is the drift velocity and t is the time we used
	So:
Charge carried by electrons in cylinder = n × A × v × t × Q
	This is the amount of charge which passes point A in time t. To find the current which this represents, we need to find the rate at which the charge has flowed. So we divide by the time t.
Current = charge / time = n × A × v × t × Q / t    =   n A v Q
	So the electric current I flowing in a wire is given by
		where n is the number of electrons per cubic metre A is the cross sectional area of the wire v is the drift velocity of the electrons Q is the charge of an electron

Semiconductors are materials with few free electrons – perhaps one-millionth of copper’s concentration. So free electrons in semiconductors have to have much higher drift velocities to carry the same current. Their speed has to make up for the smaller amount of charge that is moving. Therefore they collide with atoms much more often. The resistivity of a semiconductor is typically one million times that of copper.

Let's think of a current of 5 A that is flowing in a copper wire with a cross section of 0.5 mm² (= 0.5 * 10^-6 m²)

For copper, n = 8.5 × 10²⁸ per m³
The charge on an electron, Q = 1.6 × 10^-19 C

So,
   I = n A v Q

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

   5 = 27 200 v

   v = 7.35 × 10^-4 m s^-1

So, for this current, the drift velocity of electrons is about a tenth of a millimetre per second: pretty slow!