learning about how electricity works, the fact is that the number of electrons carrying any current in any circuit is nothing to do with the size of the current.
Instead the number of electrons is determined simply by the amount of conducting material in the circuit. All the electrons flowing in a circuit are nothing more than
electrons in the atoms of the conductors. Each copper atom for example contributes one electron for conducting electricity.
These electrons are able to move around away from their atoms within the conductors, and indeed this is what makes a conductor into a conductor. Importantly however,
the quantity doesn’t change when conducting, regardless of how much current is flowing. The only way you could change the quantity is to add or remove conducting
material from the circuit.
The actual number of conducting electrons is huge, but we can count them using their charge. Simply determined by the number of copper atoms,
the total electron charge flowing in any 1cm length of 1mm22 copper wire is actually 136 Coulombs. Whenever any current is flowing, and 136 Coulombs of electrons
are flowing in every 1cm of this wire!
So where does the size of the current come in? Well each Amp represents 1 Coulomb of electrons flowing past any point in the circuit every second.
So 4 Amps represent 4 Coulombs of electrons flowing past each point, each second. What does this mean when this current is flowing through our 1mm22 copper wire?
Well, we know that the wire has 136 Coulombs flowing in each 1cm, so we also know that the length of conductor containing 4 Coulombs must be
4136=0.029 cm =0.29 mm4136=0.029 cm =0.29 mm
In other words, all the free electrons in 0.29mm of wire flow past a point at the end of this 0.29mm of wire each second. This must mean that all the electrons in the wire are
drifting along in the 4 Amp current at 0.29mm per second.
If alternatively the same current flows through some 0.1mm22wire then this has one tenth the amount of copper and therefore one tenth the number of free electrons per cm,
ie: 13.6 Coulombs worth. Hence in this wire all the electrons in a 2.9mm length must flow past the point at the end of this length every second, ie: in this wire the electrons
travel at 2.9mm per second. In other words, the speed that the electrons travel along the wire is inversely proportional to the cross-sectional area of the wire. The finer the wire,
then the faster the electrons travel in order to maintain the same current.
So how many electrons are in this 2.9mm section of 0.1mm22 wire, flowing past the end of the section every second in the 4 Amp current? Well, we know that there are 4 Coulombs
of electrons in the 2.9mm section. We also know that each electron carries a charge of 1.6×10−191.6×10−19 Coulomb. Hence there are :
electrons in this section of wire, and indeed there are this number of electrons flowing past any point in the circuit every second. and I think this is probably the answer that you were looking for.
Just for completeness, I should point out that this only applies in a DC circuit. In AC the electrons don’t flow along like this, in fact 4 Amps of AC represents something quite different.
But that’s definitely the subject of another question.