Here is a problem I have been wondering about since I was in school. I've never found any answer so I hope someone here might help me.

I learned some rules such as resistance in series is R1 + R2 and in parallel it's 1/(1/R1 + 1/R2). Of course there are equations for all sorts of other components connected into a circuit and various other quantities than resistance, for example voltage, amperes, etc.

Of course these formula were originally found by experiments and tests, but now quantum physics has got into the understanding of what is actually inside a circuit: electrons through a crystal of metal atoms.

What I want to know is how to derive all the laws of circuitry from scratch using this atomic viewpoint. So I hope someone will find this interesting and maybe knows about it!