Understanding Ohms: A Beginner's Guide

[SaraF]

Homework Statement

This is not exactly a homework problem, but it's one that marks me as a beginner: is there an intuitive physical understanding, using dimensional analysis, of the unit combination making up the "ohm"? I don't mean a physical understanding of resistance--that's not a problem. I mean, how can I understand the meaning of volt/amp?

Homework Equations

R = V/I

The Attempt at a Solution

a volt is an amount of potential energy change per coulomb of charge...I think I understand what that means. An Ampere is the rate of flow of coulombs in a circuit, the amount of charge that flows through a given point each second. If I put them together and solve for the resistance, I get that an ohm = Joule x second / Coulomb². Does that mean anything?
Going further, a Joule is a N-m. Using Coulomb's Law, a Newton is proportional to charge² divided by distance². Put all that together, and I get the rather interesting result that an ohm is reciprocal velocity. That kind of makes sense. The bigger the resistance, the slower the velocity. But what is moving? It seems too simple to say that "electrons are moving," since I know that they really don't move very far, due to collisions with atoms in the wire. Can it be said that the electric field is moving? Can someone enlighted me about this? I'd be really grateful! Thanks in advance.

 

[tiny-tim]

Hi SaraF!

… Using Coulomb's Law, a Newton is proportional to charge² divided by distance².

No, you've left out the constant k, which itself has dimensions.

I get that an ohm = Joule x second / Coulomb². Does that mean anything?

Not really!

It's correct, of course, but … like most electric units … there's not much point in going any further than the obvious (in this case, Ω = V/A).