Question

What IS resistance in terms of the electric field of a circuit?

Answer 1

Deep and extremely difficult.
Formally speaking one needs to do Quantum-Solid-State physics to define the Electric field inside a conductor, and usually one prefers D and not E as the working object.

Answer 2

If we talk about simplified circuit theory for engineers - the resistance is INDEPENDENT of the potential difference in the circuit.

Answer 3

One does not speak (in simplified circuit theory) of fields inside a circuit.

Answer 4

See in wikiped http://en.wikipedia.org/wiki/Maxwell's_equations
This "Maxwell's "macroscopic" equations"

Answer 5

Also, are you saying that although (taking the ideal case) V=IR, changing v only tends to change current, not resistance, because of their mutual independence?

Answer 6

My vector calculus is shoddy. Could you simplify?

Answer 7

Yes that is correct

Answer 8

This has nothing to do with vectors. Forget vectors think even 1-dim.
In matter there exist polarization that kind of "substracts" from the field. So netto one has D

Answer 9

No, no, no same letter - nothing related at all

Answer 10

I guess http://en.wikipedia.org/wiki/A_Dynamical_Theory_of_the_Electromagnetic_Field [Ohm's law] relates resistance to the E field

Answer 11

It sort of makes sense, as\[\int\limits_{x}^{ \infty}E \cdot dr=IR\]

Answer 12

I think that If you want to understand (really to start understanding) what is resistance
see these
http://www.youtube.com/watch?v=QvPSVwzU-8A
http://www.youtube.com/watch?v=KprFTxjQAoE&feature=related

Answer 13

Chances are the first will be more helpful than the second. Thanks for your time, doubly so!

Answer 14

Good for your start

Answer 15

@henpen see

Answer 16

Thank you. I'll also have a look at Walter Lewin's explaination, if only because of familiarity.

Answer 17

Chaos, generally. If the electric field an electron experiences changes a lot, first accelerating it in one direction, then in the opposite, then back to the first, then it will, overall, take a lot more potential difference from the start of the circuit element to the end to get the electron to move through it at a given rate.

Think of it essentially as "city traffic" versus highway driving, as far as the electron is concerned. If it has to do a lot of stopping and starting, more "fuel" (energy) is required at the beginning of the trip to make it through. It's the local electric field that constitutes the "stop signs" and "traffic lights" that decelerate and then accelerate the electron. If a lot of that is going on, then the resistance is higher.

These small electric fields can come from many places. The most obvious is the cores of the atoms that make up the conductor. Depending on the nature of the conductor, these cores can generate large or small variations in electric field that hinder or don't much hinger the flow of electrons. Additional sources of small local fields are magnetic effects, e.g. local inductanec, and small local pockets of stored charge, e.g. local capacitance.