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The Electrical resistance is defined as the oppose of flow of charge by a material(wire for example). Also $R = \rho l/A$

What i think is that "charge" here actually means the magnitude of charge only. It doesn't mean charge particles. And the reason to say that is, when we increase the area of cross section of wire carrying current the amount of charge flowing is affected while the flow of charge particles remains uneffected. Double amount of charge starts flowing when area of cross-section is doubled because the number of electrons flowing gets doubled while the drift velocity remains same as before.

Means electrical resistance opposes the amount of charge passing through a cross section of wire.

Electrical Resistivity is also sometimes given the same definition, the oppose of flow of charge by a material. Here the "charge" should mean the charge particles.

If you replace a copper wire with tungsten of identical dimension, the electron flow reduces due to the reduction in speed of electrons or the electrons drift velocity gets reduced. If you change the cross section of wire, the amount of charge flowing changes even the material and voltage provided remains same.

It means that Electrical resistivity is the property of material(let say wire) to resist flow of charge particles (not magnitude of charge).

In short: The Resitance 'always' opposes the current whereas the Resitivity 'always' oppose the velocity of electrons contributing to current in wire. "Resistance doesn't always oppose the velocity of electrons"

I want to know your thoughts on how correct or wrong it is.

Qmechanic
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Predaking Askboss
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  • "when we increase the area of cross section of wire carrying current the amount of charge flowing is affected while the flow of charge particles remains uneffected." Where did you get that idea? At the molecular level each charged particle has a charge of either +e or -e. And in many cases the particles with +e are immobile so don't contribute to current. Then you can't increase the current without changing the number of particles flowing past a given cross section of the conductor in a given time. – The Photon Jan 22 '22 at 20:06
  • OK, should be +e, -e, or an integer multiple of e. But let's talk about metallic conductors here to keep it simple. – The Photon Jan 22 '22 at 20:08
  • When we increase area of cross section the number of atoms increases and so the number of electrons. Just because you are getting same electric field in wire when doing it( increasing cross-section) you get double amount of charge flowing with same E force same applied on each particle as before. What's the issue? – Predaking Askboss Jan 22 '22 at 20:14
  • If it is about conductors then yes you can't increase current without increasing amount of electrons passing through. And at given voltage, length and resistivity, the only way is to increase cross section which increases the number of electrons in an area( in actual you can't put electrons in an area) – Predaking Askboss Jan 22 '22 at 20:17
  • Perhaps this will help: How does a resitance affect electric current in a circuit...??(series) and Resistance and resistivity: which one is the intrinsic and which is the geometric property? Why? – Roger V. Feb 04 '22 at 16:05
  • This question of mine includes definition of resistance https://physics.stackexchange.com/questions/686786/what-sort-of-field-does-a-battery-create-inside-a-wire-or-anything-at-all-in-gen – Osmium Feb 06 '22 at 10:52

3 Answers3

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No, you have got it wrong. Firstly, you seem to be trying to say that you can have more or less charge without having more or fewer charged particles. The current flowing through a wire is electrons- the moving charge is the movement of electrons. You cannot have charge without charged particles, as they are the basic building blocks of it.

The difference between resistance and resistivity is like the difference between density and moment of inertia. All gold has the same density- it is a property of the material; but different amounts of gold arranged in different ways will have different moments of inertia. Likewise, resistivity is a fundamental property of the material, so all copper wires will have the same resistivity; but different amounts of copper arranged in different ways can have different values of resistance. An amount of copper made into a short thick wire will have lower resistance than the same amount of copper formed into a very long thin wire.

Note that you can increase a current in two ways- one is to increase the speed at which the electrons are moving and the other is to have more electrons moving in parallel.

Marco Ocram
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  • "you seem to be trying to say that you can have more or less charge without having more or fewer charged particles." Nah I never meant that. How did say that? – Predaking Askboss Jan 23 '22 at 01:48
  • Your second way is what I would like you to focus upon. When you increase thickness of wire you can compare it with adding a wire( of same length) in parallel. It means that Electric flux increases in the cross-section of wire and the strength of Electric field remains same as before. Changing area of cross-section affects the amount of charge passing not the charge particle. Each charge particle is behaving same as it was before( Here behavior specially means drift velocity) – Predaking Askboss Jan 23 '22 at 02:00
  • When I am saying "affects charge particles" I am specifically pointing to individual charge particles( or electron in wire) moving differently or with different velocity. Increasing resistivity or length can affect it while area doesn't affect it. Area only contributes to amount of charge particles flowing through cross-section. – Predaking Askboss Jan 23 '22 at 02:07
  • You actually said..."What i think is that "charge" here actually means the magnitude of charge only. It doesn't mean charge particles." How can the charge be separated from the particles? Your words, taken literally, are nonsensical. Please try to clarify what you mean. – Marco Ocram Jan 23 '22 at 09:50
  • I was talking about affecting individual charge particles which is not a work of resistance it is the work of resistivity. Current can be increased without affecting motion of any charge particle just by increasing the area of cross-section –  Jan 23 '22 at 09:52
  • I still don't understand why you think "affecting current means affecting each of the charge particle". It is not necessary. Let say there are two people( you and I) on road walking giving rise to people current. If I double the width of road and put two more people to walk, the people current increases but we both know that our motion is unaffected. We are moving with same velocity as before. –  Jan 23 '22 at 09:58
  • Then you might have said that resistance is a measure of how an object resists the movement of charged particles as a group, while resistivity is a measure of how the movement of an individual particle is resisted. – Marco Ocram Jan 23 '22 at 10:22
  • Can you tell me if there is some other issue in my description about resistance and resistivity? –  Jan 24 '22 at 09:33
  • I got what you wanted to say. Your "Group" consists of total number of all charge particles passing through a section in unit time. Increasing area doubles its quantity. So yeah you can actually say that resistance affects the total number of electrons passing through while resistivity affects motion of each electron. And since total number of electron flowing is directly proportional to their magnitude of charge. And hence resistance affects current only. –  Jan 24 '22 at 09:43
  • "Note that you can increase a current in two ways- one is to increase the speed" I'm not too keen on that. If 10 cars pass a given point per minut at 20 miles per hour, the number of cars passing per minute doesn't change just because the cars accelerate to 40 miles per hour. – Math Keeps Me Busy Feb 03 '22 at 18:28
  • @MathKeepsMeBusy that is an excellent clarification- one must keep the density constant while increasing the speed. Feel free to edit my answer if you feel so inclined! – Marco Ocram Feb 03 '22 at 21:12
  • @MathKeepsMeBusy "If 10 cars pass a given point per minut at 20 miles per hour, the number of cars passing per minute doesn't change just because the cars accelerate to 40 miles per hour." Wait a minute. This seems totally wrong! If you have double acceleration then you would also have double average velocity and there the volume displaced also gets double. Isn't it? Volume $= A L =A v_A t$ ($v_A$ is the average velocity throughout the time of current flow) –  Feb 04 '22 at 09:53
  • @ArsenalCreation I think his point was that the current doesn't depend on speed alone. If you have one car passing down a country lane every ten minutes, it doesn't matter whether they are doing 10mph or 100mph- it is still just one car every 10 minutes. – Marco Ocram Feb 04 '22 at 11:03
  • But the current means how much a thing(charge) is passing through a point in an unit time. If the the speed is higher then, more cars can pass through in a given time. Even if it is one car every time, if it is passing through a given point twice, the current gets twice. Don't extend this discussion more –  Feb 04 '22 at 11:44
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In this answer, the charge of electron is assumed to be $e$ $(e\gt0)$ for simplicity. The result is effectively the same.

$m$ is the mass of an electron.

In any (linear or ohmic) resisting conductor, resistance or resistivity arises due to the collisions of moving electrons with the nuclei.

It is assumed that the electrons come momentarily to rest after a collision with a nucleus and the average time between two collisions(average collision time) is $\tau$($\tau$ is a characteristic property of a material).

Hence the average acceleration on a moving electron is $-\frac {m\vec v}{\tau}$.

The equation of motion of an electron in such a wire under an electric field $\vec E$ along the length of the wire is

$m\frac{d\vec v}{dt}=e\vec E - m\frac {\vec v}{\tau}$

After a long time i.e., after a steady state is reached, $\vec v = \frac{e\tau\vec E}m$

The current density $\vec j = ne\vec v$ (the amount charge flowing though a unit cross-section in a unit time i.e., no. of electrons crossing in a unit time, times the charge of an electron)(where n is the electron density or no. of electrons present in a unit volume)

$\vec j=\frac{ne^2\tau}m \vec E$

Here $\frac{ne^2\tau}m$ is defined as a constant conductivity(or specific conductance) which represents the ability of a conductor to conduct, denoted by $\sigma$. It is independent of the dimensions of the conductor(as $\tau$ is unique for a material). Resistivity($\rho$) is defined as the reciprocal of conductivity and the ability of a $\mathbf {material}$(note that it is material and not wire) to resist the flow of charge.

Taking a linear conductor $|\vec E|=\frac V\ell$ (where $V$ is the voltage across the ends of the wire and $\ell$ is the length of the wire) and $|\vec j|=\frac iA$ (where $i$ is the amount of current passing through the wire and $A$ is the area of cross-section of the wire).

$i = \frac{ne^2\tau}m \frac A\ell V$

$i = \frac {\sigma A}\ell V$

$V = \frac {\rho\ell}A i$

This constant was replaced resistance($R$) known as the ability of a wire to resist the flow of charges.

If we change the cross section of a wire, the drift velocity is almost same and the current density is same, but the current changes due to the change in cross-section.

Resistivity is the characteristic property of a material and Resistance is the effective property of a wire. Both seem like resisting the flow of charges, but they are just constants that tell us about how materials behave.

Balaji Karedla
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Given a material of uniform cross section $A$ and length $L$ its resistance is $R=\frac{\rho L}{A}$ where $\rho$ is the resistivity of the material.

If $A$ and $L$ are constant then $R \propto \rho$, so any mention of difference in microscopic properties, ie the mechanism of the "opposition" to the flow of charges, is misguided.

Resistivity is an intrinsic property of the material, ie resistivity is independent of how much of a material is present and is independent of the form of the material and resistance is an extrinsic property of an object as resistance depends of the size and shape of an object.

Farcher
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  • What can you comment about my text? What are your thoughts? "Resistivity is an intrinsic property of the material " I was trying to define that intrinsic property or to tell what it has to do in Electric current. – Predaking Askboss Jan 31 '22 at 21:48