# What really is resistance? How does it generate heat?

OK I know that R= V/I. I also know that R = ρl / A But what I want to know is that what really causes resistance? Is resistance equivalent to force? or is it just a constant?

Also, what causes conductors to heat up overtime when current flows through them? I know that the electrons lose energy and that energy gets converted to heat, but what causes them to lose this energy? Electrons don't collide with atoms or other electrons.

EDIT-1

Also, how does this lost energy gets converted to heat?

• If you like this question you may also enjoy reading this Phys.SE post and links therein. – Qmechanic Jul 6 '14 at 9:57

## 4 Answers

As for the question what "really causes resistance":

When looking at a solid which has a periodic crystal structure the electrical resistance would hypothetically be zero if the crystal structure would indeed be perfect and the atoms would keep perfectly still at all temperatures. Note that resistance is a measure of how much - well, resistance - there is for free electrons moving through the solid.

However this is obviously not the case, as if one is at $T \neq 0K$, then the atoms start to oscillate around their equilibrium position. Quantum mechanically one can treat these oscillations as a quasi-particle called the Phonon. So as one leaves the realm of $T = 0 K$ there are basically new particles appearing for the electrons to bump into on their way through the solid, thus increasing the resistance for the electrons.

If one only considers contributions to the resistance from phonons, $R(T = 0 K) = 0$ would be the case. However experimentally one sees that resistance approaches a constant, non-zero value as one approaches $T = 0 K$. This can be explained due to the crystalline structure of the solid not being perfectly periodic, i.e. the solid having impurities.

Generally one can prove that electrons in a perfectly periodic potential can move ABSOLUTELY freely, so any resistance must stem from permanent impurities in the solid or temporary dislocations of individual atoms out of their equilibrium position, i.e. phonons.

So the heat that gets produced by resistance is in fact the electrons bumping into things they "see" on their way through the solid.

The other answers here are very good, but are a bit too in-depth for what I believe you're looking for. The simplest way of thinking about resistance is that the current carrying electrons are colliding with the atoms that make up the conductor. By collide I mean the electrons can interact with the atoms via the Coulomb force.

The kinetic energy of the electrons is transformed into vibrational energy of the atoms. As you should know temperature is just vibrational energy, so energy lost from resistance will heat up the conductor.

In the classical model of Drude, the resistance comes from the collision of the electron with the impurities or with the phonons (waves in the solid), depending on your material.

The phenomenon of heating up is that you dissipate the energy given from the current by collision with phonon/impurities etc...

If you want a quantum description, you should look at the Sommerfeld model and band theory.

A simpler and more intuitive answer to the second sub question is yes - Resistance is a force on the electrons moving through the conductor. It is equivalent to a frictional (damping) force as opposed to a force like induction which converts the kinetic energy to magnetism. It is a constant in correctly built resistors which give a constant damping force in opposition to the movement of the electrons. As explained in other answers it depends on the specific properties of the resistive or conductive medium used.

• This answer does not really answer the question. You have described what the action of resistance on electrons is, but what causes the resistance (e.g. air molecules)? What constitutes a resistor is what the question is asking. – GodotMisogi Oct 28 '18 at 9:43
• With the mention of Force in the question, I wanted to make a Newtonian analogy on the electron in the generalised case of current flow as the kinetic energy of the moving electron. – Marco Parigi Oct 28 '18 at 10:55