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When resistors are serially connected, the current is the same through the whole circuit. To my knowledge, the electric current is electrons traveling.

Also, the power of the generator equals the power lost...

Since current stays the same through all resistors, what exactly is being lost here? (when connected to a voltage source)

If the amount of electrons and their speed when entering the resistor is the same when they "get out" of a resistor, what generated heat? What was lost in the process of lighting a bulb? If no electrons were lost why is a battery not an infinite source of electricity?

What happened in the resistor that made it heat up?

Keep in mind all the information here are only true to my knowledge, which is flawed, if I am wrong, please correct me.


marked as duplicate by Eugene Sh., Dave Tweed Jul 26 '18 at 15:16

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • \$\begingroup\$ How do you define heat ? \$\endgroup\$ – Long Pham Jul 26 '18 at 13:19
  • \$\begingroup\$ When electrons "traveling", there is a "friction" with the resistance. When you travel in your car with constant speed, you burn the fuel as well. \$\endgroup\$ – Eugene Sh. Jul 26 '18 at 13:27
  • \$\begingroup\$ @EugeneSh. So, what is the fuel in this case and how is it 'burned'? \$\endgroup\$ – AthScc Jul 26 '18 at 13:30
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    \$\begingroup\$ Wait, isn't EE physics-based ? \$\endgroup\$ – Long Pham Jul 26 '18 at 13:43
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    \$\begingroup\$ @LongPham most things are physics based - the issue is people's understanding :) \$\endgroup\$ – Solar Mike Jul 26 '18 at 13:45

If you are confused about why the electrons don't 'disappear' yet somehow transfer energy, think of this analogy: When I pour water down over a water mill, energy is being transferred from the water flowing to the water wheel spinning, yet at the end of the day no water 'disappears' in this process. The energy is in the fact that I can get that water (or in the electrical case, the electrons) moving in the first place.

Perhaps a better analogy is the following:

Think of a belt being pulled around in a machine. The amount of belt (similar to our amount of electrons) as well as it's speed (and the speed of the electrons) stays the same for the entire belt - otherwise the belt would bunch up somewhere. Yet when something loads the belt - say a block is rubbing against the belt with a lot of friction - energy is being transferred from the motor that moves the belt to the block, and the block gets hot. The energy is being transferred because in order to keep the belt moving the motor needs to put effort (work) into the belt. The belt can't be 'used up' just like the electrons can't be used up because we would tear our belt (or in the case of the electrons, if they would stop inside the resistor, they would all bunch up and form a lot of charge there). So nothing is being 'lost', but instead the energy is needed to 'convince' the electrons to start moving in the first place. The faster you want them to move (= more current) means more effort (more voltage) and as a result more power.

More scientific:

The way the actual energy is transferred is (mainly) through collisions. In actual fact, electrons are already moving a lot in a metal, at least when that metal is at room temperature. Temperature is just a way to describe the kinetic energy of our particles (electrons, atoms, or molecules all move and vibrate). Most conductive materials have free electrons - these are electrons that do not belong to one single atom in a crystal lattice but are 'shared' between all the atoms. (there can/will also be holes in some cases, but let us pretend we only have electrons for now).

These electrons kinda just wander about, in a random way. As a result, they don't move over the long term, and they just dance around their position. Think of the analogy of dancers on a dance floor - they might all move, but in general, we don't get dancers moving from one side of the dance floor to the other, on average they all stay put. If we add energy to them, they start moving around faster. On a macroscopic scale, this speed of wandering is what we call 'heat', and more kinetic energy means the material is 'hotter'. The technical term for this moving around is 'Brownian Motion'

In the image below, on the left is the path of an electron without a current flowing through the material. The electron bounces back when it runs into the nucleus of an atom as the nucleus is positively charged (made out of neutral neutrons and positively charged protons), and the electron negatively charged. On the right, we have the same path (roughly, I've done this by hand but I think the idea is clear) but with an external electric field present (due to our voltage across the resistor). The electron will now, in addition to thermal movement, experience a drift opposite to the electric field. electron drift.

So, now that we understand all that, how does this heating thing work?

Well, every time the electron bumps into an atom, it trades some energy. Perhaps the electron now moves a bit faster after and the atom vibrates a bit less, or vice versa. This is a constant and random exchange, and since both the energy of both movements (the electron's random walking and the core of the atom vibrating) come from within the material, nothing really changes - the material does not heat up or cool down.

When we apply an electric field, things change. This electric field is external, and the electrons will constantly accelerate because of it. This is seen in the image as the curving of the electrons toward the right, no matter where the electron starts. Every collision, the electron dumps its energy into the atom it hits, giving that atom more kinetic energy. The electron then slowly accelerates due to the electric field, gaining more kinetic energy again, hits another atom, exchanging energy, etc...

In other words, as a result of this electric field we are adding more and more kinetic energy to the system, and that kinetic energy shows up as heat - our resistor is getting hotter.

But wait! How does this not break physics? We are just putting a field across a material and suddenly it heats up? Aren't we getting energy from nothing?

Not really! You see, as all of our electrons move towards the positive side of our electric field, they are moving charge in that direction. If at no point we are 'pushing' electrons back to the negative side we would get some electrons bunching up at the positive terminal, forming a negative charge there, and this would then cancel out the positive charge. Our electric field disappears.

In order to get a continuous current flow, we need to prevent this - at some point, we need to take the electrons at the positive terminal and force them back to the negative one. We can do this with a generator, where we use magnetic fields to convince them to go back.

In the case of a battery, we are not sending those same electrons back, but rather storing them at the positive side and releasing new ones at the negative terminal in a chemical reaction. Eventually, the reagents for this run out and the battery can't store any more electrons, and the field is no longer present.

This model is called the Drude model and fails to explain certain things (such as why some metals have a positive instead of negative hall coefficient, and why exactly does copper conduct so much better than iron?) but it gives a good first understanding of some of the principles at work.

  • \$\begingroup\$ +1 for the sentence: "Temperature is just a way to describe the kinetic energy ..." \$\endgroup\$ – Long Pham Jul 26 '18 at 14:33
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    \$\begingroup\$ It is interesting that no one mentions the real mechanism of interaction of electron flow with conductor structure - which is an electron-phonon scattering. Solid state conductors "keep" their energy in a form of atom lattice oscillations called "phonons". These are effectively the elements of "gas", so all classic thermodynamics (like temperature) apply. Electrons collide with this gas of phonons, and thus heat the crystal. \$\endgroup\$ – Ale..chenski Jul 26 '18 at 16:01
  • \$\begingroup\$ Thank you! This explained it perfectly, I overlooked why the current is moving in the first place, and this explained it, and more! \$\endgroup\$ – AthScc Jul 26 '18 at 16:55

It's a very interesting question, and difficult/impossible to answer.

What was lost in the process of lighting a bulb?

What was lost was energy.

How it was lost, the mechanicsm, has various explanations of varying degree of accuracy (quantum, Drude, friction).

What energy is is somewhat elusive. It's that stuff that if we compute it like we do, then it turns out to be conserved, and represents the capacity to do work.

The electrons moving through the wire before the resistor are moving at the same speed after the resistor. If we look at a hydraulic analogy, consider a river meeting a dam, losing height flowing through a turbine, and flowing away from the bottom of the dam. The volume flow at top and bottom of the dam is the same, but the water has given up its potential energy to the turbine. Potential energy in this case could be regarded as due to the gravitation attraction of the water to the earth. We need to do work on the water to raise it, it releases energy when we drop it.

The battery maintains a potential difference across its terminals. We could regard electrical potential energy as due to the attraction/repulsion of the electrons to charges in the battery which are maintained by chemical action. The electrons at the higher potential terminal have a higher potential energy than those at the lower potential terminal. That's why we use the term potential difference as a synonym for voltage. That potential energy is what's lost when electrons flow through a resistor. The battery loses energy, the resistor gains heat energy.

For the mechanism by which this transfer happens, you can select any one of a number of intuitive but inaccurate models. You could say that electrons accelerate in the electric field, and then hit stationary atoms, making them jiggle about (heat). Or that electrons have friction with respect to the lattice of atoms, because we understand that friction heats our palms when we rub them together. Or we can crank up our quantum arguments a little and talk about energy levels and scattering centres, which is not at all intuitive.

What happens is that when we connect a resistor to a battery, we observe that the resistor gets hot, and the battery loses some of its ability to do work. Everything else is models.


It takes work to move those electrons through the material - to detach them from the atoms they are weakly (depending on the material, hence varying resistivities) coupled to, work to move them through space from atom to atom (where sometimes they get reattach, dislodging others). And in the process, heat is released. Resistors do get hot.

  • \$\begingroup\$ if you're going to give a non-quantum answer, then at least give a better one that held sway for a while, the Drude Model \$\endgroup\$ – Neil_UK Jul 26 '18 at 14:06

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