# Voltage in a Circuit

Mister T
Gold Member
UMath1's point is simply wrong regardless of the underlying model of conductivity and even regardless of the nature of the charge carriers. The voltage is a measure of the potential energy, and it simply does NOT require any potential energy to move. His idea is wrong even in mechanics where you could easily envision large mechanical systems where potential energy does not change even as large massive objects move from place to place.

I understand the validity of your point. Perhaps you could help me understand its relevance.

When moving macroscopically large objects that are interacting with other objects, a force is required. If a potential energy function doesn't exist for that force, then the application of that force causes no change in potential energy. But of course if a potential energy function does exist for that force, there will be a change in potential energy.

In the case of moving (microscopically small) charge-carriers through a wire, a force is required because those charge-carriers are interacting with the wire. In the OP's case; as is typical of the case where the connection of batteries, bulbs, and wires are studied; that force is the conservative electrostatic force. A corresponding potential energy function does exist. So the only relevant way to move the charge-carriers is through a difference in potential energy. Or in other words, a difference in electric potential.

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Dale
Mentor
2021 Award
I understand the validity of your point. Perhaps you could help me understand its relevance.
The point is that UMath1 has a conceptual error about potential and kinetic energy here:
But according to kirchoff's law, the electron loses all of it energy after the last resistor, so it doesn't have any energy to move.
In other words, the problem isn't that UMath1 is confused about whether a wire has negligible or zero resistance or superconductivity, but rather that he has a mistaken belief that an object which has zero potential energy also has zero kinetic energy. His stated belief is that Kirchoff's law says that the electron will get to the end of the last resistor and then stop because it runs out of energy. He seems to be confounding having zero potential energy ("loses all of its energy") with having zero kinetic energy ("doesn't have any energy to move").

This mistaken concept of energy is followed up in his subsequent posts.

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Mister T
sophiecentaur
Gold Member
Sorry about the zero conductivity gaff. What a plonker.

Mister T
Gold Member
Sorry about the zero conductivity gaff. What a plonker.

Let's speak of it no mho.

Dale
The only reason I have this confusion is because initially in the anode the electrons have only potential energy, if all this potential energy is used up, how can there possibly be any kinetic energy? In other words, any kinetic energy must originate from the potential energy and if all the potential is used up none can be converted. Total Energy in the beginning was eV. In the end it was 0.

Mister T
Gold Member
The only reason I have this confusion is because initially in the anode the electrons have only potential energy,

If that were true an ammeter inserted at that location would read zero! But in fact, for a series circuit any place you insert the ammeter you get the same reading.

Mister T
Gold Member
There is an electric field throughout the circuit. Yes, it takes a tiny fraction of a microsecond after the switch is closed to establish that field, but once that's done the electrons are drifting everywhere throughout the circuit.

Here's a multiple choice question for you to ponder. You turn the ignition switch to start your car, setting electrons in motion along the fat wire connecting the battery to the starter motor. It takes an electron how long to move from one end of this wire to the other?

A. Less than a second.
B. A few seconds.
C. A few minutes.
D. A few hours.

The only reason I have this confusion is because initially in the anode the electrons have only potential energy, if all this potential energy is used up, how can there possibly be any kinetic energy? In other words, any kinetic energy must originate from the potential energy and if all the potential is used up none can be converted. Total Energy in the beginning was eV. In the end it was 0.

I think there is some thing wrong with your understanding of battery.Do you think that, initially all the carrier electrons needed for conduction are accumulated at anode with some potential energy,which are inturn emitted and circulated through out?

nasu
No, but kind of. I think that before the circuit is closed, the wire has an even distribution of electrons, an electron sea. After the wire is connected, the charge accumulation at the anode pushes electrons in the wire in the direction of the cathode. As electrons in the wire touching the anode move away, electrons from the anode take their place. Electrons at the cathode are pushed into the anode by the battery, and the cycle continues.

Mister T, it would be a few hours, because electrons don't move in a straight line.

Dale
Mentor
2021 Award
initially in the anode the electrons have only potential energy
As Mister T pointed out above, this is not correct. Electrons throughout the circuit have approximately the same KE.

Beyond being incorrect it is also irrelevant. The KE of the electrons in a circuit is so low as to be entirely indistinguishable from 0. The thermal energy is orders of magnitude larger. Unless you would cool the circuit down to near absolute zero you will never be able to detect the KE of the electrons.

If you ever find yourself talking about the KE of an electron in any context other than a particle accelerator, chances are high that you are discussing something entirely irrelevant.

EDIT: I just ran the numbers for the thermal energy of the copper vs the KE of the electrons for a typical USB charging cable. The thermal energy as about 16 orders of magnitude larger than the electron KE (~100 J vs. 10^-14 J)

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Jyothish
Mister T
Gold Member
After the wire is connected, the charge accumulation at the anode pushes electrons in the wire in the direction of the cathode.

That lasts for less than a small fraction of a microsecond. Afterwards there is no accumulation.

As electrons in the wire touching the anode move away, electrons from the anode take their place. Electrons at the cathode are pushed into the anode by the battery, and the cycle continues.

The electrons on or near the cathode or anode move for the same reason the electrons anywhere in the circuit move.

Mister T, it would be a few hours, because electrons don't move in a straight line.

Can you use your model to explain why, then, one doesn't have to wait for a few hours for the car to start? How much time elapses between the time the wire is connected and the starter motor starts turning?

Dale
Mentor
2021 Award
@UMath1 this thread has lasted well over 100 posts. I think that it is time to close it down. Your question has been well and thoroughly answered. You seem resistant to the answers that you have received, so there is nothing more to be done here.

I will close this thread this afternoon, giving the participants a few more hours to post any parting suggestions.

davenn
Gold Member
2021 Award
Can you use your model to explain why, then, one doesn't have to wait for a few hours for the car to start? How much time elapses between the time the wire is connected and the starter motor starts turning?

Im so looking forward to seeing your answer and I suspect a flaw in it, going by your above response to UMath1

Dave

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EDIT: I just ran the numbers for the thermal energy of the copper vs the KE of the electrons for a typical USB charging cable. The thermal energy as about 16 orders of magnitude larger than the electron KE (~100 J vs. 10^-14 J)
When you say "thermal energy of copper" do you mean just the electronic contribution? Most thermal energy in metals at room temperature is due to lattice. Electron contribution is about 1%, at room temperature. What is that 100J value?

The fact that the KE associated with the drift of electrons is much smaller than Fermi energy does not mean that it is irrelevant.
This keeps coming in discussions about electric current.
Without the electric field the electrons are in equilibrium with the rest of the metal. Even though their thermal energy is high, there is no net transfer of heat from the electrons to the lattice. The metal does not heat up.
The electric field breaks this equilibrium shifting the Fermi sphere by a small amount and there is energy transferred from electrons to lattice. This is the thermal effect. The KE change for the entire Fermi sphere is significant. The thermal velocity of electrons is actually the irrelevant one for the thermal effect of the current, even though is many orders of magnitude higher than the drift KE.

The fact that the image of electrons starting with a big amount of KE from the battery and spending it along the way is wrong is not due to the magnitude of the drift KE but simply to the fact that this is not what happens.
In resistors with higher resistivity than metals (like intrinsic semiconductors for example) the drift velocity can be many orders of magnitude higher than in metals (for the same current). This does not make it more relevant.

Dale
Mentor
2021 Award
OK, it looks like time to close. @UMath1 I hope you take some time to go through the many good answers which you have received.