Voltage in Circuits: Explaining Voltage Drops & Flow

[sophiecentaur]

I do think the charge must possesses energy

That would be Kinetic Energy? What Kinetic Energy does a Coulomb of Charge have?

 

[Jyothish]

I think I understand it better. But I am not sure exactly what you mean by steady and transient state. Is transient state when the you start the circuit and charges start moving and steady state when flow out of anode= flow in cathode?

Transient state is, as you said, when the battery is connected to the circuit through switch.Then the following events occur
1) Charges(electrons) start moving throughout the circuit
2) Due to charge separation caused by battery, some parts of the circuit start accumulating negative surface charge and other parts positive surface charge

Within nano seconds, steady state is reached where
1) There is no change in surface charge densities at various points.This means there is no further charge accumulation
2) Charges will reach a constant drift velocity at a given point in the circuit.But steady state velocities at different points in the circuit (means at different resistors in the same circuit) can vary depending on carrier density, cross section of resistor wire etc
3) The surface charge variation(spatial) in resistances establishes the exact electric field needed to overcome the resistance and to maintain the steady state drift velocity

Assuming the electrons to be particles with mass, the kinetic energy needed for the electrons is very small owing to their small mass.This KE is acquired during transient state.Now in the steady state, as they move around the circuit, you can see that , inside the battery, electrons have to move against the opposing force due to electric field.Because they have to move from positive plate to negative plate inside the battery.This work is done by battery and the resulting extra potential energy is added to electrons.This energy is utilized in resistances.Kirchoff's law implies that the energy supplied is equal to what is used up, in steady state

 

[Dale]

However, I do think the charge must possesses energy to do so. To move, energy is required.

Not potential energy.

 

[Herman Trivilino]

There might be no change in energy, but then the electron had to have some energy after leaving the last resistor. But according to kirchhoffs law, the electron loses all of it energy after the last resistor, so it doesn't have any energy to move.

In that model the assumption is that the wire has zero resistance. In fact, what is happening is that the wire has a resistance that is much much smaller than the resistance of that last resistor. Or any other resistor in the circuit. It is therefore safe to call it zero for purposes of Kirchhoff Law calculations, but it is not safe to consider it zero for purposes of understanding how the electrons move through the wire.

The only way an electron can move through a wire is if one end is at a higher potential than the other.

It's like a mechanics problem where a taught string connects two object that are accelerating. The usual approximation is to assume the string is massless, allowing one to calculate things like the acceleration of the objects or the tension in the connecting string. But using this model you can't analyze the acceleration of the string. The string's mass is very small compared to the mass of the objects, so it's safe to ignore for purposes of calculating their acceleration. But it's not safe to ignore for purposes of understanding what happens to the string. The only way it can accelerate is if the force applied to one end is larger than the force applied to the other end. Thus we have to realize that the tension along the string decreases from one end to the other. And when we subtract the force at one end from the force at the other, we get a net force. Divide that by the string's mass and you have the string's acceleration.

In a wire the conduction electrons are transferring kinetic energy to the wire's atoms, causing an increase in the wire's temperature. The electrons are speeding up due the electric field applied by the battery, and slowing down due their interaction with the atoms. Average it out and you get a drift velocity that's responsible for the reading on the ammeter.

 

[sophiecentaur]

The situation with the wire is comparable in that the conduction electrons are transferring kinetic energy to the wire's atoms, causing an increase in the wire's temperature.

This is referring to the Drude model (?), which has been superceded by a more universal Quantum model. Drude cannot cope with superconductivity, afaiaa and we are treating the connecting wires as having zero conductivity.

 

[Herman Trivilino]

I'm talking about the wires in the circuits encountered in an introductory physics textbook, classroom, and laboratory. I took that to be the context in which the OP is conversing.

I am not talking about superconductors or semiconductors. You don't need a superconducting wire to verify Kirchhoff's Laws in the laboratory. You merely arrange things so that the wires have negligible resistance.

 

[Dale]

@Mister T and @sophiecentaur it doesn't really matter whether you are using the Drude model or QM. UMath1 is mistaken about energy 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.

 

[sophiecentaur]

I am not talking about superconductors

Is there a difference between zero conductivity, 'ideal' connecting wires and superconductors? The drude model would have to treat the connecting wires as having no collisions and hence would have no voltage drop.
But, if you want to ignore super and semi conductors then you would presumably have to limit any description to circuit behaviour to exclusively resistive components. That could be a bit limiting. You would need a separate description for what happens to electrons, depending which component they happen to be flowing through.
I agree that it is nice to discuss 'School Physics' and it is useful as a step towards better understanding. I just think that it is not necessarily helpful to try to 'explain' what is not really explicable within the realm of School Science. For instance, I have read frequent 'explanations' of the effect of temperature on resistance in terms of atoms jiggling about and providing larger targets for electrons to collide with. That is clearly nonsense and far too simplistic.

 

[sophiecentaur]

you could easily envision large mechanical systems where potential energy does not change even as large massive objects move from place to place.

Absolutely. I already made that point but he seems to have a problem about where and when the Energy is relevant.

 

[Herman Trivilino]

Is there a difference between zero conductivity, 'ideal' connecting wires and superconductors?

Yes. Although it's zero resistance, not zero conductivity. Ideal connecting wires have negligible resistance, not zero resistance. There's a difference. Even if the phenomenon of superconductivity had never been observed or modeled, the "zero-resistance" wires used in the first-approximation circuit models appearing in textbooks and in the literature would be alive and well. Moreover, those models can and are used by scientists and engineers to study, design, and build stuff; where applicable.

Just as there is no such thing as a massless string. They are still used as viable models in both education and industry, where applicable. It's better to use "negligible" rather than "zero" to avoid this very type of confusion.

 

[Herman Trivilino]

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.

 

[Dale]

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 kirchhoffs 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.

 

[sophiecentaur]

Sorry about the zero conductivity gaff. What a plonker.

 

[Herman Trivilino]

Sorry about the zero conductivity gaff. What a plonker.

Let's speak of it no mho.

 

[UMath1]

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.

 

[Herman Trivilino]

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.

 

[Herman Trivilino]

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.

 

[Jyothish]

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?

 

[UMath1]

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]

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)

 

[Herman Trivilino]

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]

@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]

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

 

[nasu]

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]

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.