What causes the potential (voltage) in a conductor to rise?

[parsec]

I noticed a couple of similar threads, but I thought it might be better to start a new one for clarity.

Imagine a simple DC circuit with a static (time invariant) source of potential and a closed circuit with a simple conductor. If you were to trace the potential from the negative terminal to the positive terminal you would expect a linear gradient in potential between the two terminals.

Now, take any point on the conductor. What determines the potential at this point? In electrostatics, electric potential at a point in space is determined by the grouping of static charges and distance from those static charges.

What determines the potential inside a conductor? Do the electrons rearrange themselves within the conductor (e.g. bunching up closest to the negative terminal)? Does this occur at the speed of light?

 

[Integral]

Are you familiar with Ohm's Law? The potential at any point in the circuit is determined by the current and the resistance between the point and the source.

 

[parsec]

Yes, Ohms law is a familiar abstraction. I'm looking for a more indepth explanation of what actually creates potential in a conductor.

To clarify I know that the charges have a drift velocity and I guess the potential drop is proportional to the drift velocity and rate of collisions within the conductor, but I can't figure out what "potential drop" really means. What physical parameter within the conductor is being reduced?

 

[Integral]

So you understand the "abstraction" that is Ohm's law and are comfortable with the relationship of current, resistance, and potential? The actual mechanics are not as important as the fundamental relationship.

 

[parsec]

Yes, I understand Ohm's law. The underlying mechanics are what I'm curious about here.

 

[user111_23]

In a battery, there are two terminals, one which is more negatively charged than the other. Since there's more charge around that terminal, the charge is resisted more at that terminal. Therefore there is a difference in electric potential between both the positive and negative terminals.

As a Coulomb of charge moves towards the positive terminal, it loses electric potential energy. Since electric potential is location-dependent, you can conclude that the voltage will be a certain value depending on where you measure it.

Hope I helped.

 

[parsec]

what does it mean for the charge to lose electric potential? it isn't losing kinetic energy as the drift velocity is constant through the conductor.

 

[Kcant]

Assuming that you have ideal ohmic contacts connecting the metal and the conductor, the only "source" of voltage drop in the system is the contacts. Think about the 1D Poisson's equation. It is second-order, and requires two boundary conditions to solve. One condition just sets the potential gauge. The other sets the drop in the system.

Mathematically, it's exactly equivalent to a simple capacitor. In both cases, the potential drops linearly across a region of space, and the physical reason is the voltage (charge buildup) on the metal plates. So, perhaps the better question is why the presence of a current doesn't distort the constant field profile in the case of a conductor. If a "bump" was somehow able to form in the field, electrons would either pile up or deplete from that region, until they exactly canceled out the effect of the bump.

 

[Born2bwire]

what does it mean for the charge to lose electric potential? it isn't losing kinetic energy as the drift velocity is constant through the conductor.

It is losing kinetic energy, that is why the drift velocity is constant. If the charges did not lose any kinetic energy then they would keep speeding up since the potential applies a force on the charges. The electrons will collide with the large atoms in the conductor's lattice, losing kinetic energy and causing vibrations that give rise to heat. This is the ohmic heating that occurs due to the conductor's resistance. But this is different from what you first asked, the electric potential is set at the terminals of the voltage sources, what it is at other points in the circuit with respect to your reference points is different. We care about the potential difference.

 

[user111_23]

It is losing kinetic energy, that is why the drift velocity is constant. If the charges did not lose any kinetic energy then they would keep speeding up since the potential applies a force on the charges. The electrons will collide with the large atoms in the conductor's lattice, losing kinetic energy and causing vibrations that give rise to heat. This is the ohmic heating that occurs due to the conductor's resistance. But this is different from what you first asked, the electric potential is set at the terminals of the voltage sources, what it is at other points in the circuit with respect to your reference points is different. We care about the potential difference.

That makes sense but at the same time it doesn't. Electrons move slowly in the conductor, and they have very little mass, which makes it hard to believe that the PE of the electrons is turning into KE.

The charges have potential energy and lose it as they pass through a resistance. Yes the current does carry KE, but it's so small that it's negligible.

 

[parsec]

It is losing kinetic energy, that is why the drift velocity is constant. If the charges did not lose any kinetic energy then they would keep speeding up since the potential applies a force on the charges. The electrons will collide with the large atoms in the conductor's lattice, losing kinetic energy and causing vibrations that give rise to heat. This is the ohmic heating that occurs due to the conductor's resistance. But this is different from what you first asked, the electric potential is set at the terminals of the voltage sources, what it is at other points in the circuit with respect to your reference points is different. We care about the potential difference.

Okay, that seems fairly logical. I guess this means that locally electrons are constantly accelerating and decelerating, and the aggregate effect is a constant drift velocity. So can we say that the accelerating potential across the circuit (from negative to positive terminal) is uniform.

If so, what causes the potential at say halfway along the circuit to be half of the potential difference between the two terminals. If the drift velocity is constant then what property of the electrons or conductor sets the potential at this point?

 

[parsec]

Assuming that you have ideal ohmic contacts connecting the metal and the conductor, the only "source" of voltage drop in the system is the contacts. Think about the 1D Poisson's equation. It is second-order, and requires two boundary conditions to solve. One condition just sets the potential gauge. The other sets the drop in the system.

Mathematically, it's exactly equivalent to a simple capacitor. In both cases, the potential drops linearly across a region of space, and the physical reason is the voltage (charge buildup) on the metal plates. So, perhaps the better question is why the presence of a current doesn't distort the constant field profile in the case of a conductor. If a "bump" was somehow able to form in the field, electrons would either pile up or deplete from that region, until they exactly canceled out the effect of the bump.

In free space, the potential at an arbitrary point seems to be determined by spherical geometry (the steradian function 1/4pir^2). In a dielectric, potential distributes itself through polarisation. How does potential distribute itself in a conductor?

 

[Born2bwire]

That makes sense but at the same time it doesn't. Electrons move slowly in the conductor, and they have very little mass, which makes it hard to believe that the PE of the electrons is turning into KE.

The charges have potential energy and lose it as they pass through a resistance. Yes the current does carry KE, but it's so small that it's negligible.

This is the Drude model: http://en.wikipedia.org/wiki/Drude_model and is still an accepted model for electron conduction in metals, I just sat in on a talk yesterday that made use of it. The electrons move slowly because of the constant collisions with the lattice. Otherwise, the electrons would move very fast because, as you stated, they have very little mass and would experience a force all along the length of the conductor from the applied fields.

 

[Born2bwire]

Okay, that seems fairly logical. I guess this means that locally electrons are constantly accelerating and decelerating, and the aggregate effect is a constant drift velocity. So can we say that the accelerating potential across the circuit (from negative to positive terminal) is uniform.

If so, what causes the potential at say halfway along the circuit to be half of the potential difference between the two terminals. If the drift velocity is constant then what property of the electrons or conductor sets the potential at this point?

Yeah, spot on. The main thing to realize is that the potential difference is set by the sources, all other objects in a circuit are passive (ok, so there are active things like transistors and so on, but let's restrict ourselves to simple LRC circuits). user111_23 did hit upon this indirectly, but the actual amount of kinetic energy lost by the electrons in a conductor is very small. Because they have very little mass, they lose little amounts of kinetic energy to keep a constant slow drift velocity. But like I said, this is something separate from what you asked. Because they lose so little kinetic energy, the potential difference along a wire is almost zero, there is little energy lost. But when the charges meet a circuit element, say a resistor, then a large amount of energy will be expended (purposely as in the case of the resistor). It is this drop in energy that gives rise to the change in the potential difference across the circuit when referenced from a common point.

 

[darkSun]

If so, what causes the potential at say halfway along the circuit to be half of the potential difference between the two terminals. If the drift velocity is constant then what property of the electrons or conductor sets the potential at this point?

The way you make it sound is as though the potential at a point is a intrinsic property of the space there that is determined by the electrons and the conductors. But that isn't right, potential is a relative thing; the change in potential just means that between this point and the battery terminal, electrons are gaining/losing energy. Nothing special is happening to cause a "change" in the potential.

On a side note, if we had a perfect conductor that electrons could travel through unimpeded, if the electrons are continually gaining energy and going faster does that mean that they would eventually pile up at the negative terminal of the battery? Or would the current keep getting larger? Never thought of that before, but I guess it's moot because it's totally idealized.

And I have a question of my own, when electrons come to a resistor, the heat energy comes from their kinetic energy right? So they slow down; but electrons don't pile up at one end of a resistor. Does the battery somehow know to work harder to pump them through? Or is it like someone previously said, if there was a "bump" in the electron flow the repulsion between electrons would automatically sort it out?

 

[PhaseShifter]

The way you make it sound is as though the potential at a point is a intrinsic property of the space there that is determined by the electrons and the conductors. But that isn't right, potential is a relative thing; the change in potential just means that between this point and the battery terminal, electrons are gaining/losing energy. Nothing special is happening to cause a "change" in the potential.

You make it sound as if the potential drop across a resistor isn't a measurable quantity.

I think the point he's getting at is this:

Say we have a simple circuit consisting of a battery and a resistor connected by two wires.

Why is the measurable potential drop negligible in the wires when compared to the resistor, and how can this be explained in terms of the Drude model?

 

[user111_23]

You make it sound as if the potential drop across a resistor isn't a measurable quantity.

I think the point he's getting at is this:

Say we have a simple circuit consisting of a battery and a resistor connected by two wires.

Why is the measurable potential drop negligible in the wires when compared to the resistor, and how can this be explained in terms of the Drude model?

Because the resistance is much greater at the resistor as compared to the wires.

 

[darkSun]

PhaseShifter, perhaps I didn't think through what I said enough, but measuring potential across two points is definitely possible, I just meant we can't just look at a single point inside a circuit and decide how the potential has changed. Voltmeters can do this by making a new circuit connected to the reference point, but just by looking the some arbitrary point, what could you observe that would tell you about a change in potential?

If the resistance is greater, then in terms of the Drude model one could describe this by saying the mean free time between collisions is shorter. But if the electrons still move at their constant drift velocity after the pass the resistor, what could you observe to notice the drop in potential? I'm not sure.

 

[user111_23]

When electrical energy is converted into other types of energy, there is a voltage drop. Such as a light bulb, you know there is a drop because the energy of the electrons creates friction in the filament to produce light and heat energy.

 

[PhaseShifter]

If the resistance is greater, then in terms of the Drude model one could describe this by saying the mean free time between collisions is shorter. But if the electrons still move at their constant drift velocity after the pass the resistor, what could you observe to notice the drop in potential? I'm not sure.

I can see that mathematically--In the case of direct current, if the resistor has a lower charge density (or shorter mean free path, as you point out, or is simply narrower diameter wire) then the potential gradient must increase to compensate in order to provide a steady-state current.

I'm just trying to figure out a physical mechanism for this to take place--not in terms of bulk quantities like "resistance" and "current", but in terms of variables used in the Drude model. (acceleration due to electric field, distance between collisions, and carrier charge density)

How do you get from "Electrons collide with the lattice more frequently in this region of space" to "the field accelerating them is proportionally stronger", for instance?

 

[parsec]

Thanks, I think the reason I assumed that potential was some intrinsic property was because I was confusing it with the electric field. I did some reading and realized that they're different things. I guess potential is meaningless unless there is some avenue for it to do work through (i.e. an impedance).

Running with this classical hydrostatic-esque model, what then determines the propagation speed of a voltage "signal"? In hydrostatics/dynamics the speed of pressure propagation is a relatively straightforward concept.

I'm imagining that the potential applied at one terminal of the circuit pushes on the first charge carriers, which then push on charge carriers further inside the conductor. This idea seems a bit broken though, as it would result in a signal propagation speed that is some function of the mean free path etc. (I remember someone mentioning that the propagation speed is the speed of light)

I guess a more indepth question I was trying to resolve is, what is the mechanism for the potential being applied to charge carriers at some arbitrary distance away from the terminals. Is it the same as the hydraulic analogy where pressure is applied to one end of a tube and is then distributed through the tube through particle interactions, or is it more complicated?

 

[user111_23]

Thanks, I think the reason I assumed that potential was some intrinsic property was because I was confusing it with the electric field. I did some reading and realized that they're different things. I guess potential is meaningless unless there is some avenue for it to do work through (i.e. an impedance).

Running with this classical hydrostatic-esque model, what then determines the propagation speed of a voltage "signal"? In hydrostatics/dynamics the speed of pressure propagation is a relatively straightforward concept.

I'm imagining that the potential applied at one terminal of the circuit pushes on the first charge carriers, which then push on charge carriers further inside the conductor. This idea seems a bit broken though, as it would result in a signal propagation speed that is some function of the mean free path etc. (I remember someone mentioning that the propagation speed is the speed of light)

I guess a more indepth question I was trying to resolve is, what is the mechanism for the potential being applied to charge carriers at some arbitrary distance away from the terminals. Is it the same as the hydraulic analogy where pressure is applied to one end of a tube and is then distributed through the tube through particle interactions, or is it more complicated?

Good question, though I'm not entirely sure what you mean. I guess you are wondering what causes the charges to move far away from the terminals?

Imagine a tube of marbles like this:

It's sort of a chain reaction where the charges push other charges while transferring an amount of energy. That is why you notice a light bulb turn on at the speed of light.

 

[PhaseShifter]

:

It's sort of a chain reaction where the charges push other charges while transferring an amount of energy. That is why you notice a light bulb turn on at the speed of light.

Yes, but what happens in the resistor in that model? It doesn't explain why the potential gradient is inversely proportional to charge density and mean free path.

Is it a "traffic jam" of electrons building up behind the resistor, which would produce a charge buildup near the junction, or something else?

 

[sokrates]

Good question, though I'm not entirely sure what you mean. I guess you are wondering what causes the charges to move far away from the terminals?

Imagine a tube of marbles like this:

It's sort of a chain reaction where the charges push other charges while transferring an amount of energy. That is why you notice a light bulb turn on at the speed of light.

Light bulb doesn't turn on at the speed of light. That's grossly inaccurate. How do you even notice that? A bulb turning on in 1 microsecond would not even be noticeable to the eye...

First, the charges need to drift through the conductor, THEN they need to cause enormous amounts of scattering to transfer energy to the lattice and cause the lattice to radiate. This by itself requires extreme time scales (when compared to length of the conductor / speed of light)

Charge flow IS NEVER at the speed of light... But an excitation, a voltage WAVE or a spin WAVE could flow at the speed of light.

These concepts are fundamentally different.

 

[sokrates]

TO the OP:

Good question. Interestingly, it goes deep. First, you need to clear what you mean by potential...

USually, people talk about the electrostatic potential, which could be solved by Poisson's equation (solid state version of Gauss' Law from Maxwell's Equations)

But if you are interested in the main actors of transport, you need to learn more about the ELECTROCHEMICAL potential --- which is related to the distribution and occupation probabilities of carriers in a conductor. THESE are the causes of potential drop, a difference in electrochemical potentials across a resistor creates the voltage drop causing current flow.

It's NOT the electric field that creates current, it's the difference of the electrochemical potentials at different contacts.

OHM's LAW is not at all fundamental in this context, as incorrectly pointed out, rather a new bottom-up view emerging from insights taken out of mesoscopic physics, and quantum mechanics yield a much simpler interpretation.

Supriyo Datta is one of the pioneers in this field and I recommend you follow these links if you are really interested in nanoscale transport (because your questions are related to the microspopic definitions of voltage and resistance...)

https://nanohub.org/resources/5210

 

[sokrates]

Good question, though I'm not entirely sure what you mean. I guess you are wondering what causes the charges to move far away from the terminals?

Imagine a tube of marbles like this:

It's sort of a chain reaction where the charges push other charges while transferring an amount of energy. That is why you notice a light bulb turn on at the speed of light.

What are you getting at with this tube model? It's very, very misleading if you are trying to understand current flow like this (at any limit, ballistic, diffusive, quasi-ballistic etc...)

There's no transport model I know of which works like this. Maybe you could point out some references as to where this is used and in what context you are using it here?

 

[sokrates]

Thanks, I think the reason I assumed that potential was some intrinsic property was because I was confusing it with the electric field. I did some reading and realized that they're different things. I guess potential is meaningless unless there is some avenue for it to do work through (i.e. an impedance).

--- Potential is not meaningless even if there's no resistance. As I previously said, there are different definitions of potential, first be clear which is what you are implying.

Running with this classical hydrostatic-esque model, what then determines the propagation speed of a voltage "signal"? In hydrostatics/dynamics the speed of pressure propagation is a relatively straightforward concept.

--- Voltage signal propagation and actual charge propagation are two different things. If you are interested in the former, you just need some exposure on the Electromagnetic Wave theory. Tranmission LIne Waveguides are good places to work. Only in THAT context does the SIGNAL propagation by CHAIN reactions makes sense. In a conductor where charge flow is necessary to charge a capacitor at the output (like in a CMOS circuit) things DO NOT MOVE at the speed of light. That's why your computer STILL runs at 3 GHz at 1V supply voltage.
I'm imagining that the potential applied at one terminal of the circuit pushes on the first charge carriers, which then push on charge carriers further inside the conductor. This idea seems a bit broken though, as it would result in a signal propagation speed that is some function of the mean free path etc. (I remember someone mentioning that the propagation speed is the speed of light)---> Mean free path and signal propagation at c are VERY different. See my comments above.I guess a more indepth question I was trying to resolve is, what is the mechanism for the potential being applied to charge carriers at some arbitrary distance away from the terminals. Is it the same as the hydraulic analogy where pressure is applied to one end of a tube and is then distributed through the tube through particle interactions, or is it more complicated?

---> See this: https://nanohub.org/resources/5345
What makes current flow?

 

[user111_23]

What are you getting at with this tube model? It's very, very misleading if you are trying to understand current flow like this (at any limit, ballistic, diffusive, quasi-ballistic etc...)

There's no transport model I know of which works like this. Maybe you could point out some references as to where this is used and in what context you are using it here?

If I push a marble into the tube, the other ones will also move. Similarly with electrons; if an electron moves through the wire, the other ones will start moving as well. Sorry I confused you.

 

[user111_23]

Light bulb doesn't turn on at the speed of light. That's grossly inaccurate. How do you even notice that? A bulb turning on in 1 microsecond would not even be noticeable to the eye...

First, the charges need to drift through the conductor, THEN they need to cause enormous amounts of scattering to transfer energy to the lattice and cause the lattice to radiate. This by itself requires extreme time scales (when compared to length of the conductor / speed of light)

Charge flow IS NEVER at the speed of light... But an excitation, a voltage WAVE or a spin WAVE could flow at the speed of light.

These concepts are fundamentally different.

I'm talking about electrical energy here.

 

[sokrates]

I see... It's just not correct if you want to think about flow of current through light bulbs.

Different mechanism... Think of it as more like a flow of marbles in a river, where there's an altitude difference between two ends... Marbles are sometimes scatter back from stones, they scatter within themselves and they exhcange energy with water molecules etc...

 

[user111_23]

TO the OP:

Good question. Interestingly, it goes deep. First, you need to clear what you mean by potential...

USually, people talk about the electrostatic potential, which could be solved by Poisson's equation (solid state version of Gauss' Law from Maxwell's Equations)

But if you are interested in the main actors of transport, you need to learn more about the ELECTROCHEMICAL potential --- which is related to the distribution and occupation probabilities of carriers in a conductor. THESE are the causes of potential drop, a difference in electrochemical potentials across a resistor creates the voltage drop causing current flow.

It's NOT the electric field that creates current, it's the difference of the electrochemical potentials at different contacts.

OHM's LAW is not at all fundamental in this context, as incorrectly pointed out, rather a new bottom-up view emerging from insights taken out of mesoscopic physics, and quantum mechanics yield a much simpler interpretation.

Supriyo Datta is one of the pioneers in this field and I recommend you follow these links if you are really interested in nanoscale transport (because your questions are related to the microspopic definitions of voltage and resistance...)

https://nanohub.org/resources/5210

This continues to confuse me. If current is not created through the electric field, how can you prove that? Is the field too weak?

 

[sokrates]

No the field is not weak at all.

Google a PN junction, there are enormous electric fields, and zillions of electrons around but there's NO current flow at equilibrium.

Because in conventional theory, people also talk about a DIFFUSION current (or diffusion FLUX) which flows irrespective of an electric field...

This is a subtle but very important point. If you really want to comprehend the details, you should check the nanoHUB references I gave.

Current flows because of the electrochemical potential differences between the contacts that are willing to FILL or EMPTY the electronic states that reside in the channel. The difference in their agenda, one trying to fill up the states and one trying to empty them
creates the current flow.

Electric field by itself is NOT relevant.

 

[sokrates]

I'm talking about electrical energy here.

What do you mean by electrical energy?

 

[user111_23]

What do you mean by electrical energy?

Like I said in the tube analogy, electrons hit each other like a domino reaction, transferring energy in the process. That's why the energy flows fast.

 

[sokrates]

Look you are completely wrong about this. What domino reaction are you talking about? It doesn't work like that.

It's NOT the "flow of energy" (if you are not specifically talking about an electromagnetic wave on a waveguide etc..), it's the flow of CHARGE in a resistor.
Start from here:
http://en.wikipedia.org/wiki/Electric_current

 

[parsec]

Thanks, I think the reason I assumed that potential was some intrinsic property was because I was confusing it with the electric field. I did some reading and realized that they're different things. I guess potential is meaningless unless there is some avenue for it to do work through (i.e. an impedance).

--- Potential is not meaningless even if there's no resistance. As I previously said, there are different definitions of potential, first be clear which is what you are implying.

Running with this classical hydrostatic-esque model, what then determines the propagation speed of a voltage "signal"? In hydrostatics/dynamics the speed of pressure propagation is a relatively straightforward concept.

--- Voltage signal propagation and actual charge propagation are two different things. If you are interested in the former, you just need some exposure on the Electromagnetic Wave theory. Tranmission LIne Waveguides are good places to work. Only in THAT context does the SIGNAL propagation by CHAIN reactions makes sense. In a conductor where charge flow is necessary to charge a capacitor at the output (like in a CMOS circuit) things DO NOT MOVE at the speed of light. That's why your computer STILL runs at 3 GHz at 1V supply voltage.



I'm imagining that the potential applied at one terminal of the circuit pushes on the first charge carriers, which then push on charge carriers further inside the conductor. This idea seems a bit broken though, as it would result in a signal propagation speed that is some function of the mean free path etc. (I remember someone mentioning that the propagation speed is the speed of light)


---> Mean free path and signal propagation at c are VERY different. See my comments above.


I guess a more indepth question I was trying to resolve is, what is the mechanism for the potential being applied to charge carriers at some arbitrary distance away from the terminals. Is it the same as the hydraulic analogy where pressure is applied to one end of a tube and is then distributed through the tube through particle interactions, or is it more complicated?

---> See this: https://nanohub.org/resources/5345
What makes current flow?

Thanks. I'll be sure to check out the links. I'm fairly sure my speculation here is wrong, so think of it more as an invitation for people to poke holes in my bad understanding of these concepts.

We're driving at resolving the fundamental issue here, which I guess in a nutshell is to do with what a voltage signal is, how it propagates through a conductor and how it relates to charges flowing.

I have heard many (contradictory) ideas to do with the role of impedance in the measurement of a voltage signal, so I'm just trying to sort it all out.

 

[Born2bwire]

The circuit laws are just special cases of the electromagnetic equations given by Maxwell's equations. A signal in the circuit is propagated by an electromagnetic wave, this wave will travel on the order of the speed of light. Since the power and signal is encompassed in this wave, the signal will propagate much much faster than the charges will (and in the case of AC currents, there are no net movement of charges anyway). This is one reason why the electrons do not need to "know" what is ahead of them in the circuit, the movement of the charges and such in a DC and AC circuit settles down very very quickly. For all practical purposes, we make our measurements only after the bulk behavior of the circuit has settled in.

Voltage is the potential difference. It is the energy required to move a charge from point A to point B in the circuit. The voltage drop across a good conductor is assumed to be approximately zero. It is non-zero, it's very small, and only significant when you have a very long run of conductor or AC signals. This means that the energy lost by the charges moving along a wire is very very small. The resistor is a device that is meant to convert the movement of the electrons into heat, this relationship is described by Ohm's Law and is related on a more basic level by Drude's model. The electrons, moving along because of the applied electric field (from the electromagnetic wave or applied DC field), will collide with the material, transferring kinetic energy. The collisions create vibrations in the material which is heat. Since the resistor is designed to absorb a lot of heat from the electrons, it causes an appreciable drop in energy and thus has a voltage drop.

Voltage moves down as you go along a circuit because it is a potential difference, the energy to move a charge from point A to point B, so it stands that as A approaches B in a circuit (disregarding any sources between the two) that the voltage should decrease as well.

 

[user111_23]

The circuit laws are just special cases of the electromagnetic equations given by Maxwell's equations. A signal in the circuit is propagated by an electromagnetic wave, this wave will travel on the order of the speed of light. Since the power and signal is encompassed in this wave, the signal will propagate much much faster than the charges will (and in the case of AC currents, there are no net movement of charges anyway). This is one reason why the electrons do not need to "know" what is ahead of them in the circuit, the movement of the charges and such in a DC and AC circuit settles down very very quickly. For all practical purposes, we make our measurements only after the bulk behavior of the circuit has settled in.

Voltage is the potential difference. It is the energy required to move a charge from point A to point B in the circuit. The voltage drop across a good conductor is assumed to be approximately zero. It is non-zero, it's very small, and only significant when you have a very long run of conductor or AC signals. This means that the energy lost by the charges moving along a wire is very very small. The resistor is a device that is meant to convert the movement of the electrons into heat, this relationship is described by Ohm's Law and is related on a more basic level by Drude's model. The electrons, moving along because of the applied electric field (from the electromagnetic wave or applied DC field), will collide with the material, transferring kinetic energy. The collisions create vibrations in the material which is heat. Since the resistor is designed to absorb a lot of heat from the electrons, it causes an appreciable drop in energy and thus has a voltage drop.

Voltage moves down as you go along a circuit because it is a potential difference, the energy to move a charge from point A to point B, so it stands that as A approaches B in a circuit (disregarding any sources between the two) that the voltage should decrease as well.

YES. Exactly what I was trying to say.

 

[sokrates]

The circuit laws are just special cases of the electromagnetic equations given by Maxwell's equations. A signal in the circuit is propagated by an electromagnetic wave, this wave will travel on the order of the speed of light

This is very wrong and misleading. The entire field of photonics is trying to bring RF into the silicon chip - the sole reason is to avoid the HUGE delay in the interconnects...

If "circuits" operated at the speed of light, we would practically solve ALL VLSI problems... So before commenting further, please divide the channel length of the current day transistor ( ~ 50 nm ) to the speed of light ( 3 x 10^10 cm /s ) and calculate the delay...

let me first state a FACT : the delay of the state of the art MOSFET in a single INVERTER is 1 picoseconds... you can check this as well as other facts from itrs.gov

If you work out the numbers you'll see that we are really, really FAR AWAY from THE SPEED OF LIGHT...

It is true that, voltage perturbations CAN flow at the speed of light, but this cannot be stated in general for a circuit where a charging and discharging of a capacitor is concerned, because a comparison between the actual flow of carriers (drift velocity) and the RC time constant of the mediating medium need to be analyzed to decide whether we are really dealing with a voltage "wave" or not...

 

[Born2bwire]

I said that the signal propagation is on the order of the speed of light, you are talking about something different. The operation of a circuit element is usually done by the carriers themselves which we have already stated move very slowly.

 

[user111_23]

Look you are completely wrong about this. What domino reaction are you talking about? It doesn't work like that.

It's NOT the "flow of energy" (if you are not specifically talking about an electromagnetic wave on a waveguide etc..), it's the flow of CHARGE in a resistor.
Start from here:
http://en.wikipedia.org/wiki/Electric_current

I am not wrong at all. Look at this paragraph from http://www.allaboutcircuits.com/vol_1/index.html" :

"The tube is full of marbles, just as a conductor is full of free electrons ready to be moved by an outside influence. If a single marble is suddenly inserted into this full tube on the left-hand side, another marble will immediately try to exit the tube on the right. Even though each marble only traveled a short distance, the transfer of motion through the tube is virtually instantaneous from the left end to the right end, no matter how long the tube is. With electricity, the overall effect from one end of a conductor to the other happens at the speed of light: a swift 186,000 miles per second! Each individual electron, though, travels through the conductor at a much slower pace."

 

[sokrates]

But that's the part I am really not getting. What's the difference between signal propagation and the (accumulation of a) voltage signal at the output of a capacitor?

Or let me ask it this way, what parts of a silicon chip operate at the speed of light then?

 

[sokrates]

I am not wrong at all. Look at this paragraph from http://www.allaboutcircuits.com/vol_1/index.html" :

"The tube is full of marbles, just as a conductor is full of free electrons ready to be moved by an outside influence. If a single marble is suddenly inserted into this full tube on the left-hand side, another marble will immediately try to exit the tube on the right. Even though each marble only traveled a short distance, the transfer of motion through the tube is virtually instantaneous from the left end to the right end, no matter how long the tube is. With electricity, the overall effect from one end of a conductor to the other happens at the speed of light: a swift 186,000 miles per second! Each individual electron, though, travels through the conductor at a much slower pace."

You used the marble example in the context of the working principle of a light bulb. You are obviously a beginner in this, so instead of getting into ego wars with me, try to catch a few things and you'll learn. I am at least 10 years ahead of you, and this is what I do every day.

ALL ABOUT CIRCUITS is a good zero-level introduction to these concepts and it cannot be taken as a serious reference for me, as a scientist working in the field. These analogies are often very dangerous because they imply more than what they intend to convey... And if you read what I say carefully, I am not denying the fact that a voltage signal can propagate at c - as is the case in a transmission line waveguide (see above)

 

[user111_23]

You used the marble example in the context of the working principle of a light bulb. You are obviously a beginner in this, so instead of getting into ego wars with me, try to catch a few things and you'll learn. I am at least 10 years ahead of you, and this is what I do every day.

ALL ABOUT CIRCUITS is a good zero-level introduction to these concepts and it cannot be taken as a serious reference for me, as a scientist working in the field. These analogies are often very dangerous because they imply more than what they intend to convey... And if you read what I say carefully, I am not denying the fact that a voltage signal can propagate at c - as is the case in a transmission line waveguide (see above)

Alright I give up. I'm just a high school sophomore anyway.

 

[Born2bwire]

But that's the part I am really not getting. What's the difference between signal propagation and the (accumulation of a) voltage signal at the output of a capacitor?

Or let me ask it this way, what parts of a silicon chip operate at the speed of light then?

None, but the signal propagation along the interconnects of a chip is on the order of the speed of light (around 1%-50% of c in the medium perhaps depending on the type of transmission line) since it is done by electromagnetic waves. I'm talking about the propagation of the signal, not the creation of a signal. The charges that accumulate on the capacitor move slowly but the propagation of the changes in the voltages due to the charge accumulation propagate via a different mechanism, the electromagnetic waves.

The explanation was in response to a common question that people have, how do the charges seem to have prior knowledge of the circuit elements ahead of them before they actually reach that element? This is because the voltages/signals that create the forces that the charges respond to, whether in a passive circuit element like a resistor or the source on an active transistor, propagate throughout the circuit at a time scale much much smaller than the time scale of interest in circuit theory. As soon as the charges have built up on the drain of a transistor to create a voltage difference, this signal is propagated via electromagnetic waves down the transmission into the next element, it is not done by the physical movement of the charges from the source pin to the next element.

In your prior posts you even used the language of "signal propagation" so I do not know what you are arguing about here.

 

[sokrates]

As soon as the charges have built up on the drain of a transistor to create a voltage difference, this signal is propagated via electromagnetic waves down the transmission into the next element, it is not done by the physical movement of the charges from the source pin to the next element.

See the NEXT Element is a capacitor as well. What is the NEXT element? It is the GATE CAPACITOR of the subsequent inverter.

And you won't see an instantaneous change in the voltage across a capacitor, you HAVE to PHYSICALLY supply the charges to create the voltage difference.

So even if there's an instantaneous perturbation along the interconnects, it doesn't do anything. The charges HAVE to be move UP AND DOWN... This is why there's ELECTROMIGRATION problems in the interconnects... After all if there was no movement, why would there be any electromigration?

So, wave propagation seems irrelevant here.

 

[Born2bwire]

I never said the change is instantaneous. I said the propagation of the signal is due to electromagnetic waves which travel on the order of the speed of light. I never talked about the speed of the devices or circuit elements, I am talking about the signal propagation. Honestly, this is what you stated in a previous post yourself and at this point I have no idea why you are arguing other than as a continued gross misinterpretation of my statements.

 

[sokrates]

I think we mostly agree.

I am sorry if I misinterpreted what you are trying to say. I resolved my confusions over your posts.