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jarls
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current through a superconductor
« on: Jan 13th, 2009, 2:52pm » |
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Ohm's law dictates that voltage divided by resistance for a given circuit is equal to the current through the circuit
Given a superconductive circuit the resistance is zero. Ohm's law would then dictate that the current through this circuit would be equal to the voltage divided by zero. Certainly the current through this circuit is not infinite thus Ohm's law does not suffice in determining the current through a superconductive circuit.
Given a superconductive circuit with known voltage (really potential difference since voltage is an expression of work done on an electron through a circuit and none is through a resistance-less circuit) how would the current through this circuit be non-experimentally determined?
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towr
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Re: current through a superconductor
« Reply #1 on: Jan 13th, 2009, 3:15pm » |
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Quote:| Ohm's law dictates that voltage divided by resistance for a given circuit is equal to the current through the circuit |
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Doesn't Ohm's law dictate that voltage is resistance time current? (This is a rather important difference, for the divide-by-zero reason)
Then no resistance means no voltage, rather than infinite current.
Quote:| Given a superconductive circuit with known voltage (really potential difference |
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Is it even possible to have a potential difference between two points connected by a superconductive pathway?
I'm no electrical expert, but every experience I have with circuit problems and physics tells me no.
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| « Last Edit: Jan 14th, 2009, 12:30am by towr » |
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Re: current through a superconductor
« Reply #2 on: Jan 13th, 2009, 3:59pm » |
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on Jan 13th, 2009, 3:15pm, towr wrote:| Is it even possible to have a potential difference between two points connected by a superconductive pathway? |
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In a steady state, no.
It gets more complicated with time-varying signals and transients as the superconductor will still have some capacitance and/or inductance and so will have a complex resistance with a non-zero imaginary component.
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jarls
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Re: current through a superconductor
« Reply #3 on: Jan 13th, 2009, 6:45pm » |
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Is the matter in question really unclear here?
Imagine a circuit comprised of a conductive wire with resistance, for which the source of electricity is a battery.
The current is easily determinable by utilizing Ohm's law. The voltage of the battery divided by the resistance of the wire.
Now take that same battery and place it in a superconductive circuit. Ohm's law clearly would not work.
How would the current then be determined non-experimentally?
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| « Last Edit: Jan 16th, 2009, 10:28pm by jarls » |
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Re: current through a superconductor
« Reply #4 on: Jan 13th, 2009, 7:03pm » |
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The current in that case will be "as much as your 'battery' can supply". i.e. it depends entirely on the parasitic resistances of the conventional conductors in the circuit and not on any property of the superconductor -- all you've done is create a perfect short across the battery terminals.
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jarls
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Re: current through a superconductor
« Reply #5 on: Jan 13th, 2009, 8:26pm » |
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You say the current would be however much the battery would supply. To my understanding the current through a circuit is a measurement of electromagnetic propagation through a medium which is dependent upon time and resistance of the circuit itself. Batteries in-themselves possess no current.
Also I am assuming an idealized battery in which there is no resistance. There exists the notion of some internal voltage (voltage may not be the appropriate or correct term, but something which has to do with the difference between the concentration of electrons at the positive terminal and negative terminal. something which when increased results in proportionately increased current) within a battery which exists independently of the battery's electrodes' resistance or internal resistance. Assuming there is no resistance in the battery ,naturally, one would still be able to determine the current through a resistive circuit to which this battery was connected.
How would one analogously determine the current through a superconductive circuit to which this same idealized battery was connected?
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towr
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Re: current through a superconductor
« Reply #6 on: Jan 14th, 2009, 12:54am » |
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on Jan 13th, 2009, 8:26pm, jarls wrote:| You say the current would be however much the battery would supply. To my understanding the current through a circuit is a measurement of electromagnetic propagation through a medium which is dependent upon time and resistance of the circuit itself. Batteries in-themselves possess no current. |
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It sounds odd to me to speak of "electromagnatic propagation"; we're not talking about light here. Current is a measurement of the amount of electric charge transported in a given unit of time. One ampere is one coulomb per second.
Batteries create/supply a current by creating a difference in charge (electric potential) between the two poles, and the charge tries to reach an equilibrium by moving from high to low. A capacitor would be a simpler example, since there you have a given charge difference (which is not created by the capacitor), and you have a current between the two sides (if they are connected by a circuit) until both sides have an equal charge.
Quote:Assuming there is no resistance in the battery ,naturally, one would still be able to determine the current through a resistive circuit to which this battery was connected.
How would one analogously determine the current through a superconductive circuit to which this same idealized battery was connected? |
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Well, given all that, it would be "infinite". In an ideal short circuit, any charge would redistribute instantaneously (if we ignore the theory of relativity for a moment).
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| « Last Edit: Jan 14th, 2009, 12:55am by towr » |
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Re: current through a superconductor
« Reply #7 on: Jan 14th, 2009, 5:51am » |
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Right, if you perfectly short-circuit an ideal voltage source (battery) you get an infinite current, precisely because Ohm's law does still apply. More formally: the limit as R approaches 0 (from the positive side) of I equals the limit as R approaches 0 (from the positive size) of V/R which grows without bound.
In a real physical system both voltage sources and superconductors have maximum current capacities above which they fail -- fail to maintain the desired voltage, fail to continue superconducting, or fail to be able to handle the resulting thermal load and so fail mechanically, by melting, burning, or exploding.
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jarls
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Re: current through a superconductor
« Reply #8 on: Jan 14th, 2009, 11:24am » |
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I don't see how infinite current is a possible phenomenon.
It was incorrect of me to say that current is electromagnetic propagation. It is in fact the flow of charge (not electrons) with respect to time. Although this does not correlate to the movement of individual electrons through a wire i would imagine it is dependent upon the flow of electrons and still does correlate to some form of motion. Would infinite current not entail motion at some infinite rate. How can anything move or propagate or travel etc. at an infinite rate?
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towr
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Re: current through a superconductor
« Reply #9 on: Jan 14th, 2009, 11:35am » |
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on Jan 14th, 2009, 11:24am, jarls wrote:| I don't see how infinite current is a possible phenomenon. |
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And you think an ideal battery and a perfect conductor are? We're dealing with an idealized world here, where the impossible happens.
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jarls
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Re: current through a superconductor
« Reply #10 on: Jan 14th, 2009, 11:43am » |
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Within every circuit wire there is some drift velocity of electrons through it. If current is the flow of charge through a circuit would the current not be an expression of the velocity, the number of electrons which can fit in the cross-sectional area of the wire and the charge of each electron? I don't see what else it could be based upon.
The only factor that the nature of the wire can change is the drift velocity of the electrons flowing through it. So unless a superconductive circuit would cause there to be infinitely quickly moving electrons, I don't see how the current could be infinite.
Intuitively I want to say that the drift velocity of an electron through a superconductive medium would be that of a freely moving electron. maybe the velocity of a cathode ray or the acceleration of an electron moving in some uniform electric field.
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jarls
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Re: current through a superconductor
« Reply #11 on: Jan 14th, 2009, 11:48am » |
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There is a fundamental difference between a non-existent idealized system and phenomena which are contradictory the the laws of physics.
For instance Frictionless systems are often supposed. The notion of a particle moving with infinite velocity is never supposed. And a frictionless system will never yield an outcome incongruous with the laws of physics. One could even say it yields outcomes which are most elegantly concurrent with the laws of physics.
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SMQ
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Re: current through a superconductor
« Reply #12 on: Jan 14th, 2009, 11:55am » |
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on Jan 14th, 2009, 11:24am, jarls wrote:| I don't see how infinite current is a possible phenomenon. |
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It's not, but neither are batteries without internal parasitic resistance. In the ideal case the current is unlimited/infinite. In the real-world case, the internal resistance of the power supply is no longer negligible, and in fact will likely be the limiting factor.
You seem to be considering a hybrid case with an ideal battery but a real-world superconductor. In that case I suppose you're limited by electron density in the cross-section of the superconductor, the speed of light (or a significant fraction of it, anyway), and possibly even synchrotron radiation as the high-speed electrons need to be turned around to complete the circuit, and doing so will cause them to lose energy and slow down.
Quote:| It was incorrect of me to say that current is electromagnetic propagation. It is in fact the flow of charge (not electrons) with respect to time. Although this does not correlate to the movement of individual electrons through a wire i would imagine it is dependent upon the flow of electrons and still does correlate to some form of motion. |
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Actually, except in semiconductors, current is almost always due to the movement individual of electrons. Although the electric field -- and therefore changes in voltage -- propagates at a significant fraction of the speed of light, the current is carried by individual electrons moving (on average) much more slowly -- on the order of millimeters-per-second in copper wire.
Quote:| Would infinite current not entail motion at some infinite rate. |
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Either infinite velocity or an infinite electron density in the material, yes.
Quote:| How can anything move or propagate or travel etc. at an infinite rate? |
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Obviously it can't, but since you were proposing an ideal battery I assumed we were discussing an ideal superconductor as well.
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towr
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Re: current through a superconductor
« Reply #13 on: Jan 14th, 2009, 11:59am » |
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on Jan 14th, 2009, 11:48am, jarls wrote:| There is a fundamental difference between a non-existent idealized system and phenomena which are contradictory the the laws of physics. |
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But there is no phenomena here that is contradictory to the laws of physics. The only things we have here is a result in a model which does not correspond to the real world it intends to model (notably the model allows impossible objects such as ideal batteries). It isn't a phenomenon unless it happens in the real world. And if it were to happen in the real world, then logically it couldn't contradict the laws of physics, or otherwise it couldn't happen.
Superconductivity is subject to limits in the real world; as are batteries. Making assumptions to the contrary invalidates the results based on those assumptions.
Quote:| For instance Frictionless systems are often supposed. The notion of a particle moving with infinite velocity is never supposed. |
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In Newtonian physics it's certainly not excluded. It is perfectly valid.
Quote:| And a frictionless system will never yield an outcome incongruous with the laws of physics. |
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That depends on what model of the universe you use, and how closely it correspond to reality.
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| « Last Edit: Jan 14th, 2009, 12:01pm by towr » |
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Re: current through a superconductor
« Reply #14 on: Jan 14th, 2009, 12:11pm » |
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on Jan 14th, 2009, 11:43am, jarls wrote:| Intuitively I want to say that the drift velocity of an electron through a superconductive medium would be that of a freely moving electron. maybe the velocity of a cathode ray or the acceleration of an electron moving in some uniform electric field. |
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But there's no such thing as the drift velocity of a freely moving electron. If it's in an electric field it will be accelerated by the field. If one were to suppose an electric field of arbitrary extent, our hypothetical electron would continue to gain energy until it left the field. As it approached the speed of light relativistic effects would become important and it would gain more energy in mass than in velocity, but its velocity would still be increasing. Given enough energy and enough space a free electron can be accelerated to any desired fraction of the speed of light.
The maximum electron density of the material is likewise ill-defined. Given sufficient force to overcome the electrons' mutual repulsion they can be made to pack as densely as desired, and even, due to wave-particle duality, to overlap. It would take a fantastic amount of energy to keep them confined at that density, but there is no fundamental reason why its impossible.
In the situation you're proposing, the current in the superconductor is limited only by the energy input to the system: given enough energy it's theoretically possible approach as close to infinite current as desired. Just as, given enough energy, it's theoretically possible to accelerate a frictionless wheel as close to infinite speed as desired.
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rmsgrey
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Re: current through a superconductor
« Reply #15 on: Jan 14th, 2009, 1:14pm » |
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on Jan 14th, 2009, 12:11pm, SMQ wrote:| The maximum electron density of the material is likewise ill-defined. Given sufficient force to overcome the electrons' mutual repulsion they can be made to pack as densely as desired, and even, due to wave-particle duality, to overlap. It would take a fantastic amount of energy to keep them confined at that density, but there is no fundamental reason why its impossible. |
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Aren't electrons, as half-spin particles, subject to the Pauli exclusion principle? If multiple electrons could share the same quantum state, then the periodic table would be very different...
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Re: current through a superconductor
« Reply #16 on: Jan 14th, 2009, 1:26pm » |
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on Jan 14th, 2009, 1:14pm, rmsgrey wrote:| Aren't electrons, as half-spin particles, subject to the Pauli exclusion principle? If multiple electrons could share the same quantum state, then the periodic table would be very different... |
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Ahh, but we're talking about a superconductor here, and (at least according to widely-accepted theory) superconductivity is a manifestation of electrons forming Cooper pairs and thereby becoming subject to Bose-Einstein statistics rather than the PEP. Wouldn't that allow the Cooper pairs to overlap in space as well?
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jarls
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Re: current through a superconductor
« Reply #17 on: Jan 14th, 2009, 5:13pm » |
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on Jan 14th, 2009, 11:55am, SMQ wrote:
It's not, but neither are batteries without internal parasitic resistance. In the ideal case the current is unlimited/infinite. In the real-world case, the internal resistance of the power supply is no longer negligible, and in fact will likely be the limiting factor.
You seem to be considering a hybrid case with an ideal battery but a real-world superconductor. In that case I suppose you're limited by electron density in the cross-section of the superconductor, the speed of light (or a significant fraction of it, anyway), and possibly even synchrotron radiation as the high-speed electrons need to be turned around to complete the circuit, and doing so will cause them to lose energy and slow down.
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Infinite current entails either an infinite rate of electron flow with respect to time or infinite density of electrons. How could this be the case even in an idealized scenario?
Eliminating the limiting factor of a system does not cause the what has been limited to diverge.
I am assuming an idealized conductor as which a real world superconductor is the same.
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jarls
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Re: current through a superconductor
« Reply #18 on: Jan 14th, 2009, 5:36pm » |
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on Jan 14th, 2009, 11:59am, towr wrote:
But there is no phenomena here that is contradictory to the laws of physics.
In Newtonian physics it's certainly not excluded. It is perfectly valid.
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By phenomenon I meant conceptual notion. And both infinite rate of electron movement and infinite electron density (the two electrically dependent factors of current) are incongruous with the laws of physics.
An idealized battery can not exist. Just as a frictionless environment can not. That in-itself does not mean that there can result a conceptual physical notion which is incongruous with the laws of physics.
Imagine the internal parasitic resistance of a battery within a superconductive circuit is incrementally brought to zero. The current should not diverge to infinity. It should asymptotically approach some value.
Also it has since been discovered that the notion of Newtonian physicality is incorrect. It is merely a means of approximating phenomenal behavior. This approximation is only relatively accurate with respect to relatively small velocities. From zero velocity to through all reasonable experienceable velocities, when mass is held constant, the acceleration a body undergoes merely appears to be constant. When in fact this body, in accelerating, will have gained a slight amount of mass which will have caused its acceleration graph to, negligibly but actually, be curved and fall away from the ideal straight line of constant acceleration. This curve is just the very small first bit of a curve which asymptotically approaches the speed of light with respect to time. I don't see how a phenomenon's (conceptual notion's) being concurrent with Newtonian physics makes it concurrent with the laws of physics.
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jarls
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Re: current through a superconductor
« Reply #19 on: Jan 14th, 2009, 5:42pm » |
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on Jan 14th, 2009, 12:11pm, SMQ wrote:
Given sufficient force to overcome the electrons' mutual repulsion they can be made to pack as densely as desired, and even, due to wave-particle duality, to overlap.
Just as, given enough energy, it's theoretically possible to accelerate a frictionless wheel as close to infinite speed as desired.
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How can a massive particle occupy the same space as another massive particle for more than an instant?
How can anything (frictionless wheel) exceed in its speed the speed of light (which is very far away from infinite speed)?
I also don't understand the notion of 'as close to infinite' anything?
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SMQ
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Re: current through a superconductor
« Reply #20 on: Jan 14th, 2009, 6:52pm » |
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on Jan 14th, 2009, 5:42pm, jarls wrote:| How can a massive particle occupy the same space as another massive particle for more than an instant? |
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Welcome to quantum physics: google Bose-Einstein Condensate for one example.
Quote:| How can anything (frictionless wheel) exceed in its speed the speed of light (which is very far away from infinite speed)? |
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Sorry, I was neglecting relativistic effects -- I should have said momentum rather than speed.
Quote:| I also don't understand the notion of 'as close to infinite' anything? |
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"As close as desired", i.e. any finite value is achievable with sufficient effort.
Let's try this from the other direction: V=IR implies R=V/I, so if the voltage across the ends of the superconductor is non-zero and the current through the superconductor is finite, then the resistance is not zero. If there is any resistance then there's power dissipation. At the current levels we're talking about any resistance is disastrous: just ask the LHC team at CERN.
You seem to want to pick-and-choose which physical laws apply to your model -- which is your right in designing the model -- but it seems to have turned this into a "what am I thinking" type riddle where we have to guess which laws are in effect.
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| « Last Edit: Jan 14th, 2009, 6:54pm by SMQ » |
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jarls
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Re: current through a superconductor
« Reply #21 on: Jan 14th, 2009, 7:13pm » |
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I actually wasn't attempting to pose a riddle. I'm merely curious about this notion which for some time has puzzled me. I figured introducing it to a forum in which some fairly strong minds moderate might yield an explanation that I am able to understand.
I've not been trying to trick or out-think anyone. I'm just curious and trying to come to an understanding.
I suppose a riddle forum though is not the right place for such an inquiry.
Which laws have I neglected?
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| « Last Edit: Jan 14th, 2009, 8:01pm by jarls » |
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towr
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Re: current through a superconductor
« Reply #22 on: Jan 15th, 2009, 12:56am » |
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on Jan 14th, 2009, 5:36pm, jarls wrote:| An idealized battery can not exist. Just as a frictionless environment can not. That in-itself does not mean that there can result a conceptual physical notion which is incongruous with the laws of physics. |
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Of course it does. The idealized situation is impossible because the laws of physics don't allow for it.
Quote:| Imagine the internal parasitic resistance of a battery within a superconductive circuit is incrementally brought to zero. The current should not diverge to infinity. It should asymptotically approach some value. |
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Yeah, cause a real battery only has so much power it can produce. It's not a fundamental problem though, it's a practical one. If there was no limit to the battery output, no limit to heat dissipation (to keep the battery/circuit from heating), and probably no limits to some other parameters, then the current would diverge to infinity.
But in practice the battery will fail, the circuit will heat up, the superconductor will lose it's superconductivity, etc.
Quote:| Also it has since been discovered that the notion of Newtonian physicality is incorrect. It is merely a means of approximating phenomenal behavior. |
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Gosh, really? (And you seem to have switched meaning on 'phenomenal' here.)
Quote:| I don't see how a phenomenon's (conceptual notion's) being concurrent with Newtonian physics makes it concurrent with the laws of physics. |
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And I wasn't claiming it was. I was claiming that in physics you can have models that produce results contrary to what is possible in reality.
You shouldn't apply a model beyond it scope. And you shouldn't apply ideal laws to imperfect components as if they were ideal.
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JiNbOtAk
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Re: current through a superconductor
« Reply #23 on: Jan 16th, 2009, 2:00am » |
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Interesting discussion. However, correct me if I'm wrong, but I've always thought that Ohm's law is more of an approximation, i.e. at extreme conditions it is no longer valid. Right ?
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Re: current through a superconductor
« Reply #24 on: Jan 16th, 2009, 6:23am » |
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There are two ways of looking at it, JiNbOtAk: in an "engineering" sense you are right, in that Ohm's Law as usually stated only strictly applies at DC steady state. If any parameters of the circuit are time-varying then things get more complex. The other way of looking at it -- the "physicists" way -- is that Ohm's Law defines instantaneous resistance. At any point in time, the resistance of a circuit or circuit element is given by the ratio of the voltage differential to the current. Using this definition, "resistance" in a broader sense is itself a time-varying property.
Either way, I believe Ohm's Law is applicable to the question at hand as we're discussing an in-some-sense-ideal circuit at DC steady state.
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