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I have had some philosophical reflections about the voltage/current relationship. Assume we are somehow able to have a determined fixed current AND voltage on a device. This device could theoretically exist by having a Resistance and thereby a power dissipation that simply adjusts on the current and voltage. Ie P(U,I) where U and I are independent variables, so basically a device whose U-I relationship can not be described by a function but covers the whole UxI space. Now to my question: Does such a device exist? Or is there something approaching this concept of independent U and I.

Sorry for bothering you with a problem that probably is contradictory by itself.

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  • \$\begingroup\$ Are you talking about electronic loads? \$\endgroup\$ – PlasmaHH Jul 16 '15 at 8:31
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    \$\begingroup\$ Answered here previously: electronics.stackexchange.com/questions/38856/… \$\endgroup\$ – lyndon Jul 16 '15 at 8:32
  • \$\begingroup\$ Sure - how about a potentiometer? \$\endgroup\$ – Nick Johnson Jul 16 '15 at 8:35
  • \$\begingroup\$ A current load takes voltage as input and via feedback and outputs a certain current. My hypothetical device would take current and voltage as input and power as output. Both current and voltage are fixed and cannot be used in feedback. \$\endgroup\$ – user2351468 Jul 16 '15 at 9:14
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    \$\begingroup\$ What do you expect to happen if you make two of your device, tune them to different I/V values, and then connect them to each other? \$\endgroup\$ – The Photon Jul 16 '15 at 15:43
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From what you say it is implicit that this hypothetical device is a two-terminal device, therefore its behavior can be described, as you say, by some V-I relationship, however complicated, so not even a function, but a generic mathematical relation.

Note: in English technical literature voltages are indicated by V, not U. Since the language of this site is English, I'll stick to that convention.

The problem here is that you assume we can test this device by impressing both current and voltage and this is impossible. You have only two terminals in your device, so you either connect an (ideal) voltage source or an (ideal) current source to them. Whatever complicated system you use to create those sources, they have only two accessible terminals to your device. The problem is that to impress the current you have to put the current source in series with your device, whereas to impress the voltage you have to put the voltage source in parallel with it. If you want to impress both quantities, you should be able to put both sources together, but the requirements are incompatible: you either connect both sources in series with your device or in parallel.

schematic

simulate this circuit – Schematic created using CircuitLab

In the latter case the current source cannot impress the current in the device alone, whereas in the former the voltage source cannot impress the voltage across the device alone.

If you object that you could devise a strange "testing apparatus" that "magically" has only two terminals and puts out a fixed voltage across those terminals and impress a fixed current across them, well that is impossible either, because its V-I relationship would be a single point in V-I plane.

If you don't get why such a V-I relationship is absurd physically (mathematically is OK) think a moment about it: such a testing device is able to impress both a fixed current and a fixed voltage on whatever load it is connected to, so it is able to turn everything into a resistance of value R=V/I (that's magic!)

Ok. Maybe I misunderstood what your X-device is intended to do (your wording wasn't very clear). Let's get back to square one. You said it should have "power dissipation that simply adjusts on the current and voltage. Ie P(U,I) where U and I are independent variables". And again in your comment: "Both current and voltage are fixed and cannot be used in feedback."

That's another problem: you seem to imply that your X-device is able to draw a fixed amount of power, whatever the values of V and I, but that's impossible from the beginning. The fact that the power absorbed by any two-terminal network is given by P=VI is a physical fact, and that very relation makes it impossible to have V and I independent once you select a power value. Only two out of three can be independent, so if you fix V and I, the power your device absorbs is VI, no matter what.

EDIT (in response to a comment)

And yes, by my device I mean one that 'magically' adjusts its power/resistance in order to obey energy conservation/ohms law. At which point does such a device contradict physical law?

  1. You don't need to obey Ohm's law unless you want to create a (linear) resistor. An ideal linear resistor is, by definition, the only device that obeys Ohm's law. So, no need to do "magic".
  2. Obeying conservation of energy implies that P = VI must be satisfied at each instant of time, i.e. P(t) = V(t)I(t) for each t.
  3. This latter "requirement", from a practical point of view, makes no sense: any device you could build will satisfy that requirement because there is no phenomenon in the known universe that don't obey conservation of energy, so your device doesn't need to "adjust" anything to obey P=VI, it just will!
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  • \$\begingroup\$ Thank you very much for your detailed answer! First of all I think whether we are arguing about an adjusting R or P makes no difference since they are linked. And yes, by my device I mean one that 'magically' adjusts its power/resistance in order to obey energy conservation/ohms law. At which point does such a device contradict physical law? \$\endgroup\$ – user2351468 Jul 16 '15 at 15:29
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Assume we are somehow able to have a determined fixed current AND voltage on a device.

To see why this is logically impossible, consider these questions,

  • What does this device do when its terminals are open circuit? Where will it's fixed current come from without violating KCL?

  • What does the device do when its terminals are shorted together? How will it produce a fixed voltage output across a short?

  • What will this device do when connected to another similar device with different I or V values?

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  • \$\begingroup\$ this would be valid for an active device which has to produce current and voltage across its terminals. I am talking about a passive device capable to adjust to a given R and V. \$\endgroup\$ – user2351468 Jul 17 '15 at 11:55
  • \$\begingroup\$ @user2351468, My understanding is that the sentence I quoted was not about the load device, but a pre-supposition about a source available to power your load device. Then you asked a question about the load device. I'm saying that your pre-supposition is impossible, so it makes no sense to consider how a load device would react to a power source with fixed voltage and current. \$\endgroup\$ – The Photon Jul 17 '15 at 15:40

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