How does current affect electric potential?

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Discussion Overview

The discussion revolves around the relationship between current and electric potential, particularly in the context of two regions within a biological cell. Participants explore how current flow affects the potential difference between these regions over time, referencing Ohm's Law and potential discharge equations.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant suggests that the new voltage after current flow depends on the rate of electrochemical reactions in the cell.
  • Another participant questions the nature of objects A and B, proposing that the potential difference could become zero after some time, depending on the specifics of the system.
  • A participant clarifies that A and B represent regions of a biological cell and notes that the potential difference should decrease as current flows.
  • Concerns are raised about the applicability of Ohm's Law in this biological context, with a participant emphasizing the need for caution in quantifying current flow without it.
  • One participant introduces a formula for the discharge of a capacitor, noting that using it would involve many assumptions about the cell's behavior.
  • Another participant speculates that the relationship might resemble a decreasing curve approaching zero, suggesting an exponential form could be a reasonable approximation.
  • A later reply acknowledges the exponential form and expresses surprise at its prediction.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the applicability of Ohm's Law in biological systems and whether the behavior of the cell can be accurately modeled using electrical circuit equations. There is no consensus on the exact relationship or equations that describe the current and potential in this context.

Contextual Notes

Participants highlight the complexity of modeling biological systems with electrical analogies, noting the potential for significant assumptions and the need for empirical determination of parameters.

Apteronotus
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Suppose you have an two objects A and B having different potentials [tex]\phi_A, \phi_B[/tex] and voltage [tex]V=\phi_A- \phi_B[/tex].

Suppose you allow current to flow from one object to another for some period of time according to Ohm's Law (V=IR)
Now what is the new value of the voltage?

thanks
 
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That depends on the rate of electrochemical reaction in the cell
 
What are the objects A and B?
As you have defined V as the pd between the two objects, then it is perfectly feasible that the flow of charge is such that the pd between A and B becomes zero after a time t.
I think you need to be more specific in the question formulation.
Are A and B capacitors? Or to be treated as such?
 
The objects represent two regions of a biological cell. Current in the form of ions is allowed to flow from one region to the other. Obviously when this current is allowed to flow, the potential difference between the two regions should decrease.

I was wondering if there are any equations which can describe this relation.

Stonebridge, you are right. If enough time is allowed to pass, then the potential difference would become zero.
 
I know nothing about cell biology! I'm wondering, though, if it's asking a little too much to assume Ohm's Law is obeyed. Without that, it's not possible to quantify the current flow. And it's this current (I=V/R) which determines the rate at which the charge flows from from A to B.
Additionally, there is the relationship between the potential at A and B and the amount of charge localised at those points. (That's why I asked about capacitors).
In physics there is a formula for the discharge of a capacitor through a resistor.
V=Vo e^(-t/CR)
where Vo is initial potential difference, C is capacitance, R is resistance of circuit, t is time and V the pd across the capacitor at that time.
However, using something like this formula would be making a lot of assumptions about the way the cell behaves. What is R? What would C represent etc etc? I doubt it would work!
Maybe someone else with more knowledge of cell biology would like to try?
 
An exact formula would be pretty complicated, I'm sure (I don't know anything about cell biology either), but I would think that whatever it is, it'd still fit the general form of a decreasing curve that asymptotically approaches V=0. I doubt that the innards of a cell have complex electrical structures like transistors or diodes in them :wink: I wouldn't be that surprised if the exponential form
[tex]V = V_0 e^{-t/\tau}[/tex]
turned out to be a pretty decent approximation, for some value of [itex]\tau[/itex] which you'd probably have to determine empirically.
 
diazona said:
[tex]V = V_0 e^{-t/\tau}[/tex]

How did you guess that?
 

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