# Fundamentality of voltage to current

From Ohm's Law :

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points.

• I would like to know if writing $V\propto I$ is the same as writing $I\propto V$?

• Are they both correct?

• Are they equally dependent on each other or is only current dependent on the voltage?

• Because in circuits it is the voltage that we have as constant and not the current or is there a way to make the current the factor that determines the voltage?

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 – Qmechanic♦ May 17 '12 at 11:41

If you are wondering about causality, then I think that voltage difference $\Delta V$ is fundamental as it is the cause, and the current $I$ is the consequence.

If you want to have current, you need movement of the charges. The most obvious way to move charges is to act upon them with electric field, and each electric field is accopmained with voltage difference.

I real terms I cannot think of the quasi-electrostatic process - and Ohm's law does describe quasi-electrostatic process - in which the current would create the voltage. Hence,

$$I \propto \Delta V.$$

An interesting connection to the interpretation above are constant voltage and constant current sources. Constant current sources are actually voltage sources with quick loopback that changes voltage in order to keep the current constant.

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 Connect an inductor up with a battery to get some current flowing, then break the circuit. Inductors don't allow instantaneous changes in current, so the current will keep flowing. This results in whatever voltage difference is necessary to maintain the current, leading in this case to arcing. In this case you could say the current caused the voltage. – Nathaniel May 17 '12 at 14:33 Yes, but this is not electrostatic problem and Ohm's law does not apply to that problem. I guess that whithin Maxwell equations current density and electric field are equally fundamental, but again, this is not electrostatic problem and fundamentally different than Ohm's law – Pygmalion May 17 '12 at 15:31 Well, if you replaced the air gap in that setup with a big resistor, you'd be able to calculate the voltage using Ohm's law by plugging in the current across the inductor. I suppose you could say it's the voltage that's causing the current to flow across the resistor, but in the context of the circuit as a whole it's also the current that's causing the voltage. I remember suddenly feeling I understood electronics much better once I could let go of the idea that one must cause the other, and instead started seeing components as imposing constraints on how they relate to one another. – Nathaniel May 17 '12 at 15:52 In resistor, the voltage of the inductor definitely creates current within the resistor according to Ohm's law. While in the inductor it is all about Lenz's law and not Ohm's law.. – Pygmalion May 17 '12 at 15:57 Yes, that's essentially what I said. – Nathaniel May 17 '12 at 16:06

Yes, if you write $V \propto I$ it means:

$$V = kI$$

for some constant $k$. If you rearrange this equation to:

$$I = \frac{1}{k}V$$

this is the same as:

$$I = k^'V$$

for a new constant, $k^'$, and therefore $I \propto V$.

Response to comment: in some situations it makes sense to think of the current dependent on the voltage, but in others you would think of the voltage dependent on the current.

For example, suppose you have a battery with a known voltage, $V$, and you want to know the current. You'd normally write:

$$I = \frac{V}{R}$$

and feed in the voltage, $V$. On the other hand suppose you have some resistor, $R$, with a known current, $I$, flowing through it and you want to know the voltage drop accross the resistor. In that case you'd write:

$$V = IR$$

And of course there's a third case where you have a battery with a known voltage, $V$, and you measure the current to be $I$, you might ask what the resistance is. In that case you'd write:

$$R = \frac{V}{I}$$

All three of these equations are just rearrangements of each other, so they're all basically the same equation. You just rearrange them to suit the question you're trying to answer. This is pretty common in Physics. In due course you'll learn about ideal gases where there's a similar equation $PV = RT$, and you rearrange this equation in different ways depending on what you're trying to calculate.

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 is voltage dependent on current or is current dependent on voltage.... – The-Ever-Kid May 17 '12 at 10:23 thanks for the great answer but i already know about the gas equation .........I wanted to know about the fundamentality of both the quantities – The-Ever-Kid May 17 '12 at 12:10 Both $I$ and $V$ are equally fundamental. – John Rennie May 17 '12 at 13:15 The issue is that V is a field, while I is a response to the gradient of this field. If I asked you "does a force F cause an acceleration ma, or does acceleration of ma cause a force to act of magnitude F?" I don't think you would answer "it doesn't matter, either way is right", although in the strictest sense, you might be right, it depends on the definition of the notorious word "cause", which is ultimately a human and macroscopic notion. – Ron Maimon May 22 '12 at 5:18