Any current in an AC circuit if you moved the plates of a capacitor apart?

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Discussion Overview

The discussion revolves around the behavior of current in an AC circuit when the plates of a capacitor are moved apart, specifically examining whether an RMS current can still be measured in such a scenario. Participants explore the implications of capacitance changes due to increased plate separation and the necessity of a return path in the circuit.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question whether an RMS current would still be measurable if the distance between capacitor plates is increased significantly, suggesting that it might still exist despite the plates being far apart.
  • Others argue that increasing the distance between the plates reduces capacitance, which in turn affects the RMS current according to the relationship I_rms = V * ω * C.
  • A participant points out that while capacitance decreases with distance, the current does not necessarily go to zero, leading to the assertion that an AC current can exist without a traditional return path.
  • Some participants emphasize that the concept of an open circuit may not apply in the same way for AC circuits, as the periodic motion of charged particles could still allow for current flow.
  • There are claims that if capacitance becomes negligible, the current should also be negligible, but this is contested by others who argue that current can still flow depending on the input conditions.
  • One participant mentions that at very high frequencies, measurable current could still occur even with large plate separations, suggesting a connection to radio frequency circuits.
  • Another participant asserts that there is always a return path through the capacitor, albeit with very high reactance, which results in a very small current that may often be ignored.
  • Some participants engage in a discussion about the theoretical limits of capacitance as the distance approaches infinity, questioning the practical implications of such scenarios.

Areas of Agreement / Disagreement

Participants express multiple competing views on whether an AC current can exist without a return path and how significant the current would be under varying conditions of capacitance and frequency. The discussion remains unresolved with differing opinions on the implications of increased plate separation in a capacitor.

Contextual Notes

Limitations include the dependence on the definitions of open circuits and capacitance, as well as the unresolved mathematical relationships that govern current flow in AC circuits with varying capacitance.

mrmojorising
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capacitor question...(why does AC need a return path)

say you have an ac power source (120 v) connected to a circuit which just has one parallel plate open air capacitor, with the plates separated by, say, 1 mm.

you measure the current flowing through the circuit and you get some rms value.

now say you move the plates of the open air capacitor apart - say to 1 meter. would you still measure an rms current in the ciruit? why/why not?
 
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How is the distance between the plates related to the capacitance?
 
Also consider that the dielectric constant of practical capacitors is greater than of air.
 
ok, so if you double the distance between the capacitor plates the capacitance halves. so I_rms=V/X_c

where X_C=1/(omega*C) where I is rms current, X_c is capacitive impedance, C is capacitance, and omega is 2pi*frequency.

So I_rms=v*omega*C.

So double the distance of the capacitor plates, C halves and so does the RMS current.

Now for my real question:

Why is it that everyone says a circuit needs a return path? By taking an RC circuit and greatly increasing the distance between the plates of a parallel plate capacitor you are effectively creating an open circuit -- there is no return path! Yet as demonstrated from the equation above there will still be an rms current. It will be smaller than if the plates were close together, but it will still be there, and it doesn't fall off exponentially, but is proportional to 1/d where d is the distance between capacitor plates.

Now this is only true for AC circuits, but based on the above it seems like you don't need a return path in order for an AC current to exist: it will exist in an RC circuit whose capacitors plates are separated by a great distance (say 1 m), which is effectively an open circuit, thus a circuit without a return path.
 
mrmojorising said:
By taking an RC circuit and greatly increasing the distance between the plates of a parallel plate capacitor you are effectively creating an open circuit -- there is no return path! Yet as demonstrated from the equation above there will still be an rms current.
Where is this (theoretical) current flowing then, if there's no return path?
 
gnurf said:
Where is this (theoretical) current flowing then, if there's no return path?


I get it from the equation I_rms=v*omega*C.

As D (the distance between the cacitor plates increases) to something like 1 m the circuit effectively becomes an open circuit, which means there's no return path.

However as D increases to something like 1 meter C and thus I_rms decrease, but from the equation above do not go to zero - hence there's a current with no return path.

This would only work for AC, with the charged particles in the wire jiggling about in periodic motion. So the current is not flowing anywhere, it's composed of charged particles jiggling in periodic motion.
 
mrmojorising said:
As D (the distance between the cacitor plates increases) to something like 1 m the circuit effectively becomes an open circuit [...]
Then, effectively, no current will flow. You can't have it both ways.
 
gnurf said:
Then, effectively, no current will flow. You can't have it both ways.

why current would not flow?The capacitor plate which is given a -ve potential will induce a +ve charge on the other plate and hence electron will flow from +ve plate to +ve terminal of the battery resulting in current.
 
Since your capacitance will be extremely small after you separate the plates, you will need a very high frequency to get any (measurable) current. And now we are talking about radio frequency circuits, which as we all know *can* transmit a small (AC) current through air.
 
  • #10
amaresh92 said:
why current would not flow?The capacitor plate which is given a -ve potential will induce a +ve charge on the other plate and hence electron will flow from +ve plate to +ve terminal of the battery resulting in current.

If capacitance is negligible then current is negligible. If current is not negligible, then there isn't an open circuit, and the capacitance of the gap must be taken into account...it can not be treated as an open circuit. Whether a gap can be considered an open circuit or not depends on what you're doing...if an AC voltage is applied, there will always be current as parts of the circuit charge and discharge, however miniscule.
 
  • #11
cjameshuff said:
If capacitance is negligible then current is negligible.

how you can say the current will be negligible if the capacitance is negligible without knowing the input current.
 
  • #12
mrmojorising said:
Why is it that everyone says a circuit needs a return path?
For the same sort of reason that 'they' say current takes the path of least resistance. They are both over-simple statements which on on the right side of wrong.
If there is some value of Capacitance then there will be some value of current.
 
  • #13
amaresh92 said:
cjameshuff said:
If capacitance is negligible then current is negligible.

how you can say the current will be negligible if the capacitance is negligible without knowing the input current.

If current through such a circuit is non-negligible, then neither is the capacitance. Read the full post, rather than fixating on one small portion of it.
 
  • #14
Does current flow AS the capacitor pulled apart? I think the answer is yes, but I'm trying to think of an expression for this current.
 
  • #15
There is a return path; it's through your very, very, very small capacitor which has a crapton of reactance. Because the reactance is so high, the current will be very, very, very small, so small that it can be ignored for the vast majority of applications.
 
  • #16
Capacitance decreases as the plates are separated. Let me know when you figure out the distance that reaches zero farads.
 
  • #17
Skaperen said:
Capacitance decreases as the plates are separated. Let me know when you figure out the distance that reaches zero farads.
Infinity.
 

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