Capacitors in Series: Understanding Top Plate Action

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Discussion Overview

The discussion revolves around understanding the behavior of capacitors in series, specifically in a scenario where two metal plates are separated by a dielectric material and air. Participants are exploring the concept of how the dielectric layer interacts with the electric field and capacitance calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a setup with two metal plates and a dielectric material (κ) occupying part of the space between them, questioning how the top layer can act as a capacitor without a metal plate.
  • Another participant asks for clarification on what "k" refers to, leading to an explanation that κ is the dielectric constant, with specific values for air and insulators.
  • A participant suggests that a visual representation might clarify the situation further.
  • One participant reiterates the initial setup and expresses confusion about the calculation method used in the example, specifically regarding the series capacitance formula.
  • Another participant clarifies that the two materials are treated as separate capacitors for calculation purposes, noting that adding a metal layer would not change the outcome since no charge would move through it.

Areas of Agreement / Disagreement

Participants generally agree on the setup involving two different materials acting as capacitors, but there is ongoing confusion and debate about the role of the dielectric and the calculation methods involved.

Contextual Notes

There are unresolved questions regarding the specific calculations performed in the example and the implications of adding a metal layer between the dielectric and air.

Who May Find This Useful

This discussion may be useful for individuals interested in capacitor theory, dielectric materials, and the mathematical treatment of capacitors in series.

oneplusone
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I read about an example in which you had two metal plates, and in between them one third of the distance from the top plate downwards (towards the bottom plate) was made up of κ, and the rest was air. THe problem proceeded to calculate the capacitance of them in series.
I don't get how the top layer acts as a capacitor though. There's no metal plate? Can someone please help me understand what's going on?
 
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What is "k"?
 
A picture would make this a bit clearer ...
 
oneplusone said:
I read about an example in which you had two metal plates, and in between them one third of the distance from the top plate downwards (towards the bottom plate) was made up of κ, and the rest was air. THe problem proceeded to calculate the capacitance of them in series.
I don't get how the top layer acts as a capacitor though. There's no metal plate? Can someone please help me understand what's going on?

If I understand you correctly, you have 2 metal plates separated by a distance d, with an insulator of k > 1 of thickness d/3 and air k =1 of thickness 2d/3 between the plates.

How was the calculation performed in the example?
Normally it would be 1/C = 1/C1 + 1/C2 for series capactitances.
If one would put a metal layer on the material, can you see that the metal layer would have a certain voltage, so you have 2 capacitors connected in parrallel - one with the insulator and one with air as the dielectric.

Or were they calculating the electric field between the plates?
 
Sorry for being unclear.

@above you are correct; that's what we did. The problem i was having was understanding why they are two different compactors.
 
They are treated as separate capacitors as a calculation technique. The metal plate in between isn't necessary (no electric charge would move if you added an infinitesimally thin metal plate between the insulator and the air, so it won't affect the calculation.
 

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