Capacitors in Series: Understanding Top Plate Action

In summary, the conversation was discussing an example with two metal plates separated by an insulator and air. The problem was to calculate the capacitance of the plates in series, but there was confusion about how the top layer acts as a capacitor without a metal plate. The concept of dielectric constant, or relative permittivity, was also mentioned. Ultimately, the top layer was treated as a separate capacitor in the calculation.
  • #1
oneplusone
127
2
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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  • #2
What is "k"?
 
  • #3
A picture would make this a bit clearer ...
 
  • #5
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?
 
  • #6
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.
 
  • #7
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.
 

1. What is the purpose of connecting capacitors in series?

The purpose of connecting capacitors in series is to increase the overall capacitance in a circuit. When capacitors are connected in series, the total capacitance is equal to the inverse of the sum of the inverses of each individual capacitor's capacitance. This can be expressed mathematically as Ctotal = 1/((1/C1) + (1/C2) + (1/C3) + ...).

2. How does the top plate action work in capacitors connected in series?

The top plate action refers to the sharing of charge between the top plates of capacitors connected in series. When capacitors are connected in series, the top plates of each capacitor are connected to each other, creating a single conductive path. This allows for charge to be shared between the capacitors, resulting in a larger overall charge being stored.

3. What happens to the voltage across each capacitor in a series connection?

In a series connection, the voltage across each capacitor will be the same. This is because the total voltage in a series circuit is equal to the sum of the individual voltages. Since the capacitors are connected in series, the voltage across each capacitor is part of the total voltage in the circuit and therefore must be the same.

4. Can capacitors in series be replaced with a single equivalent capacitor?

Yes, capacitors in series can be replaced with a single equivalent capacitor. The equivalent capacitance can be calculated using the formula Ctotal = 1/((1/C1) + (1/C2) + (1/C3) + ...). This equivalent capacitor will have the same total capacitance and voltage rating as the series combination of capacitors.

5. What are the potential drawbacks of using capacitors in series?

One potential drawback of using capacitors in series is that the total capacitance may not be precisely what is needed for the circuit. This is because the total capacitance is dependent on the individual capacitance values of each capacitor. Additionally, if one capacitor in the series fails, it can affect the functioning of the entire circuit.

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