Capacitance for a capacitor with two dielectrics

In summary, the geometry of a capacitor can be cylindrical or spherical and the total capacitance can be found by testing either alternative. It also depends on the problem setup, which may involve two dielectrics in series or in parallel. In the first case, the capacitors have the same dimensions and are stacked on top of each other, while in the second and third cases, the capacitors are next to each other with different dimensions.
  • #1
Homework Statement
If I have two parallel conductive plates, that is, a capacitor, with two dielectrics k1 and k2 between the plates, and I want to know how much is the capacitance, knowing that I can solve the problem finding the equivalent capacitance for the two capacitors, one with k1 and the other with k2, how to determine whether they are in series or in parallel?
Relevant Equations
kQ = CV
The geometry of the capacitor can be either cylindrical or spherical.
 
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  • #2
If you already know the what the total capacitance looks like then you can test either alternative and see which one matches of course. If you don't you can think of what physical property must be in series and go from there.
 
  • #3
It depends on the exact problem setup (for which you are a bit vague I must admit).

If we have a parallel plate capacitor with ##d## the distance between the plates and ##l## the length of the plates (and ##w## the depth of the plates) and has two dielectrics between the parallel plates then(assuming the capacitor plates are up and down):
  • if one dielectric is a slab with dimensions ##\frac{d}{2} \times l\times w## and the other also a slab of the same dimensions this means that one dielectric is in top of the other and then you have two capacitors in series. The two capacitors have area ##A=l\times w##, distance between plates ##\frac{d}{2}## and one is with dielectric ##k_1## and the other with dielectric ##k_2##
  • if one dielectric is a slab with dimensions ##d\times \frac{l}{2} \times w## and the other again the same and each dielectric slab is next to the other. The two capacitors are in parallel now, each capacitor has now area ##A=\frac{l}{2}\times w##, but distance between the plates ##d## and one is with dielectric ##k_1## and the other with dielectric ##k_2##.
  • the case that each dielectric slab is ##d\times l\times \frac{w}{2}## is similar to the second case.
 

1. What is capacitance?

Capacitance is the ability of a capacitor to store electrical charge. It is measured in farads (F) and is determined by the physical characteristics of the capacitor, such as the distance between the plates and the type of dielectric material used.

2. How does capacitance change when a capacitor has two dielectrics?

When a capacitor has two dielectrics, the overall capacitance is the sum of the individual capacitances for each dielectric. This is because the presence of multiple dielectrics increases the overall electric field between the plates, resulting in a higher capacitance.

3. What is the equation for calculating capacitance for a capacitor with two dielectrics?

The equation for calculating capacitance for a capacitor with two dielectrics is C = (ε₁A/d₁) + (ε₂A/d₂), where C is the total capacitance, ε₁ and ε₂ are the permittivity of the two dielectrics, A is the area of the capacitor plates, and d₁ and d₂ are the distances between the plates and each dielectric, respectively.

4. How does the dielectric constant of each material affect the overall capacitance?

The dielectric constant, also known as the relative permittivity, is a measure of how well a material can store electric charge. The higher the dielectric constant, the greater the capacitance. Therefore, using materials with higher dielectric constants will result in a higher overall capacitance for a capacitor with two dielectrics.

5. Can the two dielectrics in a capacitor have different thicknesses?

Yes, the two dielectrics in a capacitor can have different thicknesses. However, the overall capacitance will still depend on the individual capacitances of each dielectric, as well as their respective permittivities and the area and distance between the plates. The thickness of each dielectric will also affect the electric field strength and the amount of charge that can be stored in the capacitor.

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