Calculating capacitance of capacitor filled with 2 dielectrics

In summary, the conversation discusses the formation of a capacitor using two square metal plates separated by a distance d and filled with dielectrics of different dielectric constants. The individual attempted solutions involve integrating the parallel combination of elemental capacitors and taking them in series, with the second approach resulting in a correct answer. The individual asks for help in identifying the flaw in their initial approach and seeks opinions and assistance from others.
  • #1
darkv0id
3
0

Homework Statement



A capacitor is formed by 2 square metal plates of edge a and separated by distance d. Dielectrics of dielectrics constants K1 and K2 are filled in the gap as shown.

capacitor1.jpg


2. The attempt at a solution

This was my initial approach:

capacitor.jpg


I integrated the parallel combination of elemental capacitors dC1 and dC2, but I didnt get the correct answer.

Next, I tried taking the elemental capacitors in series instead of parallel:

Untitled.png


This time my answer turned out to be correct.:smile:

Can someone help me identify the flaw in my initial approach? I suspect I was wrong in assuming that the elemental capacitors were in parallel in the first place.

Opinions?
 
Last edited:
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  • #2
Anyone ?
 
  • #3
No one?:frown:

Please, can anyone help me out?
 

Related to Calculating capacitance of capacitor filled with 2 dielectrics

1. How do you calculate the total capacitance of a capacitor filled with two dielectrics?

To calculate the total capacitance of a capacitor filled with two dielectrics, you can use the formula C = C1 + C2, where C1 and C2 are the capacitances of each dielectric. Alternatively, you can use the formula C = (A * ε1 * ε2) / (d1 + d2), where A is the area of the capacitor plates, ε1 and ε2 are the permittivities of the two dielectrics, and d1 and d2 are the distances between the plates and each dielectric.

2. How does the presence of two dielectrics affect the capacitance of a capacitor?

The presence of two dielectrics in a capacitor increases the total capacitance compared to a capacitor with only one dielectric. This is because the permittivity of the dielectrics affects the electric field and allows for more charge to be stored on the plates. The specific effect on capacitance will depend on the values of the permittivities and distances involved.

3. What factors affect the capacitance of a capacitor filled with two dielectrics?

The factors that affect the capacitance of a capacitor filled with two dielectrics include the permittivities of the two dielectrics, the distance between the plates and each dielectric, and the area of the capacitor plates. The type of material the dielectrics are made of can also affect the capacitance.

4. Can the total capacitance of a capacitor filled with two dielectrics ever be less than the capacitance of either individual dielectric alone?

No, the total capacitance of a capacitor filled with two dielectrics will always be greater than the capacitance of either individual dielectric alone. This is because the presence of the two dielectrics increases the overall capacitance of the capacitor due to their permittivities and distance from the plates.

5. How does the arrangement of the two dielectrics inside the capacitor affect the capacitance?

The arrangement of the two dielectrics inside the capacitor does not have a direct effect on the capacitance. However, the distance between the two dielectrics and the plates can affect the overall capacitance, as well as the orientation or thickness of the dielectrics. It is important to consider these factors when calculating the total capacitance of a capacitor filled with two dielectrics.

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