# What is the capacity of the capacitor?

1. Jun 22, 2013

### tsgkl

1. The problem statement, all variables and given/known data
The space between the plates of a parallel plate capacitor is filled consecutively with two dielectric layers of thickness d1 and d2 respectively.If A is the area of each plate,what is the capacity of the capacitor?

2. Relevant equations
C=$\frac{εA}{d}$
(for parallel plate capacitor with air as dielectric)

3. The attempt at a solution
i honestly don't know how to attempt this question...can anyone give me some clues.....
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jun 22, 2013

### Staff: Mentor

Were you given the relative permittivity for each dielectric material?

Hint: Dielectric layers which parallel the plates of the capacitor will effectively behave like capacitors in their own right, carving the original space into a set of capacitors in series. The surface boundaries between materials are the locations of the "plates" of these capacitors. Dielectric surfaces in contact with the conductive plates of the capacitor are considered to be a single plate of one such capacitor (consider the plate to be the electrical contact of that sub-capacitor).

3. Jun 22, 2013

### tsgkl

nope, relative permittivity for each material ain't given.......

4. Jun 22, 2013

### Staff: Mentor

Then you'll have to create your own variable names for them. No big deal since numerical values for the thicknesses and area weren't given either, so a symbolic result is expected.

5. Jun 22, 2013

### tsgkl

just tell me one thing is effective thickness of dielectric 1/ε the actual thickness?

6. Jun 22, 2013

### Staff: Mentor

d1 and d2 are the actual thicknesses. I suppose one could consider the effective thicknesses to be $\frac{1}{ε_1}d_1$ and $\frac{1}{ε_2}d_3$, where ε1 and ε2 are the relative permittivities. Although it is more usual to see the effective permittivity specified as εεo and the distances left alone.

7. Jun 22, 2013

### tsgkl

as you said the effective thickness to be d11 and d22 so the answer should be εA/d11+d22

8. Jun 23, 2013

### Staff: Mentor

You should use parentheses in your expressions to disambiguate the order of operations. Even so, your expression doesn't have the right form.

How do capacitors in series add?

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