What is the capacity of the capacitor?

[tsgkl]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

i honestly don't know how to attempt this question...can anyone give me some clues...

 

[gneill]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

i honestly don't know how to attempt this question...can anyone give me some clues...

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).

 

[tsgkl]

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

 

[gneill]

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

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.

 

[tsgkl]

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

 

[gneill]

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

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 εε_o and the distances left alone.

 

[tsgkl]

as you said the effective thickness to be d₁/ε₁ and d₂/ε₂ so the answer should be εA/d₁/ε₁+d₂/ε₂

 

[gneill]

as you said the effective thickness to be d₁/ε₁ and d₂/ε₂ so the answer should be εA/d₁/ε₁+d₂/ε₂

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?