How Does Capacitance Change with Multiple Dielectric Materials in a Capacitor

[xcutexboax]

Hey Guys,

I was just doing a question on capacitance and i was wondering since capacitance is usually determined by a fixed formula which is dependent on the di electric material that is contained within a capacitor.. However it struck me that a capacitor does not neccesarily contain only one kind of material. How does the expression of the formula changes if a capacitor can contain more than one kind of di-electric materials... pls enlighten me... IS it based on the area they occupy? ThAnks.

 

[freemind]

IIRC, for multiple dielectric capacitors, you would simply use the modification of one of Maxwell's equations, namely: $$V = \int{\kappa\overrightarrow{E} \cdot d\overrightarrow{s}$$. In this case, you integrate over the thickness of one capacitor, then over the thickness of the other capacitor, then add the two results to find the electric potential across the plates.

 

[xcutexboax]

If I was referring to the formula C=k*epsilon*A/d where k is the dielectric constant of the material, how does finding the potential change the above expression? I mean if a capacitor can contain like 3 dielectric materials of different k, how does it affect the above expression/formula? =)

 

[freemind]

If you have a capacitor with two distinct materials as dielectrics in between the plates with dielectric constants $\kappa_1$ & $\kappa_2$ (and assuming you're dealing with a standard, flat parallel plate capacitor here), if the thickness of material one is the same as that of material two (let's say a thickness of $$d$$), then the equivalent capacitance is given by $$C_{eq} = \frac{C_1 C_2}{C_1+C_2}$$, where $$C_1 = \frac{\kappa_1 \epsilon_0 A}{d}$$, and same for $$C_2$$. Of course, in this case, I'm taking the actual plate-distance to be $$2d$$.

 

[xcutexboax]

Oh i finally understand... u took the capacitor like a circuit which contatins other "capacitors". Marvellous... Okie thanks for the tip.