A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance Co. Now one-third of the material is replaced by another material with dielectric constant 2K , so that effectively there are two capacitors one with area 1/3 A , dielectric constant 2K and another with K. if the capacitance of this new capacitor is C then C/ Co is?

Question

A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance Co. Now one-third of the material is replaced by another material with dielectric constant 2K , so that effectively there are two capacitors one with area 1/3 A , dielectric constant 2K and another with K. if the capacitance of this new capacitor is C then  C/ Co is?

priyar · Answer

In this Q.. they haven't specified what the arrangement is like.. that is whether the dielectrics are vertical or horizontal.. only then we can proceed right? i know how to solve this... but i am confused whether to assume parallel or series..

priyar · Answer

@ganeshie8 @mayankdevnani

priyar · Answer

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ganeshie8 · Answer

is the answer 8/3 ?

priyar · Answer

no..

ganeshie8 · Answer

4/3 perhaps ?

ganeshie8 · Answer

Btw, it doesn't matter where you put the new dielectric... 

all arrangements give you the same capacitance

priyar · Answer

yes i know what you did..! you found out for both series and parallel..! 4/3 is correct.. but how to decide first..?

ganeshie8 · Answer

you just pick the arrangement that is easy to sovle

priyar · Answer

how will both arrangement give the same answer?

ganeshie8 · Answer

It says 1/3rd of the material is replaced by the new dielectric

ganeshie8 · Answer

This means, 1/3rd of the volume is replaced by the new dielectric, yes ?

priyar · Answer

yes

priyar · Answer

oops ! they have given its parallel combo indirectly.. the areas are different.. so its the second arrangement! thanks

ganeshie8 · Answer

Then it says, ` so that effectively there are two capacitors one with area 1/3 A`

This clearly means a parallel arangement

ganeshie8 · Answer

yeah, but the answer would be same no matter what the arrangement is

priyar · Answer

how is that?

ganeshie8 · Answer

because the energy stored in a capacitor depends on the "volume" between the plates

ganeshie8 · Answer

heard of "energy density" before ?

priyar · Answer

yeah!

ganeshie8 · Answer

Energy stored  = $\frac{1}{2}\epsilon E^2 V $


here V is the volume between the plates
electric field is constant in the region between the plates, so the energy stored increases linearly with the volume

priyar · Answer

yes..

ganeshie8 · Answer

maybe lets work it in series arrangement and see if we get the same answer

priyar · Answer

it can't be series as "A" is different

ganeshie8 · Answer

just read the first part of the problem

ganeshie8 · Answer

`A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance Co. Now one-third of the material is replaced by another material with dielectric constant 2K , `

ganeshie8 · Answer

I am saying that the new capacitance would be same no matter where you insert the new dielectric

priyar · Answer

oh ok.. ya 1/3(Ad) in both cases..

ganeshie8 · Answer

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