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CBSE Class 12-science Answered

Derive an expression for the capacitance of parallel plate capacitor how can its capacitance be increased  
Asked by akhilesh6476 | 05 Jun, 2018, 01:44: PM
answered-by-expert Expert Answer
 
Let us assume two parallel plates of area A are kept so that their separation distance is d.
One plate is positively charged and the other is negatively charged. 
This charging can be done by connecting the parallel plates across the terminals of battery.
Let σ be the surface charge density. Compare to the dimensions of plate, the separation distance is very small.
With this assumption, we can have electrical field due the charged plate is same as that of infinitely charged plate.
Since the charges on the plate are opposite, electric fields due to each charged plate is in same direction inside
the region between plates as shown in figure.
Hence the net electric field E in the inside region between plates is given by
begin mathsize 12px style E space equals space sigma over epsilon subscript 0 space end style .....................(1)
where ε0 is the permitivity of free space. But we have E = V/d , where V is potential difference between plates.
Also σ = Q/A , where Q is the magnatiude of total charge on each plates.
Using these relations Eqn.(1) is rewritten as
begin mathsize 12px style V over d equals space fraction numerator begin display style bevelled Q over A end style over denominator epsilon subscript 0 end fraction space equals space fraction numerator Q over denominator A epsilon subscript 0 end fraction space........................... left parenthesis 2 right parenthesis b u t space w e space h a v e space b y space d e f i n i t i o n space o f space c a p a c i tan c e comma space C space equals space Q over V U sin g space e q n. left parenthesis 2 right parenthesis comma space w e space c a n space w w r i t e space C equals space Q over V equals space fraction numerator A epsilon subscript 0 over denominator d end fraction end style
----------------------------------
Capacitance of capacitor is increaed by having dielectric materials between parallel plates.
If K is the dielectric constant of dielectric material present betwenn parallel plates,
then the capacitance of capacitor becomes K times of capacitance of paralle plate capacitor without dieletric material
Answered by Thiyagarajan K | 05 Jun, 2018, 04:41: PM

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