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Grade: 12th pass
        
A parralek plate capacitor of area A separated by a distance d between them. It is for with a dielectric which has a dielectric constant that varies by as k(x)=k(1+alpha x). Where x is the distance measured from one of the plate. The total capacitance off the system is given by
2 months ago

Answers : (1)

waqar malik
14 Points
							
let ‘d ‘ be the distance between the plates .
at distance x from one plate, E(x)=E(electric field when there is no dielectric)/k(x)
                                                E(x)=E/k(1+alpha x)
Now,   p.d. between the plates V=∫E(x).dx
integrating it carefully within the limit of x from ‘0’ to ‘d’ you will get ,
                                                   V=E.log(1+alpha.d)/k.alpha...........................1
 let C1 be the capacitance without any dielectric,
 then, initial capacitance b/w the plates , C1=Q/E.d...................2
now, final capacitance , C=Q/V=Q.k.alpha/E.log(1+alpha.d)
Hence ,from eqn 1 and 2 it is cleared that
                                       C=C1.d.k.alpha/log(1+alpha.d)
2 months ago
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