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A parallel plate capacitor has plate are...

A parallel plate capacitor has plate area of A separated by distance between them. It is completely filled with dielectric medium, its dielectric constant increases linearly as move from one plate to other plate from `k_(1)` to `k_(2)` . Then the capacitance of system is given by :

A

`(3epsilon_(0)A(k_2-k_1))/(llog_(e)(k_2/k_1))`

B

`(2epsilon_(0)A(k_2-k_1))/(llog_(e)(k_2/k_1))`

C

`(epsilon_(0)A(k_2-k_1))/(llog_(e)(k_2/k_1))`

D

`(epsilon_(0)A(k_2-k_1))/(2llog_(e)(k_2/k_1))`

Text Solution

Verified by Experts

The correct Answer is:
C
`dC=(kepsi_(0)A)/(dx)`
`k=alphax+beta`
At `x=0," "k_(1)=beta`

At `x=l," "k_(2)=alphal+k_(1)`
`k_(2)-k_(1)=alphal," "alpha=(k_(2)-k_(1))/(l)`
`k_(2)-k_(1)=alphal," "alpha=(k_(2)-k_(1))/(l)`
`k=k_(1)+((k_(2)-k_(1))/(l))x," "dc=(epsi_(0)[k_(1)+((k_(2)-k_(1))/(l))x]A)/(dx)`
`(1)/(c)=int(1)/(dC)" "," "(1)/(C)=int_(0)^(l)(dx)/(epsi_(0)[k_(1)+((k_(2)-k_(1))/(l))x]A),C=(epsi_(0)A(k_(2)-k_(1)))/(l log_(e)((k_(2))/(k_(1))))`
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