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A parallel plate capacitor has plates of...

A parallel plate capacitor has plates of area A separated by distance ‘d’ between them. It is filled with a dielectric which has a dielectric constant that varies as `k(x)=K(1+ax)` where ‘x’ is shown in figure. If `(al)lt lt 1` , the total capacitance of the system is best given by the expression:

A

`(in_0 AK_0)/(d) (1 + (betaA)/2)`

B

`(in_0 sqrt(A)K_0)/(d) (sqrt(A) + (betasqrt(A))/2)`

C

`(in_0 AK_0)/(d) (1 + (betasqrt(A))/2)`

D

`(in_0 sqrt(A)K_0)/(d) (1 + (betasqrt(A))/2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`dC = (in_0 (sqrt(A)dy)k(y))/(d) , dC = (sqrt(A) in_0 K_0 (1 + beta y)dy)/d`
`:. C = (sqrt(A) in_0 K_0)/(d) int_0^(sqrtA) (1 + beta y) dy`
`= (sqrt(A) in_0 K_0)/(d) (sqrt(A) + (betaA)/2) implies (in_0 AK_0)/(d) (1 + (betasqrt(A))/(2))`
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