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A parallel plate capacitor has square pl...

A parallel plate capacitor has square 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(y)=K_0(1+betay)` where 'y' is the distance measured from bottom of capacitor. The total capacitance of the system is given by the expression:

A

`(in_0AK_0)/d(1+(betaA)/(2))`

B

`(in_0AK_0)/d(sqrtA+(betasqrtA)/(2))`

C

`(in_0AK_0)/d(1+(betasqrtA)/(2))`

D

`(in_0sqrt(AK_0))/d(sqrtA+(betasqrtA)/(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)))(tay)dy)/(d)`
`therefore C=(sqrt(A)in_(0)K_(0))/(d) Int_(0)^(sqrt(A)) (1+betay)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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