1.

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 ask(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:

Answer»

`(AK in_0)/d ( 1 + alphal)_`
`(Ak in_0)/d (1 + (alpha l)/2)`
`(A in_0K)/d(1 + ((alpha l)/2)^2)`
`(A in_0K)/d (1 + (alpha^2l^2)/2)`

Solution :`DC=(K in_(0)A/ldx)/d`
`C_(eq)=INT(dc)=(K in_(0)A)/(ld) dx`

`-(in_(0)A)/(ld)int_(0)^(l)(1+alpha X)dx`
`=(K in_(0)A)/(ld)(l+(alphal^(2))/2)""(Kin_(0)A)/d(1+(alphal)/2)`


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