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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

`(AK in_0)/d ( 1 + alphal)_`

B

`(Ak in_0)/d (1 + (alpha l)/2)`

C

`(A in_0K)/d(1 + ((alpha l)/2)^2)`

D

`(A in_0K)/d (1 + (alpha^2l^2)/2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`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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