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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 dielectric constant that varies as `K (y) = k _(0) (1+ alpha y)` where ‘y’ is the vertical distance measured from base of the plates. The total capacitance of the system is best given by: `(K _(0)` is constant)

A

`(A in _(0) K _(0))/(d) (1+ (alpha ^(2) l ^(2))/(2 ))`

B

`(Ain _(0) E _(0))/(d ) (1 + alpha l )`

C

`(Ain _(0) K _(0))/(d ) (1 + (2 l ^(2))/(4))`

D

`(A in _(0) K _(0))/(d ) (1 + (alpha l )/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
All dC’s are in parallel.

`C = int dC, " " dC = ( in _(0) bdyK)/(d)`
`thereforeC = (in _(0)bK _(0))/(d) int _(0)^(l) (1+ alpha y) dy = (in _(0) bK_(0)l )/(d) (1+ (alphal)/(2))`
`C = (A in _(0) K _(0))/(d ) (1+ (alpha l )/(2))`
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