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A paralled plate capacitor is made of tw...

A paralled plate capacitor is made of two square plates of side 'a' , separated by a distance d (dltlta). The lower triangular portion is filled with a dielecttic of dielectric constant K, as shown in the figure. Capacitance of this Capacitor is :

A

`(Kepsilon_(0)a^(2))/(2d(K+1))`

B

`(Kepsilon_(0)a^(2))/(d)lnK`

C

`(Kepsilon_(0)a^(2))/(d(K-1))lnK`

D

`(1)/(2)(Kepsilon_(0)a^(2))/(d)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let.s consider a strip of thickness dx at a distance of x from the left end as shown in the figure.
`(y)/(x)=(d)/(a)impliesy=((d)/(a))x`

`C_(1)=(epsilon_(0)adx)/((d-y)),C_(2)=(Kepsilon_(0)adx)/(y)`
`C_(1)=(epsilon_(0)adx)/((d-y)),C_(2)=(Kepsilon_(0)adx)/(y)`
Now integrating it from 0 to a
`underset(0)overset(a)int(Kepsilon_(0)adx)/(Kd+(1-K)(d)/(a)x)=(Kepsilon_(0)a^(2)lnK)/(d(K-1))`
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