A parallel plate capacitor is made of two dielectric blocks in series. One of the blocks has ghickness `d_(1)` and dielectric constant `K_(1)` and the other has thickness `d_(2)` and dielectric constant `K_(2)` as shown in figure. This arrangement can be thought as a dielectric slab of thickness `d(=d_(1)+d_(2))` and effective dielectric constant K. The is

Options

A. `(K_(1)d_(1)+K_(2)d_(2))/(K_(1)+K_(2))`
B. `(K_(1)K_(2)(d_(1)+d_(2)))/((K_(1)d_(2)+K_(2)d_(1)))`
C. `(2K_(1)K_(2))/(K_(1)K_(2))`
D. `(K_(1)d_(1)+K_(2)d_(2))/(K_(1)+K_(3))`

Answer

C

Explanation

`(1)/(C)=(1)/(C_(1))+(1)/(C_(2)) or C=(C_(1)C_(2))/(C_(1)+C_(2))=((k_(1)epsi_(0)A)/(d_(1))(K_(2)epsi_(0)A)/(d_(2)))/((k_(1)epsi_(0)A)/(d_(1))+(K_(2)epsi_(0)A)/(d_(2)))=(K_(1)K_(2)epsi_(0)A)/(K_(1)d_(2)+K_(2)d_(1))`.
`C=(Kepsi_(0)A)/(d_(1)+d_(2)) implies K=(K_(1)K_(2)(d_(1)+d_(2)))/(K_(1)d_(2)+K_(2)d_(1))`.