  Question

A dielectric slab of thickness is placed between the plates of a parallel plate capacitor. If the distance between plates is reduced by , the capacity of the capacitor remains the same. Find the dielectric constant of the medium.

A
B
C
D
Medium

Solution Verified by Toppr
Correct option is D)

for a parallel plate capacitor              C = ε K   A / dIt is possible that we have air/vacuum and then a medium in between the parallel plates.  Initially there is a medium of dielectric constant K and of thickness d.    Let  K1 be the dielectric constant of the slab.       let d1 be the thickness of slab = 6cm.Formula for capacity with multiple media in between the plates is              C =  ε A / [ d1/K1 + d2 / K ]          total gap =  d1 + d2 = d + 4 cm          =>  d2 = d + 4 cm - 6 cm = d - 2         d / K =  d1/ K1 + d2 / K          d/ K = 6 / K1  + (d-2)/K          d - (d-2)  = 6 K / K1                 K1 = 3 K  If there was air originally in between the plates,  K = 1,  then answer is 3. 0 0