Question

A dielectric slab of thickness $6cm$ is placed between the plates of a parallel plate capacitor. If the distance between plates is reduced by $4cm$, the capacity of the capacitor remains the same. Find the dielectric constant of the medium.

• A. $6$
  
• B. $2$
  
• C. $4$
  
• D. $3$
  

Answer 1

Answer: (D)

for a parallel plate capacitor

C = ε K A / d

It 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.