For changing the capacitance of a given paralle plate capacitor, a dielectric material of dielectric…

For changing the capacitance of a given paralle plate capacitor, a dielectric material of dielectric constant K is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is 34d, where d is the separation between the plates of parallel plate capacitor. The new capacitance C' in terms of original capacitance C0 is given by the following relation :
  1. C'=3+K4KC0
  2. C'=4+K3C0
  3. C'=4K K+3C0
  4. C'=43+KC0

Solution

C0=ϵ0A d

C'=C1 and C2 in series.

i.e. 1C'=1C1+1C2

1C'=3d/4ϵ0KA+d/4ϵ0 A

1C'=d4ϵ0A3+KK

C'=4KC03+K

Asked in: JEE Main 2021 (16 Mar Shift 1)

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