Q69 / 90 · JEE Main 2022 (28 Jul Shift 2) · Physics

A slab of dielectric constant K has the same crosssectional area as the plates of a parallel plate capacitor and thickness 34d, where d is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be :
(Given C0= capacitance of capacitor with air as medium between plates.)

  • Correct answer
    A
    4KC03+K
  • B
    3KC03+K
  • C
    3+K4KC0
  • D
    K4+K

Solution

Figure

From the above diagram, we can write,

x+y+3d4=d

x+y=d4

Initially, when there is no dielectric inserted between the plates the capacitance will be, C0=ϵ0A d.

When the dielectric slab is inserted, we can assume there are 3 capacitors that are connected in series.

C1=ϵ0Ax, C2=4Kϵ0A3d and C3=ϵ0Ay

The equivalent capacitance,

1C=1C1+1C2+1C3⇒1C=1ϵ0Ax+3d4K+y⇒1C=1ϵ0Ad4+3d4K⇒C=4ϵ0AKd3+K⇒C=4KC03+K

Hence, the correct answer is option: 'A'.

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