A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates.
A sheet having thickness ( 1 ─── 3 )rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

Question

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates.

A sheet having thickness ( 1 ─── 3 )rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

G1 Physics · Accepted Answer

Initially, C = ε₀A ──── d . The dielectric sheet occupies thickness d ─── 3 , while the remaining vacuum thickness is 2d ─── 3 . These two portions behave like capacitors in series. For the vacuum portion, C₁ = 3ε₀A ───── 2d = 3C ─── 2 . For the dielectric portion, C₂ = 3Kε₀A ────── d = 3KC. The equivalent capacitance is C₍eq₎ = C₁C₂ ────────── C₁ + C₂ . Now, C₁C₂ = 9KC² ───── 2 , and C₁+C₂ = 3C(2K + 1) ────────── 2 . Therefore, C₍eq₎ = 9KC² ─────────── 3C(2K + 1) = 3KC ─────── 2K + 1. Correct…