In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be :
(Given area of plate = A)

Solution

Physics sir · 3 steps

The slabs sit one after another between the plates, so treat them as three capacitors in series.

1. Spot the arrangement. Each slab fills the full plate area A, and the slabs are stacked along the gap. The same charge passes through all three, so they act as capacitors in series.
2. Each capacitor. For a slab of thickness t and constant Kᵢ, C = (Kᵢ ε₀ A)/t. That gives C₁ = (Kε₀ A)/d, C₂ = (3Kε₀ A)/2d and C₃ = (5Kε₀ A)/3d.

   1/C = d/(Kε₀ A)(1 + 2/3 + 3/5) = d/(Kε₀ A)×(15 + 10 + 9)/15 = 34/15 d/(Kε₀ A)

3. So. Taking the reciprocal, C = 15/34 (Kε₀ A)/d, which is option (a).

The idea to keep. Slabs stacked across the gap are in series: add tᵢ/Kᵢ. Slabs placed side by side, each sharing part of the area, are in parallel: add Kᵢ Aᵢ.

Answer from the NTA final answer key. Solution by PrepWiser.