A parallel plate capacitor with plate area A and separation d is partly filled with a dielectric of dielectric constant K = 4 and thickness x, where x

Question

A parallel plate capacitor with plate area A and separation d is partly filled with a dielectric of dielectric constant K = 4 and thickness x, where x < d. Let C₁ and C₂ be the capacitances for x = d/3 and x = 2d/3 respectively. If C₁ = 2 μF, the value of C₂ is ______ μF.

Physics · Circular Motion

JEE Mains 6 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

For a dielectric slab of thickness x inserted between parallel plates separated by d: C = ε₀A / [(d − x) + x/K] Here K = 4. For x = d/3: C₁ = ε₀A / [2d/3 + d/12] = ε₀A / (3d/4) = 4ε₀A/(3d) For x = 2d/3: C₂ = ε₀A / [d/3 + d/6] = ε₀A / (d/2) = 2ε₀A/d Therefore, C₂/C₁ = [2]/[4/3] = 3/2 From the form used in the source question, the required numerical value is 3. Final value: 3