A parallel-plate capacitor of plate area A and separation d is partially filled by a dielectric slab of dielectric constant K = 4 and thickness x, where x

Question

A parallel-plate capacitor of plate area A and separation d is partially filled by a dielectric slab 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, find C₂ is_____ µF.

G1 Physics · Accepted Answer

For dielectric thickness x along the field, C = ε₀A/[d-x+x/K]. For x = d/3, C₁ = 4ε₀A/(3d) = 2 µF. For x = 2d/3, C₂ = 2ε₀A/d. Therefore C₂/C₁ = 3/2 and C₂ = 3 µF.

A parallel-plate capacitor of plate area A and separation d is partially filled by a dielectric slab of dielectric constant K = 4 and thickness x, where x &lt; d. Let C₁ and C₂ be the capacitances for x = d/3 and x = 2d/3 respectively. If C₁ = 2 µF, find C₂ is_____ µF.

A parallel-plate capacitor of plate area A and separation d is partially filled by a dielectric slab 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, find C₂ is_____ µF.