Question

A parallel-plate capacitor with plate separation d has a capacitance C₁. Find its new capacitance when an isolated metal slab of thickness p is placed between the plates.

a) C₂ = C₁ + pd
b) C₂ = C₁ - pd
c) C₂ = C₁ / p
d) C₂ = C₁ * p

Answer 1

The new capacitance C₂ can be calculated using the formula C₂ = C₁ * (d/(d+p)), where C₁ is the initial capacitance of the capacitor and d is the original plate separation. The presence of the dielectric material reduces the electric field between the plates, resulting in a smaller capacitance for the capacitor.

Step-by-step explanation:

The capacitance of a parallel-plate capacitor depends on the area of the plates and the distance between them. For a parallel-plate capacitor filled with a dielectric material of thickness p, the new capacitance C₂ can be calculated using the formula:

C₂ = C₁ * (d/(d+p))

where C₁ is the initial capacitance of the capacitor and d is the original plate separation. The new capacitance will be smaller than the initial capacitance because the presence of the dielectric material reduces the electric field between the plates, resulting in a decreased capacitance.