# Problem: A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C0.What is the capacitance if an insulator with dielectric constant κ and thickness d/2 is slipped between the electrodes? Assume plate separation is unchanged.Express your answer in terms of the variables d, C0, and κ.C = ?

###### FREE Expert Solution

Equivalent capacitance for capacitors:

$\overline{)\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{e}\mathbf{q}}}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{C}}_{\mathbf{2}}}}$

The capacitance of a parallel plate capacitor:

$\overline{){\mathbf{C}}{\mathbf{=}}\frac{{\mathbf{\epsilon }}_{\mathbf{0}}\mathbf{k}\mathbf{A}}{\mathbf{d}}}$

For a vacuum, k = 1. For other materials, it is greater than 1.

Before inserting a dielectric, the capacitance of the capacitor is

###### Problem Details

A vacuum-insulated parallel-plate capacitor with plate separation d has capacitance C0.

What is the capacitance if an insulator with dielectric constant κ and thickness d/2 is slipped between the electrodes? Assume plate separation is unchanged.

Express your answer in terms of the variables d, C0, and κ.
C = ?