# Capacitance - Dielectric Constant Relation?

1. Sep 28, 2008

### Apteronotus

Hi,

Does anyone know if there is a relation between a materials capacitance (C) and its dielectric constant (K)?

Thanks,

2. Sep 28, 2008

### Apteronotus

So I think I may have figured it out, and for people reading the post here is my attempt at the answer:
$$K_{e}=1+\chi_{e}=1+\frac{\epsilon-\epsilon_{0}}{\epsilon_{0}}=1+\frac{\epsilon_{r}\epsilon_{0}-\epsilon_{0}}{\epsilon_{0}}=1+\epsilon_{r}-1=\epsilon_{r}$$
$$\epsilon_{r}=\frac{C_{x}}{C_{0}}$$
So
$$K_{e}=\frac{C_{x}}{C_{0}}$$

where

$$K_{e}$$ - dielectric constant
$$\chi_{e}$$ - electric susceptibility
$$\epsilon$$ - permittivity of the dielectric material
$$\epsilon_{r}$$ - relative permittivity
$$\epsilon_{0}$$ - permittivity of free space
$$C_{x}$$ - capacitance of the dielectric material
$$C_{0}$$ - capacitance of vacuum

Please feel free to correct me.