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Formula: **Plate Capacitor**

$$C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d}$$
$$C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d}$$
$$A ~=~ \frac{C \, d}{ \varepsilon_0 \, \varepsilon_{\text r} }$$
$$d ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{C}$$
$$\varepsilon_{\text r} ~=~ \frac{C \, d}{ \varepsilon_0 \, A }$$
$$\varepsilon_0 ~=~ \frac{C \, d}{ \varepsilon_{\text r} \, A }$$

## Capacitance

`$$ C $$`Unit

`$$ \mathrm{F} $$`

Capacitance is a measure of how much charge the plate capacitor can "store".

As can be seen from the formula, the capacitance depends only on the geometry of the plate capacitor, i.e. only on the plate area \(A\) and the distance \(d\) between the plates.

## Plate area

`$$ A $$`Unit

`$$ \mathrm{m}^2 $$`

Plate area is the area of one side of the capacitor plate. For a rectangular plate, \(A\) is the area of a rectangle: \(A = a \, b \). For a circular electrode, \(A\) is the area of a circle: \(A = \pi \, r^2 \).

The larger the plate area, the greater the capacitance of the plate capacitor.

## Plate distance

`$$ d $$`Unit

`$$ \mathrm{m} $$`

Distance between the two capacitor plates. The closer the plates are to each other, the greater the capacitance of the plate capacitor.

## Relative permittivity

`$$ \varepsilon_{\text r} $$`Unit

`$$ - $$`

Relative permittivity is a dimensionless number that describes the dielectric (e.g. air, water, glass) between the two capacitor plates.This number indicates how well the dielectric transmits the electric field between the plates.

In a vacuum the relative permittivity has the value \( \varepsilon_{\text r} = 1 \). Water at room temperature: \( \varepsilon_{\text r} \approx 1.77 \). Glass: \( \varepsilon_{\text r} \approx 7 \). Consequently, a dielectric which allows the E-field to pass through less well (relative permittivity is high) increases the capacitance of the plate capacitor.

## Vacuum Permittivity

`$$ \varepsilon_0 $$`Unit

`$$ \frac{\mathrm{Vs}}{\mathrm{Am}} $$`

The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value:

`$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$`