Parallel Plate Capacitor Capacitance Calculator

Formula

The formula to calculate the capacitance of a parallel plate capacitor is:

$C = \frac{\varepsilon_0 \varepsilon_r A}{l}$

Where:

$C$ is the capacitance in farads (F)
$\varepsilon_0$ is the permittivity of free space ( $8.85 \times 10^{-12} \, \text{F/m}$ )
$\varepsilon_r$ is the relative permittivity (dielectric constant) of the material
$A$ is the area of one of the plates in square meters ( $m^2$ )
$l$ is the separation between the plates in meters ( $m$ )

What is Capacitance?

Capacitance is a measure of a capacitor's ability to store charge. It depends on the physical characteristics of the capacitor, such as the surface area of the plates, the distance between them, and the dielectric material between the plates. Capacitors are widely used in electronic circuits for various purposes, including filtering, energy storage, and signal coupling.

Example Calculation

Let's assume the following values:

Plate Area ( $A$ ): 200 cm $^2$
Plate Separation ( $l$ ): 2 mm
Dielectric Material: Aluminum Oxide ( $\varepsilon_r = 6$ )

Step 1: Convert the area from cm $^2$ to m $^2$ :

$A = 200 \times 10^{-4} = 0.02 \text{ m}^2$

Step 2: Convert the separation from mm to m:

$l = 2 \times 10^{-3} = 0.002 \text{ m}$

Step 3: Calculate the capacitance:

$C = \frac{8.85 \times 10^{-12} \times 6 \times 0.02}{0.002} = 5.31 \times 10^{-10} \text{ F}$

Convert to microfarads:

$C = 5.31 \times 10^{-10} \text{ F} \times 10^6 = 0.531 \text{ µF}$