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Formula: Plate Capacitor Capacitance   Plate area   Plate distance   Relative permittivity  

Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.
\[ C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d} \] \[ C ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{d} \] \[ A ~=~ \frac{C \, d}{ \varepsilon_0 \, \varepsilon_{\text r} } \] \[ d ~=~ \varepsilon_0 \, \varepsilon_{\text r} \, \frac{A}{C} \] \[ \varepsilon_{\text r} ~=~ \frac{C \, d}{ \varepsilon_0 \, A } \] \[ \varepsilon_0 ~=~ \frac{C \, d}{ \varepsilon_{\text r} \, A } \] Rearrange formula
Plate capacitor

Capacitance

\( C \)
Unit \( \text{F} \)
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 \( \text{m}^2 \)
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 \( \text{m} \)
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 \( \frac{ \text{As} }{ \text{Vm} } \)
Vacuum permittivity is a physical constant that always occurs with electric phenomena. The constant has the following value: \( \varepsilon_0 = 8,854 \cdot 10^{-12} \, \frac{ \text{As} }{ \text{Vm} } \).
Details about the formula

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  • Summary: With this formula you can calculate the capacitance of a plate capacitor if its area A and its distance d are given.
  • This formula was added by FufaeV on .
  • This formula was updated by FufaeV on .
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