Topic # 12.14 : Capacitance of parallel plate capacito | Dielectric Constant | Prove that C=A𝜖o/d

The capacitance of a parallel plate capacitor is influenced by the medium between its plates. When there is no medium (i.e., vacuum or air) between the plates, the capacitance 𝐶 is given by the formula 𝐶=𝜖o𝐴/𝑑, where 𝜖o is the permittivity of free space, 𝐴 is the area of one plate, and 𝑑 is the separation between the plates. Introducing a dielectric medium between the plates changes this capacitance.
A dielectric material increases the capacitor's capacitance by a factor known as the dielectric constant (𝑘 or 𝜅).
The new capacitance is 𝐶′=𝑘𝜖o𝐴/𝑑. The dielectric constant is a measure of a material's ability to store electrical energy in an electric field compared to a vacuum.
Thus, inserting a dielectric medium enhances the capacitor’s ability to store charge, effectively increasing its capacitance by reducing the electric field strength between the plates for the same charge stored.
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