# The Parallel Plate Capacitor – Formula, Definition, Derivation

0
108

## What is a Parallel Plate Capacitor?

When two parallel plates are connected across a battery, the plates are charged and an electric field is established between them, and this setup is known as the parallel plate capacitor.

## Parallel Plate Capacitor Formula Where:

• ϵo is the permittivity of space (8.854 × 10−12 F/m)
• k is the relative permittivity of dielectric material
• d is the separation between the plates
• A is the area of plates

## Parallel Plate Capacitor Derivation

• A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. • Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is
• Suppose two plates of the capacitor have equal and opposite charge Q on them. If A is the area of each plate then surface charge density on each plate is • We have already calculated field between two oppositely charged plates using Gauss’s law which is and in this result effects near the edges of the plates have been neglected • Since electric field between the plates is uniform the potential difference between the plates is where d is the separation between the plates.

• Thus, capacitance of parallel plate capacitor in vacuum is • We see that quantity on which capacitance of parallel plate capacitor depends i.e.,ε0 , A and d are all constants for a capacitor.
• Thus we see that in this case capacitance is independent of charge on the capacitor but depends on the area of its plates and separation distance between the plates.