Parallel Plate Capacitor | Formula

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Capacitor-

 

Before you go through this article, make sure that you have gone through the previous article on Introduction to Capacitor.

 

We have learnt-

  • A capacitor is an arrangement of two conductors of any shape separated by a non-conducting medium.
  • Generally, capacitors are named on the basis of the shape of the conductors used.
  • The capacitance of a capacitor is given by the formula-

 

 

where-

  • Q = Magnitude of charge on either conductor
  • V = Potential difference between the two conductors

 

In this article, we will learn about the parallel plate capacitor.

 

Parallel Plate Capacitor-

 

A parallel plate capacitor is an arrangement of two equally and oppositely charged plates of equal area separated by a certain distance through a dielectric.

 

Capacitance of Air Filled Parallel Plate Capacitor-

 

Let us consider a parallel plate capacitor having-

  • Q = Magnitude of charge on each plate
  • A = Area of each plate
  • d = distance between its two plates
  • Air as dielectric between its two plates

 

 

Now, we wish to find the capacitance of an air filled parallel plate capacitor.

 

Step-01: Calculating the Potential difference Across Capacitor (V)-

 

We know,

  • A uniform electric field exists between the two plates of capacitor.
  • If σ is the surface charge density of each plate, then electric field between the two plates (in free space) is given by-

 

(Equation-01)

 

Also Read- Electric Field Due To Plane Sheet of Charge

 

Let VA = Electric potential of plate A and VB = Electric potential of plate B.

To calculate the potential difference across the capacitor, we find the potential difference between its two plates i.e. VA – VB.

 

We travel from plate A to plate B and write the changes in electric potential. Then, we have-

 

(Equation-02)

 

Step-02: Calculating the Capacitance of Capacitor (C)-

 

We know, the capacitance of a capacitor is given by the formula-

 

 

Substituting equation-02, we get-

 

 

Thus, the capacitance of an air-filled parallel plate capacitor is given by the formula-

 

 

If a dielectric of permittivity ε completely occupies the space between the plates of capacitor, then capacitance is given by the formula-

 

 

If K = dielectric constant of the dielectric, then ε = εoK. So, the above formula can be written as-

 

OR

 

where-

  • C = Capacitance of parallel parallel capacitor with a dielectric
  • Co = Capacitance of an air-filled parallel plate capacitor

 

Important Note

On introducing a dielectric between the plates of capacitor, its capacitance increases to K times

where K = dielectric constant of the dielectric.

 

Factors Affecting Capacitance of Parallel Plate Capacitor-

 

The capacitance of a parallel plate capacitor depends on the following factors-

  • Area of the plates of capacitor
  • the distance between the plates of the capacitor
  • the nature of the dielectric medium or insulator between the plates of the capacitor

 

Read the next article on-

Parallel Plate Capacitor Partially Filled With Dielectric

 

Get more notes & other study material of the Chapter Electrostatic Potential & Capacitance.


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