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

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)

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