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 V_{A} = Electric potential of plate A and V_{B} = Electric potential of plate B.
To calculate the potential difference across the capacitor, we find the potential difference between its two plates i.e. V_{A} – V_{B}.
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 = ε_{o}K. So, the above formula can be written as-
OR
where-
- C = Capacitance of parallel parallel capacitor with a dielectric
- C_{o} = Capacitance of an air-filled parallel plate capacitor
Important NoteOn 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.