Question

Define parallel palte capacitor. Explain its construction and working principle of parallel plate capacitor. Derive an expression for its capacitance ?

Answer 1

PARALLEL PLATE CAPACITOR (PPC)— An arrangement of two plates one plate is positive and other plate is negative placed parallely separated by dielectrics to store large amount of electric charge in small space is called parallel plate capacitor. It is the simplest form of any kind of capacitor.

PRINCIPLE—It works on the principle that electric change stored on the plate is directly proportional to the potential difference between two plates.

CONSTRUCTION:—

Expression For Capacitance—

Let us consider two plates A and B having equal Area separated by a small distance. The surface change density of plate is ‘σ’

As we know that electric field is negative gradient of potential.

:.  E  = –dv/dr  …(3)

Taking magnitude only. 

E = dv/dr  …(4)

If electric field is uniform

dv = V

dr = r = d  …(5)

E  = V/d …(6)

V = Ed 

Now, calculation of electric field,

E = E₁ + E₂   .....(7)

Where, E₁ is electric field of +ve plate.

E₂ is electric of –ve plate.

Eqⁿ —(12) is the general expression for capacitance of a parallel plate capacitor.

Conclusion—Capacitance of a parallel plate capacitor is

 (i) Directly proportional to the area of the plate. 

(ii) Inversly proportional to the distance between the plates.