PRINCIPLE OF A CAPACITOR
A capacitor is a device for storing a large quantity of electric charge.
A conduct can store a small amount of charge and hence it possesses a small capacitance . To store a large amount of charge, two or more conductors are arranged to form a capacitor . Thus, a capacitor possesses a large capacitance to store charge and that too in a small space.
To understand the principle of a capacitor, consider an insulated metal plate A. Suppose that it is given positive charge, till its potential becomes maximum. The metal plate will not hold any more charge over it . If charge is given to the metal plate A, it will leak to the surroundings . Now , place another metallic plate B near plate A. Due to the induction, negative charge will be induced on the nearer face of plate B and positive charge on its farther face . The potential of plate A gets lowered due to induced negative charge on plate B and a bit raised due to the induced positive charge. Since the metal plates have finite thickness , induced negative charge is nearer to the plate A than the induced positive charge on plate B is.Therefore,on the whole,the potential of plate A gets lowered,though by a very small amount.In order to make the potential of the metal plate A again the same,an additional small amount of charge has to be given to plate A.It indicates that the capacitance of a conductor increases by a small amount,when another uncharged conductor is placed near it.
Now,connect the metal plate B to the earth.The induced positive charge on plate B will immediately flow to the earth as it is repelled by positive charge on plate A.However,the induced negative charge on plate B will stay on it.It does not flow to earth as it is attracted by the positive charge on plate A.Thus,the metal plate B will have only negative charge on it after being connected to earth.Due to induced negative charge on plate B,the potential of plate A will get lowered by a large amount.In order to raise the metal plate A again to the same potential,a large amount of charge has to be given to it.Thus,it follows that the capacitance if a conductor gets increased greatly,when an earth connected conductor is placed near it.It forms the principle of a capacitor and such an arrangement of two metal plates is called a capacitor.
An arrangement of two metallic conductor,so that when one conductor is connected to the earth;the other conductor has the ability to store a large amount of charge on it,is called a capacitor.
The two metallic conductors are called coatings of the capacitor.If the coatings are plane,spherical or cylindrical ;the capacitor is accordingly called a parallel plate capacitor,spherical capacitor or cylindrical capacitor.
The insulating medium between two plates is called dielectric.If the insulating medium between the two plates is air,it is called air capacitor.If dielectric has dielectric constant K,the capacitance of the capacitor becomes K times its capacitance as air capacitor.
PRINCIPLE OF A CAPACITOR
PARALLEL PLATE CAPACITOR:
It is most commonly used capacitor . It consists of two conducting plates placed parallel to each other. The separation between the plates is very small as compared to the area of the plates. Due to small separation between the plates, the fringing of electric field at the boundaries is negligible.
If the charge + q is given to the first plate , then the charge – q is induced on the face second plate and charge + q on its right face flows to the earth. Due to charge + q on first plate and – q on second plate, electric field is set up between the two plates.
The electric field between the two plates is related to the potential gradient as
E. = dV/ dr. ( In magnitude) .
Between the two parallel plates , the electric field is uniform and perpendicular to the plates . Therefore , if V is potential difference between the two plates, then
E. = V/d
Or V = Ed
If ∆ is surface charge density of the plates , then the electric field between the two plates is given by
E. = ∆/€°
Where €° is absolute permittivity of the free space. ( It is assumed that medium between the plates is vacuum or air ).
Here in the obtained equation, substituting for E, we have
V= ∆d/ ¢°
If A is the area of each plate , then
∆ = q/A
If C is the capacitance of the parallel plate capacitor, then
C = q/ qd/€°A
It gives the capacitance of a parallel plate capacitor when it’s plates are held in air or vacuum.
PRINCIPLE OF A CONDUCTOR.