parallel plate capacitor-12 CBSE- simple to understand
What is a parallel plate Capacitor?
A parallel plate capacitor is the simplest form of the capacitor which is obtained by pairing of two metallic plates, of equal area A and separated by a small distance between them. The space between the plates may be an air space, vacuum or may have inserted with a slab of dielectrics or conducting material as the case may be as per our need.
Capacitance of a parallel plate capacitor with the air or vacuum between the plates
Consider a parallel plate capacitor having two metallic plates P and Q, each plate has an area A, separated by a distance d, such that the distance between the electric field is very mall as compared to the area of each plate (d <<< A), and air/vacuum is put in between the plates. As the separation between the plates is small, so the fringing of the electric field is negligible at the boundaries.
Let us suppose that a source of steady emf is connected across the parallel plate capacitor resulting in the accumulation of +q and -q charges on the plates P and Q respectively and V is the potential difference developed between these plates. By definition, the electric field is the negative gradient of potential(E=-dv/dt), therefore the magnitude of the electric field between the plates of the capacitor will be
This equation 05, gives the capacitance of a parallel plate capacitor when its plates are held in air or vacuum, which shows that the capacitance is directly proportional to the area of the plates and is inversely proportional to the distance between the plates of the capacitor.
Effect of dielectric medium on the capacitance of parallel plate capacitor.
Let us suppose that the space between the two plates of the parallel plate capacitor is filled with a dielectric medium of dielectric constant K, then the electric field between the two plates is given by.
This equation is 09. gives us the capacitance of a parallel plate capacitor with the dielectric medium of dielectric constant K placed between its plates. Thus, it is concluded that the capacity of the capacitor increases K times when a dielectric medium of dielectric constant K is inserted between the plates of the capacitor.
The capacitance of a parallel plate capacitor, when a dielectric slab partially fills the space between the plates
Let us consider a parallel plate capacitor, having two metallic plates each of area A and separated by a distance d from each other. The capacitance of this parallel plate capacitor, when there is a vacuum between the two plates is given by.
Let us suppose that when the capacitor is connected to a battery, the electric field of strength Eₒ is produced between the two plates of the capacitor. Further, suppose that when the dielectric slab of thickness t(t<d) is introduced between the two plates of the capacitor as shown in Figure, the electric field Eₒ is reduced to E due to the polarization of the dielectric medium. Now, between the two plates of the capacitor. over a distance of t, the strength of the electric field is E and over the remaining distance, (d – t), the strength of the electric field is Eₒ. If V is the potential difference between the plates of the capacitor, then we can write,
The dielectric constant is always greater than one (K > 1), so the capacitance of the parallel plate capacitor always increases when the dielectric medium is inserted between the plates of a parallel plate capacitor
Capacitance of a parallel plate capacitor, when a conducting slab partially fills the space between the plates.
The capacitance of a parallel plate capacitor having two plates each of area A, separated by a distance of d from each other is given by
Let us suppose that an electric field E0=q/ [(epsilon)0 A] sets up between the plates of the capacitor when it is connected to a battery. When a slab of the conducting material of thickness t (t < d) is inserted between the plates of the capacitor, then we observe that the electric field does not exist inside the conducting slab. Thus, out of the total separation d between the plates of the parallel plate capacitor, the electric field exists only over the distance (d – t). As a result, the potential difference between the plates will be reduced and is given by
Thus, we see that the capacitance of the parallel plate capacitor becomes infinite when the space between the plates is completely filled with the slab of conducting material. In other words, whatsoever amount of energy is delivered to the plate P of the capacitor, it will accept it. The reason is that when the conducting slab, completely fills, the space between the two plates, plate P also gets connected to the earth.
As such, when charge is delivered to the plate P, it simply flows to the earth through the plate Q which already earth connected. The Observer will see as if the capacitance of the capacitor has become infinite.
Energy Stored in a Charged Parallel Plate Capacitor
Consider an electric circuit in which a parallel plate capacitor is connected to a battery. When the key K is pressed, the charge stars accumulate on the plates of the capacitor and it is said to start charging the work done by the battery in the process of charging the capacitor. As the Capacitor charges, the potential difference across its plates increases, and more and more work has to be done by the battery in delivering the same amount of charge to the capacitor due to the continuously increasing potential difference across its plates.
The work done in charging a capacitor is stored in the form of electric energy. Let us suppose that a parallel plate capacitor of capacitance C initially does not have any charge. When the key K in the circuit is closed, the battery starts charging it. If at any time t,
the plates are charged to value q and the potential difference between the plates is V, then,
q = C V
The small amount of work done by the battery, in further charging the capacitor through an infinitesimal charge dq in the light of the definition of potential difference will be
Therefore, the eqns. 16, 17, and 18 are the required equations of the energy stored with in the capacitor.