You must have seen that capacitors would have been installed in many places. Today we are going to see how a capacitor works and what is the principle of a capacitor. After all, why is this capacitor installed and what is its function? Does it store energy or does it do something else? If it stores energy then how does it do that? What are the advantages or disadvantages of storing its energy? If there is an advantage then what and if there is a loss then what? We will discuss some such things but before knowing about the capacitor, know what is it.
So let’s know about the capacitor’s principle or Principle of a capacitor
What is a Capacitor
A capacitor is a device used to store charge or energy without any change in shape and size.
A capacitor is a device that has the capacity or ability to store energy in the form of an electric charge creating a potential difference, which is a constant voltage, much like a small rechargeable battery.
A capacitor is a system of two conductors separated by an insulator. The conductors have charges, say Q1 and Q2, and potentials V1 and V2. Usually, in practice, the two conductors have charges Q and – Q, with potential difference V, = V1 – V2 between them.
Note:
Even one conductor can be used as a capacitor assuming the other to be infinite.
The conductors may be so charged by connecting them to the two terminals of a battery.
The total charge of the capacitor is zero.
The electric field in the region between the conductors is proportional to the charge Q.
It is not possible to construct a capacitor of capacitance 1F.
Generally, all the capacitors possess capacitance in terms of a microfarad, pF, nF etc.
High potential difference refers to the strong electric field around the conductors.
Now, the potential difference V is the work done per unit positive charge in taking a small test charge from the conductor 2 to 1 against the field. Consequently, V is also proportional to Q, and the ratio
Q/V is a constant:
C = Q/V
Where constant C is called the capacitance of the capacitor.
The capacitance of a capacitor is defined as its ability or capacity to store some charge.
The SI unit of Capacitance is 1 farad.
The capacitance C depends only on the shape, size, and separation of the system of two conductors.
According to (C = Q/V), a capacitor with large capacitance can hold a large amount of charge Q at a relatively small V.
The maximum electric field that a dielectric medium can withstand without break-down is called its dielectric strength; for air, it is about 3 × 106 V/m.
For separation between conductors of the order of 1 cm or so, this field corresponds to a potential difference of 3 × 104 V between the conductors.
Working Principle of a Capacitor
A parallel plate capacitor consists of two large plane parallel conducting plates separated by a small distance. We first take the medium between the plates Vacuum. Let A be the area of each plate and d be the difference between them. There are Q and -Q charges on both plates. Since the linear dimension of d is much smaller than plates. We can use the result on the electric field by an infinite plane sheet of uniform surface charge density. Plate 1 has a surface charge density σ = Q/A and plate 2 has a surface charge density –σ.
Outer region I (region above the plate 1)
E = σ/2ε0 – σ/2ε0 = 0
Outer Zone II (Area of Underplate 2),
E = σ/2ε0 – σ/2ε0 = 0
In the inner region between plates 1 and 2, the electric fields are by connecting two charged plates, which give
E = σ/2ε0 + σ/2ε0 = σ/ε0 = Q/ε0A
The direction of the electric field is from the positive to the negative plate.
Thus, the electric field is localized between the two plates and remains the same throughout the field. The field lines bend outwards Edges – an effect called ‘Fringing of the field‘.
Now for a uniform electric field
V = Ed = Qd/Aε0
The capacitance C of the parallel plate capacitor is then
C = Q/V = Aε0/d
Effect of dielectric on capacitance
Now we discuss the effect of dielectric on capacitance in the principle of a capacitor. Dielectrics are those insulators that can conduct the application of the electric field.
As before, we have two large plates, each of area A, separated by a distance d. The charge on the plates is ±Q, corresponding to the charge density ±Ïƒ (with σ = Q/A). When there is a vacuum between the plates,
E0 = σ/ε0 and V0 = E0d and capacitance is C0 = Aε0/d
Next, consider a dielectric that is completely inserted between the plates occupying the interference region. The dielectric field is polarized by the field, the effect is equal to two charge sheets with surface charge densities σp and -σp.
The electric field in the dielectric corresponds to the case when the net surface charge density on the plates is ± (σ – σp) i.e.,
E = σ-σp/ε0
The Potential difference across the plates
V = Ed = (σ-σp)d/ε0
For linear dielectrics
σ – σp = σ/K
where K is a constant characteristic of the dielectric.
Clearly, K > 1. Then we have
V = σd/K
V = σd/Kε0 = Qd/Aε0K
The capacitance C with a dielectric between the plates then is
C = Q/V = Kε0A/d
The product ε0K is called the permittivity of the medium and is denoted by ε.
ε = ε0K
For vacuum K = 1 and ε = ε0; ε0 is called the permittivity of the vacuum.
The dimensionless ratio
K = ε/ε0
is called the dielectric constant of the substance.
K = C/C0
Thus, the dielectric constant of a material is the factor (>1) by which the capacitance increases from its vacuum value when the dielectric is completely passed between the plates of the capacitor.
Combination of Capacitors
Capacitors in parallel
C = C1 + C2
C = C1+C2+C3 +…… +Cn
Capacitors in Series
1/C = 1/C1+1/C2
1/C = 1/C1 + 1/C2 + . . . . . . + 1/Cn
Energy stored in a Capacitor
Work done in charging a capacitor is stored in the capacitor in the form of electric energy.
The energy density of the electric field
We are successfully studying the principle of a capacitor.
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