Introduction to Dielectric Capacitor: Charging and Discharging

Introduction to Dielectric Capacitor

(i). A capacitor fundamentally is composed of two conducting surfaces or two metal surfaces, which are mutually separated through an insulating medium. The insulating medium is called dielectric. Any one of the materials like air, oil, ceramics, plastics, mica, and glass, etc., can be used as a dielectric. A capacitor essentially consists of two conducting surfaces separated by a layer of an insulating medium called dielectric. Remember that conducting surfaces are round, rectangular, or cylindrical type plates. The objective of a capacitor in a dielectric is to store energy through electrostatic stress. A capacitor is also occasionally known as a condenser.

(ii). A component which basically consists of two metal plates, which are separated mutually through inserting an insulating medium between these plates, is called capacitor.

(iii). An electronic component which can store energy in the form of electrostatic field, is called capacitor.

(iv). If two metal plates are placed nearer to each other and some kind of an insulator (e.g., mica, air, glass, or oil, etc.) is placed between them, and these plates are provided an electric charge by means of connecting the two plates with the source of potential difference, then this type of component is called capacitor.   

(v). Any two conductors between which an electric field can be maintained form a capacitor.

(vi). In its simple form, capacitor tends to be an electrical device, composed of two parallel conductive plates, which have been separated through an insulating medium (called dielectric).

Figure 6.8; The basic capacitor and its symbol

Connecting leads are connected to the parallel plates. A basic capacitor has been illustrated in fig. 6.8 (a), while its symbol in fig. (b). A capacitor is an electrical device constructed of two paralleled conductive plates by an insulating material called dielectric.

In figure 6.9, a parallel plate capacitor has been shown. One of the plates is connected to the positive end of the supply, whereas the second plate is connected to the negative end of the supply, or it is earthed. When this type of capacitor is provided supply through a battery, then the flow of electrons takes place momentarily from plate A towards plate B (because plate A has more charge due to plate B plate being earthed. As negatively charged electrons emit from plate A and stored on plate B, thus as a result of expulsion of electrons, a positive charge appears on plate A, and a negative charge on plate B due to the excess of electrons. Thus, a potential difference between plate A and b sets up. As a result of transient flow of electrons, an increase in charging current. The strength of charging current is maximum at that time when both the plates are uncharged. But it reduces afterwards, and when the potential difference found across plates gradually becomes opposite and equal to the battery’s e.m.f, then it finally ends. 

Fig. 6.9; Parallel plate capacitor

How a Capacitor Stores Charge

It has become evident from the afore-mentioned discussion that in a neutral state, both plates of a capacitor consist of equal quantity of free electrons, as has been reflected in figure 6.10 (a). When a capacitor is connected to voltage source through a resistor, as has been shown in figure (b), the emission of electrons (having negative charge on them) from plate A starts, and an equal number of electrons emitted from plate A, stores on plate B. As electrons emit from plate A, and store on plate B, as such a positive charge creates on plate A and a negative charge on plate B respectively. In other words, plate A becomes positive as compared to plate B. During this charging process, electrons only pass through the connecting leads and source. No electron passes through the dielectric, because it is an insulator. The motion of electrons stops when voltages found parallel to the capacitor become equal to the source voltages. As has been depicted in fig. (c). If capacitor is dissociated from the source, then charge stored on it maintains for a long period of time. The period of time depends on the value and type of the capacitor. And voltages are also found parallel to it. As can be seen in fig. (d). In fact, a charged capacitor can function as a temporary battery. 

Fig. 6.10; Illustration of a capacitor storing charge

Capacitance

(i). Capacitance is a measure of a capacitor’s ability to store charge or the property of a capacitor to store electricity may be called its capacitance. 

(ii). The amount of charge required to create a unit potential difference (p.d) between its plates iis called capacitance of a capacitor. Let us assume that out of the two plates, we provide a charge of Q coulomb (1 Coulomb = 6.29 x 10¹⁸) to one plate. Now, if a potential difference of one volt is also provided between these two plates, then capacitance of the capacitor will be as follows;

C = Q/ V = Charge / Potential Difference

In other words, capacitance is the charge required per unit potential difference.

(iii). The quantity of charge, that a capacitor can store per unit voltage, is known as its capacitance. That’s C = Q /V or Q = CV or V = Q / C. Here, C means capacitor’s capacitance, Q means charge, and V means voltage.

(iv). The ratio of Q/V is called capacitance. It is denoted by C.

The Unit of Capacitance

The unit of capacitance is Farad, and it is indicated by F. One farad equals one coulomb per volt, i.e., 1 farad = 1 coulomb / volt. A farad may be defined as follows;

(i). The capacitance of a capacitor is one farad at a time when it requires a potential difference of one volt in order to sustain charge of one coulomb.

(ii). The capacitance of a capacitor which requires a p.d of one volt to maintain (or to establish) a charge of one coulomb, or the capacitance which require a charge of one coulomb to establish a p.d of one volt between its plates.

When a charge of one coulomb is required to be stored at a pressure of one volt parallel to the plates, then quantity of capacitance tends to be one farad. It should be remembered that a farad is a very large unit, therefore, normally small units e.g., micro farad (μ F), nano farad (n F) and micro -micro farad (μ μ F) or pekoe farad (pF).

1 farad = 10 ⁶ μ F = 10 ⁹ n F = 10¹² pF

The capacitance of a capacitor is directly proportional to the area of plates, inversely proportional to the internal difference, and equally proportional to the dielectric constant. All the three points mentioned above (i.e., plate area, internal distance between these plates, and dielectric constant) are known as parameters or physical characteristics of a capacitor. See figure 6.11. These three components can be written in the form of a formula as follows;

C= A Ԑ_r (8.854 x 10^-12 F/m) / d 

Fig. 6.11; Factors controlling capacitance

Area (A) square meter, distance (d) and capacitance (C) are in farad (F). The absolute permittivity value (Ԑ₀) of free space tends to be 8.85 x 10^-12 F/m, and the dielctric ‘s permittivity (Ԑr) value can be determined with the help of the following formula;

Ԑ_r = Ԑ / Ԑ₀

Some common dielectric materials and their dielectric constants have been shown in the table 6.1;

Table 6.1

Example; Determine the capacitance of a parallel plate capacitor having a plate area of 0.01m2 and a plate separation of 0.02 m. The dielectric is mica which has a dielectric constant of 5.0.

Solution;

C = A Ԑ_r (8.854 x 10 ^-12 F / m)

= (0.01 m²) (5.00 (8.854 x 10^-12 F/m)

= 22.13 pF Ans.

Dielectric

The insulating material between the plates of a capacitor is called the dielectric, e.g., paper, oil, glass, and mica, etc. They play a very crucial role in the designing and structure of a capacitor. Different capacitances values can be obtained from different dielectric. It is a feature of every dielectric material that it concentrates the lines of force of an electric field existing between the capacitor’s two oppositely charged plates. Thus, it enhances the capacity of energy storage.

Dielectric Constant or Permittivity

The measure of a material’s ability to establish an electric field, is called dielectric constant or relative permittivity. In other words, the ability or characteristic of a dielectric to establish an electric charge, is known as its dielectric constant. Or dielectric (or insulator) is something, wherein there is no need for the existence of mobile electrons for electric conduction. Capacitance is directly proportional to the dielectric constant. The dielectric of a vacuum is treated as one and dielectric constant of air is also considered to be near to one. These values are used as a reference value, and the values of all other materials are specified with respect to air or vacuum. In other words, considering the value of air equal to unity, the dielectric values of all other materials are specified with reference to the air. For example, if the dielectric constant value of any material is 8 (Ԑ_r = 8), it means that all other factors considering the same, capacitor’s capacitance will be 8 times higher with respect to air by using this material as a dielectric. Some materials and their dielectric constants have been given in table 6.1.

Breakdown Voltage

There is a limit of every capacitor according to its voltage, within which voltages can provided parallel to the plates. If a capacitor is provided voltage in excess of this limit, capacitor turns out to be useless permanently. The maximum DC voltage, which can be provided to a device without the infliction of any sort of damage, indicates the voltage rating of the corresponding device.

If voltages provided parallel to a dielectric, increase beyond a certain limit (i.e., voltage rating), then the dielectric breakdowns, and flow of an excessively heavy electric current starts from it. If an insulator is made from a solid material, it gets punctured or cracked. The maximum voltages which are required to breakdown an insulator, are known as its breakdown voltages. In other words, maximum voltages which are to be supplied, as a result of which it breakdowns, are called breakdown voltages. If a further addition is made in the breakdown voltages, then the capacitor damages permanently and it becomes totally useless. Whenever a capacitor is required to be used in a circuit, its voltage rating and capacitance must essentially be kept in view. The selection of value of capacitance is done according to the specific requirements of a circuit, whereas voltage ratings must always be higher related to the circuits expected maximum voltages.

Dielectric Strength

Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down. It must be remembered that breakdown voltages of any capacitor can be determined through the dielectric strength of an insulating material which has been applied on it. In other words, the maximum pressure (in volts) which a dielectric medium can withstand without breaking down, is called dielectric strength. Its unit is volt / meter (v / m), however, it is often expressed as Kv / mm.  

For example, when we say that the dielectric of air is 3kv / mm, it means that if the air layer is one mm in thickness, then the maximum potential difference, at which air can maintain its dielectric strength without breaking down, is 3kv (or 3000 volts). If a further addition is made to this maximum voltage limit, then air’s dielectric or insulation, will breakdown, as a result of which excessive current will begin to flow through it. The dielectric strengths of a few materials have been given in table 6.2.

Energy Stored in a Capacitor

When a capacitor is being charged, then some part of the energy which is provided to the capacitor from a charging agency or charging unit, is consumed. This energy stores into an electrostatic field which has been built in the dielectric medium. This field eliminates as soon as the capacitor discharges, and the energy stored therein, tends to release.

A capacitor stores energy in the form of an electric field and this electric field is established as a result of supplying opponent charges on both plates of the capacitor. Electric or electrostatic field is reflected by means of the lines of force existing between positive and negative charges and this field is concentrated within the dielectric, as has been shown in fig. 6.12.

Table 6.2  

Figure. 6.12; The electric field stores energy in a capacitor.

Initially, when capacitor is not fully charged, very little work has to be done to transfer charge from one plate to another. When some charge has been deposited or stored on the capacitors’ plates, then in order to store more charge, a higher energy has to be consumed compared to the energy consumed initially. How much energy a capacitor having C capacitance will require to charge up to voltage V, its detail is as below;

Let us assume that the potential difference found parallel to the plates at any stage of charging is V. According to the definition, this potential difference shifts one coulomb charge from one plate to another. Thus, its value equals turns out to be equal to the work done. If dq be the charge, which is desired to be transferred to other plates, then work done will be as follows;

dw = 𝜐. Dq

Now, q = c 𝜐 ∴ dq = C. d 𝜐

∴ dw = C 𝜐. d 𝜐

The total amount of work to be done can be ascertained through providing the potential of V units, i.e.,

W = ₀ʃ^v C 𝜐. d 𝜐 = C ∣ V2/2 ∣^v ₀ ∴ W = ½ CV²

If C is in farad and V in volts, then energy is expressed in joules (w). that’s;

W = ½ CV² joules

Or W = ½ QV joules (∴ C = Q/V)

Or W = ½. Q²/C joules (∴ V = Q/C)

In figure 6.12, a line of force formed between a positive and negative charge has been illustrated. Whereas in fig. 6.13,

various opposite charges formed on a capacitors’ plate have been shown. Hence, numerous lines of forces are formed, which create an electric field, and this electric field stores energy in the dielectric.

The larger the number of forces formed on a capacitor’s plates; the higher will be the magnitude of energy to be stored. Therefore, quantity of the stored energy, is directly proportional to capacitance, because according to coulomb’s law, the larger the number of charges to be stored, the higher will be the force. 

Moreover, magnitude of the stored charge apart from capacitance, also tends to be directly proportional to the voltage (i.e., Q = CV). That’s why, quantity of the stored energy, also depends on the voltage’s square parallel to the capacitor’s plate. Thus, the magnitude of energy stored in a capacitor is as follows;

W = ½ CV² Joules

Alternative Method of Explanation

Suppose that a capacitor having a capacitance of C farad, has been connected to a supply voltage V. After closing the circuit’s switch, the quantity of charging current at time “t” will be as follows;

i = C d 𝜐/ dt

After multiplying the sides of this equation by 𝜐dt , we get an energy equation, i.e.,

𝜐i dt = C 𝜐 dt

= ₀ʃ^v C 𝜐. d = C [V2/2] ^v₀

₌ 1/2 CV² joules

Next Topic: 

Previous Topic: Introduction to Electrostatics with Solved Examples