Dimensional Formula of Dielectric Constant

Dielectrics, as a general rule, can be portrayed as materials that are extremely helpless conveyors of electric flow. They are essentially protectors and contain no free electrons. Dielectrics can be effortlessly spellbound when an electric field is applied to them. Along these lines, their conduct in an electric field is altogether unique in relation to that of conveyors as would be obvious from the accompanying conversation. 

Dielectric Materials

The dielectric material is a substance that is a non-conductor, yet a storage of electrostatic fields.This is how a capacitor stores energy with dielectric materials. They are additionally utilised in the development of radio-recurrence transmission lines.

Practically speaking, most dielectric materials are strong. A few fluids and gases can fill in as great dielectric materials. Dry air is a brilliant dielectric and is utilised in factor capacitors and a few kinds of transmission lines. Refined water is a fair dielectric. 

A significant property of a dielectric is its capacity to help an electrostatic field while dissipating negligible energy as heat. The lower the dielectric heat loss, the more compelling is the material. Substances with a low dielectric consistency include ideal vacuum, dry air, and generally unadulterated, dry gases like helium and nitrogen. Materials with moderate dielectric constants include pottery, refined water, paper, mica, polyethene, and glass. Metal oxides, as a general rule, have high dielectric constants.

Dimensional Formula of Dielectric Constant

C= κϵ₀Ad

Here K is Dielectric Constant

Dielectric Constant is also written as  K = ϵϵ₀

We know that ϵ and ϵ₀ have the same dimension so if we take the ratio of ϵ  and ϵ₀, Then resultant quantity will be dimensionless.

So Dimensional Formula of Dielectric Constant = [M0 L0 T0] or we can say Dielectric Constant is dimensionless quantity.

Capacitors

The capacitor is one of the essential parts of the electric circuit, which holds the charges and stores them to balance the electric charges in the circuit. This component stores the electrical energy in an electric charge and produces the potential difference or static voltage between the electrical plates. 

The capacitor is a two-terminal device that possesses two electrical conductors at a certain distance. The distance between electric conductors is definite: a vacuum holds the insulating material. The insulating material is the dielectric element, the convertible form of the bad conductor of electricity or the insulators. The ability to store the electric charge between the capacitor is called capacitance. 

Factors Affecting the Capacitance

Here are certain factors which are responsible for the variation in the values of the capacitance of the capacitor:

● Spacing of the plates: The more distance between the plates, the less the capacitance value

● Area of the plates: The large area of plates increases the value of capacitance of the capacitor

● Dielectric: The higher permissible dielectric materials allow more charge storage, and thus the value of capacitance increases

Dimensions in Units and Measurements

The dimensions can be written as the powers of the fundamental units of length, mass, and time. It depicts their nature and does not show their magnitude. 

Example of writing Dimensions

Let’s take the formula of the area of the rectangle

Area of the rectangle = length x breadth

= [L1] X [L1]

= [L2]

Here, we can see the length to the power of 2 and we cannot find the dimension of mass and time.

Hence, the dimension of the area of a rectangle is written as [M0 L2 T0]

Dimensional Formula

The dimensional formula depicts the dependency of physical quantity with fundamental physical quantity, along with the powers.

Example

Let’s take the formula of speed

Speed = Distance / Time

The distance can be written in length [L]

Time can be written as [T]

The dimensional formula would be [ M0 L1 T-1]

Hence, we can conclude that the speed is dependent on only length and time, not mass.

Dimensional Equation

The physical quantity is equated with the dimensional formula, to get the dimensional equation. 

Example

Velocity =  [ M0 L1 T-1]

Here, velocity is the physical quantity, which is equated to the dimensional formula.

Conclusion 

In this topic, dimensional formula, we have learned the dimensional formula of dielectric Constant.  The dielectric constant is useful in detaching two capacitors. Capacitors are devices used for storing electrical energy in a circuit. Various capacitors are available, like ceramic, electrolytic, mica, film, paper, and non-polarized capacitors. The standard unit of capacitance is Farad. Capacitors are widely used in light production, oscillators, signal processing, and electric power conditioning.