Dielectric Constant: Formula, Units, & Values

Dielectric Constant is the ratio of the substance’s electric permittivity to the electric permittivity of the free space. A dielectric is a material that has poor electrical conductivity but can store an electric charge due to Dielectric polarization. Therefore, showing only displacement current makes it an ideal choice for building a capacitor (to store and return electrical energy). The dielectric constant is denoted by the greek letter ‘κ’ (kappa). The formula of Dielectric constant can be represented by:

Dielectric Constant, \(K = \frac {\epsilon}{\epsilon_0}\) 

Here, 

• κ = Dielectric Constant
• ε = Permittivity of the substance
• ε₀ = Permittivity of the free space

Dielectric constant is also known as electric permittivity or simply permittivity. Dielectric constant is also called relative permittivity since it is measured relatively from the permittivity of free space (ε₀). Dielectric constant depicts the ability of plastics to preserve electrical energy. 

Read More: Capacitance Formula

What is Dielectric Constant?

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The ratio of the substance’s permittivity to the permittivity of the free space is defined as the dielectric constant of a substance. The dielectric constant shows the extent to which a material can hold electric flux in it.

Dielectric constant, also called relative permittivity or specific inductive capacity, is a property of an electrically insulating material equivalent to the ratio of the capacitance of a capacitor filled with the respective material to the capacitance of one identical capacitor present in vacuum without the dielectric material.

Dielectric Constant Formula

Dielectric Constant formula can be expressed as:

Where,

• κ = Dielectric Constant
• ε = Permittivity of the substance
• ε₀ = Permittivity of the free space

Dielectric Constant Unit

The dielectric constant is the ratio of two like entities, therefore it is a unit-less and dimensionless quantity.

Dielectric Constant Symbol

Dielectric constant symbol can be expressed using the Greek letter kappa ‘κ’. The relative permittivity of a dielectric substance can also be referred to as Dielectric Constant.

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Dielectric Constant Theory 

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Dielectric constant is the relative permittivity of a dielectric substance and is abbreviated as ‘κ’ (kappa). The dielectric constant is an important parameter to define a capacitor.

• A capacitor is a type of electronic component that is used to store electric charge.
• It can be constructed by sandwiching a dielectric insulating plate in between the metal conducting plates.
• How effectively a capacitor can store charge depends upon the layer of dielectric material.

Capacitor

Hence, it is important to choose the correct dielectric material. The expression can be written as:

Here,

• The value of E₀ is always greater than or equal to E.
• Therefore, the value of a dielectric constant is always greater than 1.
• The greater the value of κ the more will be the charge stored in a capacitor.

In the capacitor, the capacitance is given by:

C = κC₀

In the parallel plate capacitor, the capacitance is given by:

C = κε₀A/d

Where,

• C = Capacitance of the parallel plate capacitor
• κ = Dielectric Constant
• ε₀ = Permittivity of the free space
• A = Area of parallel conducting plates
• D = Separation between parallel conducting plates

The value of capacitance can be increased by increasing the value of the dielectric constant and decreasing the separation between the parallel conducting plates.

Dielectric Constant Value 

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The following table depicts some important dielectric constant value of dielectric materials:

Effect of Dielectric on Capacitance 

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Suppose there is a capacitor with parallel plates of area A and separated by a distance d. Now, for a capacitor with charge Q, the charge on each plate will be +Q and –Q. The area of the plate is A therefore the charge density will be ±σ:

⇒ σ = Q/A

Now, if the two plates have a vacuum between them, the potential energy across the capacitor will be:

⇒ V₀ = E₀d = V₀ σ/ε₀ d

Thus, the capacitance of the capacitor will be:

⇒ C₀ = Q/V₀ = ε₀ A/d

Let us take another capacitor with the same specifications as taken earlier. We will insert a dielectric between the plates in such a way that it fully occupies the space between the plates. The dielectric is polarized by the field as it enters the field between the plates and the charges are arranged so that they act as two charged sheets with a surface charge density of σp and – σp. The net surface charge density becomes equal to ±(σ – σp).

And, the potential energy across the capacitor will be,

⇒ V = Ed = (σ – σp / ε₀) d

In the case of linear dielectrics, σp is proportional to E0 and therefore it is proportional to σ. Thus, we can say that the value (σ – σp) is also proportional to σ.

⇒ σ − σp = σ/K

Where K is a constant whose value depends upon the selected dielectric medium.

The potential energy across the capacitor will be:

⇒ V = σd/ε₀K = Qd/Aε₀K

And the capacitance between the plates will be:

⇒ C = Q/V = ε₀KA/d

Here ε0K is the permittivity of the medium, which can also be written as,

⇒ ε = ε₀K

Here the value K is the permittivity of the medium such that, for a given medium,

⇒ K = ε/ε₀

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Factors Affecting Dielectric Constant

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The dielectric constant depends on various factors such as:

• Frequency: One of the factors that influence the dielectric constant is the frequency of the voltage applied. The value of the dielectric constant becomes non-linear with the increase in the frequency of the applied voltage.
• Applied voltage: The value of the dielectric constant decreases when we apply direct current voltage and increases when we apply alternating current voltage.
• Temperature: The molecule alignment in the dielectric material becomes difficult at low temperatures. But when we increase the temperature, the dipoles present in the dielectric material become dominant which results in an increase in the dielectric constant.
• Humidity and moisture: The strength of the dielectric material decreases with the increase in humidity or moisture.
• Heating effect: The dielectric loss occurs when the dielectric material is heated. The dissipation of energy in the form of heat when molecules in a material move as it comes in contact with an alternating current voltage is known as dielectric loss.
• Structure & morphology: The dielectric constant also gets influenced by the structure and morphology of the material.

Previous Year Questions

1. A spherical drop of capacitance … [KCET 2004]
2. Two equal capacitors are first connected in series … [JEE Mains 2021]
3. A point charge +q is placed at the centre of a cube … [NEET 1996]
4. The energy stored in a capacitor of capacity C and potential V is given by … [NEET 1996]
5. What is the flux through a cube of side a if a point charge … [NEET 2012]
6. In a certain region of space with volume … [NEET 2020]
7. A hollow cylinder has a charge q … [NEET 2007]
8. What is the effective capacitance between points … [NEET 1999]
9. When air is replaced by a dielectric medium of constant K … [NEET 1999]
10. A conducting sphere of radius … [NEET 2004]
11. In a region, the potential is represented by … [NEET 2014]
12. The electrostatic force between the metal plate … [NEET 2018]
13. Three charges, each +q, are placed … [NEET 2011] 
14. A capacitor of capacitance C₁ … [NEET 2002]
15. A capacitor is charged by a battery … [NEET 2017]

Things to Remember

• Dielectric Constant is the ratio of the substance’s electric permittivity to the electric permittivity of the free space and it is denoted by ‘κ’ (kappa).
• Dielectric constant is a dimensionless quantity.
• The formula for Dielectric Constant is given by, \(K = \frac {\epsilon}{\epsilon_0}\)_.
• The factors affecting dielectric constant are frequency, applied voltage, temperature, humidity, moisture, heating effect and structure & morphology.

Check Important Handwritten Notes: