Question

1-how each dielectric material has its own unique specific dielectric constant. The textbook and other resources refer to the constant as "k" but wouldn't each material having its own constant ruin the purpose of a "constant" being the same value for every dielectric material?

2-What the dielectric does exactly?

3-why we only consider one of two similar junctions in a circuit. Why do we not consider the other junction if they are equivalent equations?

Answer 1

(1) This is a good question to clear the concept of dielectric in capacitors..

The dielectric constant - also called the relative permittivity indicates how easily a material can become polarized by imposition of an electric field on an insulator. Relative permittivity is the ratio of "the permittivity of a substance to the permittivity of space or vacuum".

Relative permittivity can be expressed as

K =  ε_r = ε / ε₀

where

ε_r = relative permittivity - or dielectric constant (k)

ε = permittivity of substance (C²/(N m²))

ε₀ = permittivity of vacuum or free space (8.854187817 10^-12 C²/(N m²))

Relative permittivity - ε_r - and permittivity - ε - for some substances. Note that permittivity may change with temperature for most materials.

NOTE: The constant k is constant just for saying.. Actualy, its value varies according to the permittivity of substance as it can be seen from the formula.

(2)

The insulating medium separating charged surfaces is called a dielectric. A dielectric is a material that does not allow current to flow. Dielectrics are often called insulators as they are the opposite of conductors. All the electrons in a dielectric material are bound tightly to their parent nucleus, so no free electrons are available to carry the current. Thus the electrical conductivity of dielectrics is very low. The dielectric constant is a measure of the ability of a material to store electrical energy and is defined as the ratio of the capacitance (or permittivity) of the dielectric material to the capacitance of a vacuum. Therefore, all the capacitance values are related to the permittivity of vacuum. Each different dielectric material has its own value of permittivity.

FUNCTION OF DIELECTRICS:

Dielectric materials have very high resistivity compared to conductors, thus they are used to separate conductors at different potentials, such as capacitor plates or electric power lines. When a dielectric is placed between charged plates, the capacitance of the system increases.

The main property of a dielectric material is its ability to withstand high electric stress while dissipating minimal energy in the form of heat.

APPLICATIONS:

The main use of dielectrics is in fabricating capacitors. A dielectric material has very high resistivity, thus used to separate conductors at different potentials, such as capacitor plates or electric power lines.

(3)

As per my understanding of your question, referring to the figure below, all these nodes inside the selected area '"b" are considered as ONE because the pottential at all the three nodes is same (or say there is no potential drob between the nodes). Same is the case with nodes includded in selected area "c".

I'm sorry if this wasnt what you asked. Maybe i didn't understand this part of your question. Could you please elaborate on it if that is the case? i'll be happy to help you out in the comment section or a new question, whatever you prefer.