# Electrical Conductivity: Definition, Formula and Application:

Electrical conductivity is a fundamental property of materials that characterizes their ability to conduct electrical current. It is an important physical property that has numerous applications in various fields such as electrical engineering, materials science, and chemistry. The electrical conductivity of a material is determined by its resistivity, which is a measure of how much a material resists the flow of electrical current. In this article, we will explore the concept of electrical conductivity, the conductivity formula, and its applications in various fields.

## What is Electrical Conductivity?

Electrical conductivity is a measure of how easily an electric current can pass through a material. It is the reciprocal of resistivity and is defined as the ability of a material to conduct electricity. The electrical conductivity of a material is determined by the number of free electrons in its lattice structure and their mobility. Metals are good conductors of electricity because they have a high number of free electrons in their lattice structure that can move freely in response to an applied electric field. Insulators, on the other hand, have a low electrical conductivity because they have a low number of free electrons in their lattice structure that cannot move freely in response to an applied electric field.

The electrical conductivity of a material is measured in units of siemens per meter (S/m) or mho per meter (℧/m), which is the reciprocal of an ohm. The siemens is the standard unit of electrical conductance and is defined as the reciprocal of the ohm. It is named after Ernst Werner von Siemens, a German inventor who made significant contributions to the development of electrical engineering.

Electrical conductivity is an important physical property that has numerous applications in various fields such as electrical engineering, materials science, and chemistry. It is used to design electrical devices, such as wires, cables, and electronic components, and to study the properties of materials, such as metals, semiconductors, and insulators.

## What is the Conductivity Formula?

The conductivity formula is the inverse of resistivity and is given by:

σ = 1/ρ

where σ is the electrical conductivity and ρ is the resistivity of the material. The conductivity formula is used to calculate the electrical conductivity of a material based on its resistivity. The resistivity of a material is a measure of how much it resists the flow of electrical current and is defined as the resistance of a unit length of a material with a unit cross-sectional area. The unit of resistivity is ohm-meter (Ω-m).

The conductivity formula is an important tool in materials science and electrical engineering. It is used to design electrical devices, such as wires, cables, and electronic components, and to study the properties of materials, such as metals, semiconductors, and insulators. The conductivity formula is also used in the design of batteries, fuel cells, and solar cells.

## Conductivity of Metals

Metals are good conductors of electricity because they have a high number of free electrons in their lattice structure that can move freely in response to an applied electric field. The electrical conductivity of metals is dependent on the number of free electrons and their mobility. The number of free electrons in a metal is determined by its atomic structure and the number of valence electrons in its outer shell.

The mobility of free electrons in a metal is determined by the crystal structure of the metal and the presence of impurities. The crystal structure of a metal affects the mobility of free electrons because it determines the distance between the atoms in the lattice structure. The presence of impurities in a metal can affect its electrical conductivity because impurities can scatter free electrons, reducing their mobility and increasing the resistance of the metal.

The electrical conductivity of metals decreases with increasing temperature because the increased thermal vibrations of the lattice structure scatter free electrons, reducing their mobility and increasing the resistance of the metal. The electrical conductivity of metals also decreases with increasing impurity concentration because impurities can scatter free electrons, reducing their mobility and increasing the resistance of the metal.

## Electrical Conductivity of Semiconductors

Semiconductors are materials that have a conductivity between that of metals and insulators. They have a resistivity that is higher than that of metals but lower than that of insulators. The electrical conductivity of semiconductors is dependent on the presence of impurities, which can increase or decrease the number of free electrons in the lattice structure.

The electrical conductivity of semiconductors can be increased by doping the material with impurities. Doping is the process of adding impurities to a semiconductor to increase its conductivity. The impurities are added in small concentrations, and the type of impurity added determines the type of semiconductor created. For example, adding impurities such as boron or aluminum creates a p-type semiconductor, while adding impurities such as phosphorus or arsenic creates an n-type semiconductor.

P-type semiconductors have a high concentration of holes, which are vacancies in the valence band where an electron is missing. N-type semiconductors have a high concentration of electrons in the conduction band. The electrical conductivity of a semiconductor is determined by the concentration of free electrons or holes in the lattice structure and their mobility.

## Electrical Conductivity of Insulators

Insulators are materials that have a high resistivity and a low conductivity. They are used as electrical insulators to prevent the flow of electrical current. The resistivity of insulators is due to the absence of free electrons in the lattice structure. Insulators have a valence band that is completely filled with electrons and a conduction band that is completely empty. The energy gap between the valence band and the conduction band is too large for the electrons to move from the valence band to the conduction band.

The electrical conductivity of insulators can be increased by adding impurities to the material. This process is called doping, and it is similar to the doping process used in semiconductors. The impurities are added in small concentrations, and they create new energy levels in the energy gap between the valence band and the conduction band. These energy levels allow electrons to move from the valence band to the conduction band, increasing the conductivity of the material.

## Applications of Conductivity Formula

The conductivity formula is an important tool in materials science and electrical engineering. It is used to design electrical devices, such as wires, cables, and electronic components, and to study the properties of materials, such as metals, semiconductors, and insulators. Some of the applications of the conductivity formula are:

### Electrical Wiring

The conductivity formula is used in the design of electrical wiring. Electrical wires are made of materials that have a high electrical conductivity, such as copper or aluminum. The conductivity formula is used to calculate the electrical conductivity of the wire based on its resistivity. This information is used to determine the size of the wire needed for a particular application.

### Electronic Devices

The conductivity formula is used in the design of electronic devices, such as transistors and diodes. These devices are made of semiconductors, which have a conductivity that can be controlled by doping the material with impurities. The formula is used to calculate the electrical conductivity of the semiconductor based on its resistivity and the concentration of impurities.

### Batteries

The conductivity formula is used in the design of batteries. Batteries are made of materials that have a high electrical conductivity, such as metals or graphite. The conductivity formula is used to calculate the conductivity of the battery based on the resistivity of the materials used.

### Corrosion Control

The conductivity formula is used in the prevention of corrosion in metals. Corrosion occurs when metals are exposed to an environment that causes them to oxidize. The conductivity formula is used to calculate the electrical conductivity of the metal, which is used to determine the rate of corrosion. By controlling the conductivity of the metal, the rate of corrosion can be reduced.

Electrical conductivity is a fundamental property of materials that characterizes their ability to conduct electrical current. It is an important physical property that has numerous applications in various fields such as electrical engineering, materials science, and chemistry. The electrical conductivity of a material is determined by its resistivity, which is a measure of how much a material resists the flow of electrical current. The conductivity formula is the inverse of resistivity and is used to calculate the electrical conductivity of a material based on its resistivity. The conductivity formula is an important tool in materials science and electrical engineering, and it is used to design electrical devices, study the properties of materials, and prevent corrosion in metals.