# Resistivity

On the topic of electric current, the density of electric current has been discussed, so also the electric field has been explained in-topic about the electric field. The electric field and electric current are in a conductor if there is a potential difference in the conductor, whereas if there is no potential difference then there is also no electric field and electric current.

In almost all metal conductors, the electric field is directly proportional to the density of the electric current, where the ratio of the electric field to the density of the electrical current is constant. The value of the comparison of the electric field to current density is called resistivity. Mathematically the relationship between the electric field, current density, and resistivity is stated in the equation:

ρ = E / J

*ρ = resistivity, E = electric field, J = current density*

One of the electric field formulas is E = V/d where V = electric potential difference = electric voltage and d = distance so that the electric field unit is Volt/meter (V/m). The formula of current density is J = I/A where I = electric current and A = cross-sectional area of the conductor, so the unit of current density is Ampere/meter squared (A/m^{2}). The equation of the resistivity is ρ = E/J so that the resistivity unit is V/m : A/m^{2} = V/m x m^{2} / A = V/A (m) = Ω m (read: Ohmmeter). Ω = Volt / Ampere is a unit of electrical resistance.

The biggest resistivity value is owned by electrical insulators or while the smallest resistivity is owned by a good electrical conductor. The better a conductor delivers an electric current, the smaller the resistance of the type of conductor. The order of metal conductors having the largest to smallest resistivity is tin, steel, aluminum, gold, copper, silver. So it can be concluded that the resistance value of an object states a measure of the object’s ability to inhibit an electric current.

A good conductor and obeying Ohm’s law, at a certain temperature the resistivity value does not depend on the electric field, meaning that if the electric field changes the value of the resistivity does not change. Conversely, for conductors that do not comply with Ohm’s law, the resistivity value depends on the electric field, meaning that if the magnitude of the electric field changes then the R-value also changes.

The resistivity of the metal conductor depends on the temperature. If the metal temperature increases, the resistivity of metal increases, whereas if the metal temperature decreases, the resistivity of metal decreases. As temperature increases, atoms move faster and are arranged irregularly so that they block the movement of electrons, causing the flow of electrons to be slower. When the temperature decreases, the atoms move slowly and are arranged more regularly so that the electron flow is smoother.

The opposite of resistivity is conductivity. Mathematically, the relationship between resistivity and conductivity is stated through the equation:

σ = 1/*ρ*

*σ = conductivity of conductor, ρ = resistivity.*

The unit of resistivity is Ωm so that the unit of conductivity is 1 / Ωm = (Ωm)^{-1}

The greatest conductivity value is owned by an electrical conductor while the smallest conductivity value is owned by an electrical insulator or a bad conductor of electricity. The better a conductor delivers an electric current, the greater the conductivity of the conductor. The order of metal conductors having the largest conductivity to the smallest is silver, copper, gold, aluminum, steel, tin. So it can be concluded that the value of the conductivity of an object expresses the measure of the ability of the object to carry an electric current. Silver has a large conductivity but expensive so that copper is more widely used as an electric conductor.