Current Electricity and Resistivity

Electric current is a continuous flow of electric charge from one location to another along a path, measured in amperes or amps (A). The material through which the electric current passes offers both resistivity and resistance. The resistivity, or electrical resistivity, of a substance, is its intrinsic feature, and it depends on its molecular and atomic structure and is temperature-dependent. Let’s get to know what resistivity is further in this article. 

Before understanding the resistivity definition, let us have a  brief on what is an electric current. 

Electric current

The flow of electrons in a conductor is known as an electric current. The number of charges that travel across the wire every second is measured in amperes (amps). The condition for the current to flow is that the circuit must be closed; that is, there must be an unbroken path from the power source, through the circuit, and back to the power source.

An analogy of electric terms:

Voltage

Voltage, often known as electric potential, is a unit of measurement. The total energy necessary to transfer a small electric charge from one place to the other, divided by the charge’s size, is the voltage between two locations in a circuit.

Resistance

The forces that block the passage of electron current in a wire are measured in ohms and are referred to as resistance. Resistance can be put into use in a number of applications like converting the electrical energy lost in a resistor into heat energy (as in an electric stove), light energy (a light bulb), sound energy (radio), mechanical energy (an electric fan), or magnetic energy (as in a magnet). We should pick a wire with as minimal resistance as possible if we want current to flow directly from one point to another.

Circuit

A circuit is a channel through which electric current can flow.

Conductor

A conductor is a material made up of atoms that hold electrons loosely, allowing them to move more freely across it.

Phenomenon of current

Metals (conductors) have free electrons, which is one of their characteristics. The bond between free electrons and their parent atoms is only limited. These electrons are free to flow in any direction. However, when exposed to a weak electromagnetic field, they all travel in the same direction. This is the current of electricity. The current is strong when a large number of electrons flow through a piece of metal in a short period of time. The current is weaker when fewer electrons pass through.

Current density

When a voltage is connected to a conductor, an electrical field E is formed, which causes charges in the conductor to feel a charge. The current density J that results is determined by the electrical field and the material parameters. The current density in several materials, particularly metals at a given temperature, is roughly proportional to the electrical field. 

J =σE

• σ  is the electrical conductivity, 

• E is the electric field, and, 

• J  is the current density 

Electrical conductivity (σ)

Electrical conductivity is a way of measuring a material’s ability to conduct or transport electricity, similar to thermal conductivity. Electrical conductivity is greater in conductors than in insulators. The units are J/E because the electrical conductivity is equal to J/E. 

σ =[J]/ [E]=(A/m2) / (V/m) =A/V⋅m.

The unit of electric current conductivity is (Ω⋅m)-1.

One ohm equals one volt per amp:

1Ω = 1V/A

What is resistivity?

Resistivity is a measurement of how strongly a substance resists the flow of electrical current. The lowercase Greek letter rho is the sign for resistivity, and resistivity is the opposite of electrical conductivity.

ρ=1/σ.

The  SI unit of resistivity is the ohm-metre  (Ω⋅m)

When a voltage source is linked to a conductor, it creates a potential difference(V) which in turn forms an electric field. The electrical field, in turn, causes current by exerting force on free charges. The amount of current is determined not only by the magnitude of the voltage but also by the properties of the substance through which the current flows.

Relationship between resistivity, electrical field, and current density

ρ = E/J

E is the electrical field, and J is the current density.

Thus, the greater the field required to produce a particular current density, the higher the resistivity. The higher the current density produced by a given electrical field, the lower the resistivity. High conductivity and low resistance are characteristics of good conductors. Low conductivity and high resistivity are characteristics of good insulators.

Resistivity and temperature dependence 

Some materials have a strong relationship between temperature and resistivity. For example, the resistivity of copper increases as the temperature rises. In fact, the resistance of most conducting metals increases as the temperature rises. As the temperature rises, the vibrations of the atoms in the metal’s lattice structure increase, obstructing electron movement.  In a few cases like carbon, the resistivity diminishes as the temperature rises. 

The dependence is nearly linear in many materials and may be represented using a linear equation:

ρ = ρ0[1+α(T − T0)],

• ρ  is the resistivity of the material at temperature T,  

• α  is the temperature coefficient of the material, and  

• ρ0  is the resistivity at T0, usually taken as T0=20.00°C.

Resistance

A circuit component or device’s electrical resistance is measured as the proportion of the voltage applied to the electric current flowing through it:

R =V/I

If the resistance doesn’t change over a wide range of voltages, Ohm’s law, I = V/R, can be utilised to anticipate how the substance would behave. Although the definition above refers to DC current and voltage, the same definition applies to resistors used in AC applications.

Whether or not a material obeys Ohm’s law, its bulk resistivity can be used to define its resistance.

Temperature affects the resistivity, and hence the resistance. A temperature coefficient of resistance can be used to forecast temperature dependency of both resistivity and resistance over large temperature ranges.

Conclusion

The concept of resistance and resistivity is one of the most fundamental and important aspects of the concept of current and electricity. The main distinction between resistance and resistivity of a material is that resistance resists electron passage, but resistivity is a material feature that precisely characterises the substance’s resistance.