Electrical Resistivity

What is Electrical Resistivity

Electrical resistivity, also known as specific electrical resistance, is a measure of a material’s ability to resist the flow of electric current. In other words, electrical resistivity is a measure of how difficult it is for electricity to flow through a material. Materials with high electrical resistivity are poor conductors of electricity, while materials with low electrical resistivity are good conductors.

Electrical resistivity is typically denoted by the Greek letter “rho” (ρ)

Diagram showing electrons collision within a material — The collision between moving electrons and other atoms within a material

The resistivity of a material is determined by the amount of collision between moving electrons and other atoms within the material. The higher the collision in a material, the harder it’s for an electric current to flow through it, and vice versa. Therefore, a low-resistivity material (like copper) has a low collision rate, and a material with high resistivity (like iron) has a much higher collision rate.

Electrical resistivity and resistance are closely related properties, however, they are not the same thing. Resistivity is an intrinsic property of the material itself, whereas resistance is a property of a particular electrical component and depends on the dimensions of that component.

Formula & Unit

𝜌 = \frac{RA}{L}

Where:

ρ is the electrical resistivity
R is the electrical resistance
A is the cross-sectional area
L is the length

The SI unit of electrical resistivity is ohm-meter (Ωm).

Electrical Resistivity Calculation

Find the resistivity of a wire with a length of 180 cm, and a radius of 2 cm. (The resistance of the wire is 3 Ω).

Solution

Step 1) We write down the given parameters:

L = 180 cm r = 2 cm R = 3 Ω

Step 2) We find the cross-sectional area of the wire:

A = π (r)² = π (2)² = 12.6 cm²

Step 3) Now, we can find the resistivity of the wire:

𝜌 = \frac{RA}{L} = \frac{3 \times 12.6}{180} = 0.21 Ω . cm

Factors Affecting Electrical Resistivity

The main factors that affect the electrical resistivity of a material are:

Temperature: The effect of temperature on electrical resistivity depends on the type of material. In general, most materials experience an increase in resistivity with increasing temperature. This is due to the increased thermal agitation of atoms and electrons, which leads to more collisions between them and therefore increased resistance to the flow of electric current.
Impurities: The presence of impurities or defects in a material can increase its resistivity. Impurities can disrupt the flow of electrons and make it more difficult for electric current to flow through the material.
Crystal structure: The resistivity of a material can depend on its crystal structure. The arrangement of atoms in a crystal lattice can affect the flow of electrons and, therefore, the material’s resistivity.
Pressure: Pressure can affect the resistivity of some materials. Increasing pressure can decrease the resistivity of some materials, while for others, it can increase the resistivity.
Magnetic field: The presence of a magnetic field can affect the resistivity of some materials. This is known as the magnetoresistance effect and can be used in applications such as magnetic sensors.

Understanding these factors and how they affect electrical resistivity is important in the design and optimization of electronic devices and circuits, as well as in various fields such as materials science, geophysics, and electrical engineering.

Applications of Electrical Resistivity

Electrical resistivity has many applications in various fields, including:

Geophysics: Electrical resistivity imaging (ERI) is a geophysical technique that is used to study the subsurface structure and properties of the Earth. ERI is used in a variety of applications, including groundwater exploration, mineral exploration, and environmental monitoring.
Electrical engineering: Resistivity is a key parameter in the design and analysis of electrical devices and circuits. It is used to calculate the resistance of conductive materials and to determine the power dissipation and voltage drop in electrical components.
Medical imaging: Electrical impedance tomography (EIT) is a medical imaging technique that uses electrical resistivity measurements to create images of the electrical conductivity distribution within the body. EIT is used in a variety of applications, including lung imaging, breast cancer detection, and brain imaging.
Non-destructive testing: Electrical resistivity measurements can be used to detect defects, cracks, and corrosion in conductive materials without damaging or altering them. This makes it a useful tool in the inspection and testing of industrial components and structures.

Electrical Resistivity Summary
Definition	The material’s resistance to the flow of electric current
Symbol	ρ "rho"
Formula	$𝜌 = \frac{RA}{L}$
Units	Si unit (Ω.m)

What is the relation between resistivity and conductivity?: Electrical resistivity is the inverse of electrical conductivity.

How electrical resistivity varies with temperature?: The electrical resistivity of most materials typically increases with an increase in temperature. This is because as temperature increases, the thermal vibrations of atoms and electrons in the material also increase, making it more difficult for electrons to flow through the material.

What are the units of electrical resistivity?: The SI unit of electrical resistivity is the ohm-meter (Ω⋅m). However, other units such as the ohm-centimeter (Ω⋅cm) and the ohm-inch (Ω⋅in) may also be used, depending on the specific application.

Which metal has the lowest resistivity?: Silver has the lowest electrical resistivity of any metal at room temperature (1.59 x10^-8 Ωm), followed closely by copper and gold.

Which metal has the highest resistivity?: Of the commonly used metals, tungsten has the highest electrical resistivity at room temperature (5.6 x10^-8 Ωm). This property makes tungsten useful for applications where high resistance is desired, such as in light bulb filaments, heating elements, and electrical contacts that need to withstand high temperatures.

Can electricity affect rubber?: Rubber is generally an electrical insulator and does not conduct electricity well. However, if the voltage or current is high enough, or if the rubber is contaminated with conducting materials, it is possible for electricity to affect rubber.