Electrical resistivity plays a vital role in understanding how materials conduct or resist electric current. This property helps engineers and scientists select appropriate materials for electrical and electronic applications.
In this article, you’ll learn the definition, symbol, formula, unit, and how resistivity varies with temperature across different materials.
Resistivity Definition
Electrical resistivity, also known as specific resistivity, is the electrical resistance of a specific specimen of the material of unit length and unit cross-sectional area. The electrical resistivity shows the current opposing property of a conductor.
If the resistance of the material specimen of 1-meter length and 1 square meter cross-sectional area is 1 ohm. It means the resistivity of the material is 1 Ohm- meter.
The stronger the opposition, the higher the resistivity and the lower the current passing through it. Therefore, the resistivity of the material has paramount importance in electrical engineering.
Formula: ρ = RA/L
Unit: Ohm-meter (Ω·m)
Symbol: Greek letter rho (ρ)
Symbol of Resistivity (ρ)
The symbol of electrical resistivity is the Greek letter rho (ρ). This symbol is commonly used in physics and electrical engineering to represent the resistivity of a material.
In terms of the resistivity sign, the Greek letter ρ (rho) is universally accepted as the standard notation. It is important to note that this sign indicates a material’s intrinsic property to resist the flow of electric current.
Electrical Resistivity Formula (ρ = RA/L)
The resistance of the conductor depends on the following parameters.
- Resistivity of the material(ρ)
- Cross-sectional area(A)
- Length(L)
The formula for calculating electrical resistivity is:
Where:
- ρ (rho) is the resistivity in ohm-meter (Ω·m)
- R is the resistance in ohms (Ω)
- A is the cross-sectional area in square meters (m²)
- L is the length of the conductor in meters (m)
Derivation of Electrical Resistivity Formula
The resistance of a conductor is directly proportional to the resistivity of the material.
R ∝ ρ — (1)
The resistance is directly proportional to the length of the conductor.
R ∝ L — (2)
The resistance is inversely proportional to the cross-sectional area.
R ∝ 1/A — (3)
Combining equations (1), (2), and (3):
R=ρL/A — (4)
Rearranging to solve for resistivity:
ρ=RA/L — (5)
SI Unit of Resistivity (Ω·m)
The SI unit of electrical resistivity is ohm-meter (Ω·m). This unit reflects the resistance of a material that is one meter long with a one-square-meter cross-sectional area.
The electrical resistivity of the material is directly proportional to the cross-sectional area and inversely proportional to the length.
ρ ∝ RA, Also ρ ∝ L
Therefore,
ρ ∝ R (A/L)
To justify the SI unit, let’s consider the standard resistivity formula:
From above, the unit of resistivity is
ρ ∝ R(A/L)
Substituting the units:
ρ = (Ω × m²) / m = Ω·m
The unit of resistance is Ohm. In the mks ( meter-kilogram-second) system, the ratio of area and length is simplified to just meters. Thus, in the MKS system, the unit of resistivity is ohm-meter.
If the length & cross-sectional area is in the centimeter & square of centimeters respectively, then the unit of resistivity is ohm-centimeter.
Note: In CGS units, it becomes ohm-cm. But for most scientific and engineering calculations, Ω·m is the standardized form.
The reciprocal of the resistivity is the conductivity. The electrical conductivity shows the ability of the material to pass the electric current through it.
Hence, conductivity is measured in siemens per meter (S/m), making it easier to quantify how well materials conduct electricity.
Electrical Resistivity of Materials
It is easy to compare various materials usages on the basis of materials resistivity.The resistivity of various materials is as given in the below table.
| Material | Resistivity (Ω·m) at 20°C |
| Silver | 1.59 × 10⁻⁸ |
| Copper | 1.68 × 10⁻⁸ |
| Gold | 2.44 × 10⁻⁸ |
| Aluminum | 2.82 × 10⁻⁸ |
| Tungsten | 5.60 × 10⁻⁸ |
| Zinc | 5.90 × 10⁻⁸ |
| Nickel | 6.99 × 10⁻⁸ |
Silver has the least resistivity, making it the best conductor.
Copper has less resistivity as compared to aluminum. Therefore, copper is the best conductor for electricity.
The resistivity of insulators is in the range of 1012 to 1020 ohm-meters. Therefore, the insulators have excellent current blocking property,
Effect of Temperature on Resistivity
The resistivity of the conducting materials increases with an increase in temperature. The electrons collide and hinder the path of electrical current at higher temperatures. As a result, the resistivity of the conductor increase with an increase in temperature.
Contrary to this, the resistivity of the insulators & semiconductors decreases with an increase in temperature. As a result, these materials start easily passing the electric current through them.
If the temperature increase is beyond the maximum permissible temperature limit, the insulator fails.
Therefore, the insulators and semiconductors function reliably if the temperature remains well below the maximum permissible temperature range,
Solved problems on Electrical Resistivity
Problem 1: Calculate the resistivity of the given material whose resistance, cross sectional area and length are 4 Ω , 50cm2 and 30 cm respectively?
Data given,
R = 4 Ω
l = 30 cm = 0.3 m
A = 50 cm2 = 0.25 m2
Resistivity formula is
ρ = RA/L
=( 4 x 0.25)/0.3
= 3.33 Ωm
Problem 2: The conducting wire has length, area & resistance 0.4 m, 1.5 m2 & 2 Ω respectively. Calculate the resistivity?
Given
R = 2 Ω
l = 0.4 m and
A = 1.5 m2
Resistivity formula is
ρ = RA/L
=( 2 x 1.5)/0.4
= 7.5 Ωm
Problem 3: Calculate the resistance of 100 m length of a wire having a uniform cross-sectional area of 0.2 mm2, if the wire is made of manganin having a resistivity of 50 × 10−8 Ω-m.
ℓ = 100 meter
A = 0.2 mm2 = 0.2 X 10-6 m2
ρ = 50 × 10 -8 Ω-m.
Problem 4: The resistance of a conductor 1 mm2 in cross-section and 40 m long is 0.692 Ω. Determine the specific resistance of the conducting material.
ℓ = 10 meter
A = 1 mm2 = 1 X 10-6 m
R = 0.692 Ω
ρ = ?
Conclusion
Electrical resistivity is a foundational concept in electrical and electronic engineering. It quantifies a material’s inherent ability to resist electric current and is crucial for selecting conductors, semiconductors, or insulators for specific applications.
By understanding the formula ρ=RA/L, its units, and how resistivity varies with temperature, engineers can predict how different materials behave under electrical stress.
Whether designing power systems, PCB circuits, or insulation systems, knowledge of resistivity ensures performance, safety, and efficiency.
FAQs
Electrical resistivity is the measure of how strongly a material opposes the flow of electric current. It is expressed in ohm-meters (Ω·m).
The formula of resistivity is ρ = RA / L, where R is resistance, A is area, and L is length.
The SI unit of resistivity is ohm-meter (Ω·m).
The symbol of resistivity is ρ (rho), a Greek letter.
Related Articles: