Electrical resistivity is a fundamental property that helps us understand how well a material resists the flow of electric current. It plays a key role in electrical engineering, materials science, and electronics design.
Whether you’re choosing a wire for power transmission or designing a PCB, knowing the resistivity of materials helps ensure efficiency, safety, and cost-effectiveness.
What is Electrical Resistivity?
Electrical resistivity, also known as specific resistance, is the measure of a material’s ability to oppose the flow of electric current. It is denoted by the Greek letter ρ (rho).
Definition: Electrical resistivity is the resistance offered by a material of unit length and unit cross-sectional area.
In simple terms, lower resistivity means better conductivity, while higher resistivity indicates poor current conduction.
Symbol of Resistivity
The symbol of resistivity is the Greek letter ρ (rho).
It is used universally in electrical engineering to represent electrical resistivity in equations and technical documentation.
- Symbol: ρ
- Pronunciation: Rho (sounds like “row”)
- Resistivity Sign: Always positive, since resistivity quantifies a material’s opposition to current flow and cannot be negative.
In all resistivity formulas, such as ρ = RA ⁄ L, the ρ stands for the intrinsic property of a material that resists electric current. Understanding this symbol is essential when interpreting circuit calculations, material specifications, and resistivity tables.
Formula of Electrical Resistivity
The resistivity of a conductor is calculated using the formula:
Where:
- ρ: Electrical resistivity in ohm-meter (Ω·m)
- R: Resistance in ohms (Ω)
- A: Cross-sectional area in square meters (m²)
- L: Length of the conductor in meters (m)
Electrical Resistivity Calculator
Want to quickly calculate resistivity for your application? Use the calculator below by entering resistance (R), area (A), and length (L):
Once all values are entered, the calculator will compute the resistivity (ρ) in ohm-meter (Ω·m).
Derivation of the Formula
The resistance R of a conductor depends on:
- Its length (L) → R∝L
- Its cross-sectional area (A) → R∝1/A
- The resistivity (ρ) → R∝ρ
Combining these gives:
R=ρ⋅L/A⇒ρ=RA/L
This formula helps engineers calculate the resistivity of different materials used in circuits and components.
SI Unit of Electrical Resistivity
The SI unit of electrical resistivity is Ω⋅m (Ohm-meter)
This means a material with 1 meter in length and 1 square meter in area has 1 ohm resistance, its resistivity is 1 Ω·m.
In CGS system: Resistivity is expressed in ohm-centimeter (Ω·cm), but Ω·m is universally accepted.
Relation Between Resistivity and Conductivity
Electrical conductivity (σ) is the reciprocal of resistivity: σ=1/ρ
- High resistivity ⇒ Low conductivity (e.g., glass, rubber)
- Low resistivity ⇒ High conductivity (e.g., copper, silver)
Unit of conductivity: Siemens per meter (S/m)
Electrical Resistivity of Materials
The table below lists the resistivity values of various common materials, ranging from excellent conductors like silver and copper to insulators like quartz and hard rubber.
| Material | Resistivity ρ (Ω·m) |
| Silver | 1.59 × 10⁻⁸ |
| Copper | 1.68 × 10⁻⁸ |
| Copper, Annealed | 1.72 × 10⁻⁸ |
| Aluminium | 2.65 × 10⁻⁸ |
| Tungsten | 5.6 × 10⁻⁸ |
| Iron | 9.71 × 10⁻⁸ |
| Platinum | 10.6 × 10⁻⁸ |
| Manganin | 48.2 × 10⁻⁸ |
| Lead | 22 × 10⁻⁸ |
| Mercury | 98 × 10⁻⁸ |
| Nichrome (Ni.Fe.Cr) | 100 × 10⁻⁸ |
| Constantan | 49 × 10⁻⁸ |
| Carbon* (graphite) | 3–60 × 10⁻⁵ |
| Germanium* | 1–500 × 10⁻³ |
| Silicon* | 0.1–60 |
| Glass | 1–10,000 × 10⁹ |
| Quartz (fused) | 7.5 × 10¹⁷ |
| Hard rubber | 1–100 × 10¹³ |
Materials with low resistivity are used in conductors, while high resistivity materials are chosen for insulators.
Effect of Temperature on Resistivity
- In conductors (like metals), resistivity increases with temperature.
- Reason: Electron collisions increase at higher temperatures, resisting flow.
- In semiconductors and insulators, resistivity decreases with temperature.
- Reason: More charge carriers become available for conduction.
Engineers must account for temperature variations while selecting materials to avoid failure or inefficiency.
Difference Between Resistance and Specific Resistivity
Resistance (R) is the opposition to current in a given conductor. Resistivity (ρ), also called specific resistance, is an intrinsic property of the material and independent of the conductor’s shape or size.
| Property | Resistance (R) | Resistivity (ρ) |
| Depends on | Material, length, and area | Only on material |
| Formula | R = ρL/A | ρ = RA/L |
| SI Unit | Ohm (Ω) | Ohm-meter (Ω·m) |
| Symbol | R | ρ (rho) |
Solved Problems on Electrical Resistivity
Problem 1: A wire has a resistance of 5 Ω, length 0.2 m, and cross-sectional area 0.0005 m². What is the resistivity?
Solution:
Problem 2: A copper wire of length 2 m and cross-sectional area 1 mm² has a resistivity of 1.68 × 10⁻⁸ Ω·m. Find its resistance.
Solution:
Convert area: 1 mm2=1×10−6 m2
Conclusion
Electrical resistivity is a vital parameter that determines how well a material conducts electricity. From designing electrical systems to choosing materials for insulation, understanding ρ = RA/L, its unit (Ω·m), and behavior under different conditions is essential.
By mastering this concept, engineers can design efficient, safe, and long-lasting electrical systems.
FAQs
Resistivity is a measure of how much a material opposes the flow of electric current. Materials with low resistivity let current flow easily, while those with high resistivity restrict it.
Electrical resistivity (ρ) is calculated using the formula:
ρ = (R × A) / L,
where R is resistance, A is cross-sectional area, and L is length of the conductor.
The SI unit of electrical resistivity is the ohm-meter (Ω·m). It represents the resistance of a 1-meter-long conductor with a 1 m² cross-sectional area.
The standard symbol used for resistivity is the Greek letter ρ (rho).
In physics, resistivity represents a material’s inherent opposition to electric current flow. Low resistivity means high conductivity and vice versa.
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