ρ = ρ20 * [1 + α(T - 20)]
σ = 1 / ρ
ρ = Resistivity at desired temperature (Ω·m)
ρ20 = Resistivity at 20°C (Ω·m)
T = Desired temperature (°C)
α = Temperature coefficient at 20°C
σ = Conductivity (S/m)
Calculate electrical resistivity and conductivity of copper, aluminum, silver, gold, and iron at different temperatures using IEC 60028 and IEC 60889 standards. Includes temperature dependence formula ρ(T) = ρ₀[1 + α(T-T₀)] for accurate material modeling in power systems, motors, and PCBs.
"Calculation of the resistivity and conductivity of a material based on temperature. Resistivity strongly depends on the presence of impurities in the material. Copper resistivity according to IEC 60028, aluminium resistivity according to IEC 60889."
Electrical resistivity is a fundamental property of a material that measures how strongly it resists electric current.
Electrical conductivity is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current.
Temperature coefficient of resistance for the conductor material.
ρ(T) = ρ₀ [1 + α (T - T₀)]
Where:
ρ(T): Resistivity at temperature T
ρ₀: Resistivity at reference temperature T₀ (20°C)
α: Temperature coefficient of resistance (°C⁻¹)
T: Operating temperature in °C
| Material | Resistivity @ 20°C (Ω·m) | Conductivity (S/m) | α (°C⁻¹) | Standard |
|---|---|---|---|---|
| Copper (Cu) | 1.724 × 10⁻⁸ | 5.796 × 10⁷ | 0.00393 | IEC 60028 |
| Aluminum (Al) | 2.828 × 10⁻⁸ | 3.536 × 10⁷ | 0.00403 | IEC 60889 |
| Silver (Ag) | 1.587 × 10⁻⁸ | 6.300 × 10⁷ | 0.0038 | – |
| Gold (Au) | 2.44 × 10⁻⁸ | 4.10 × 10⁷ | 0.0034 | – |
| Iron (Fe) | 9.7 × 10⁻⁸ | 1.03 × 10⁷ | 0.005 | – |
Even small amounts of impurities can increase resistivity by up to 20%. For example:
Pure copper: ~1.724 × 10⁻⁸ Ω·m
Commercial copper: up to 20% higher
Use high-purity copper for precision applications like power transmission lines.
Power Line Design: Calculate voltage drop and select wire size
Motor Windings: Estimate resistance at operating temperature
PCB Traces: Model thermal behavior and signal loss
Sensors: Calibrate RTDs and compensate for temperature drift
As temperature rises, atomic thermal vibrations intensify inside the material, impeding the directional movement of electrons and increasing resistivity. This calculator applies the formula ρ(T) = ρ₀[1 + α(T−T₀)] for temperature correction, ensuring calculation accuracy under different operating conditions.
Significantly. Even small amounts of impurities can increase resistivity by up to 20%. For example, commercial copper may have a resistivity up to 20% higher than pure copper. Therefore, high-purity copper should be used for precision applications such as power transmission lines.
Because they are governed by different IEC standards: copper resistivity is defined by IEC 60028, and aluminum resistivity by IEC 60889. The two standards specify different reference temperatures and values, so the correct standard must be selected accordingly.
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