Convert between electrical conductivity and resistivity for material characterization and electrical engineering applications.
Materials Science • Electrical Engineering • 2024
Resistivity ρ (Ω·m)
1.6779e-8
Formula: ρ = 1 / σ
Electrical conductivity σ (siemens per meter, S/m) measures material's ability to conduct electric current. Resistivity ρ (ohm-meters, Ω·m) measures material's opposition to current. Relationship: ρ = 1/σ (reciprocal). Perfect reciprocal relationship means doubling conductivity halves resistivity. Conductivity units: S/m = 1/(Ω·m). Higher conductivity → easier electron flow → lower resistivity. Examples: Copper (excellent conductor) σ ≈ 5.96×10⁷ S/m → ρ ≈ 1.68×10⁻⁸ Ω·m (extremely low resistivity). Air (insulator) σ ≈ 10⁻¹⁵ S/m → ρ ≈ 10¹⁵ Ω·m (huge resistivity). Semiconductors (intermediate) silicon σ ≈ 10⁻⁶ S/m → ρ ≈ 10⁶ Ω·m. Temperature dependence: metals conductivity decreases with temperature (increased atomic vibration scatters electrons); semiconductors increase with temperature (more mobile charge carriers). Hall coefficient extends this: combines conductivity with magnetic field measurements to determine charge carrier type (electrons vs holes) and concentration. Practical engineering: wire gauge selection based on resistivity; higher resistivity requires larger diameter to achieve target resistance.
Material science applications: conductivity measurements characterize material purity (impurities increase conductivity sometimes or decrease, depending on dopant type in semiconductors). Anisotropic materials: single crystals exhibit directional dependence—different conductivity along different crystal axes. Tensor representation: σ_ij for general case. Superconductivity: perfect conductor achieved at low temperature—σ → ∞, ρ → 0 (zero resistance). Frequency-dependent effects: conductivity changes with signal frequency (AC vs DC); skin effect causes current concentration near surface in conductors. Ionic conductivity in electrolytes: ions carry current instead of electrons; formula ρ = 1/σ still applies. Temperature coefficient: α = (1/ρ₀)(dρ/dT); metals positive (resistivity increases), semiconductors negative (resistivity decreases). Contact resistance: material interfaces have additional resistance beyond bulk resistivity; important in integrated circuits. Grounding and shielding: low-resistivity materials preferred for current paths; high-conductivity metals (copper, aluminum) used for EMI shielding.
Know Measured Conductivity: Measure or look up σ in S/m (siemens per meter).
Check Units: Ensure conductivity in S/m (not μS/cm or other units).
Apply Reciprocal: ρ = 1/σ. Simple inversion formula.
Result in Ω·m: Resistivity automatically in ohm-meters.
Convert if Needed: To Ω·cm: multiply by 100. To MΩ·cm: divide by 10⁶.
Material Comparison Table (at 20°C):
Copper example: σ = 5.96×10⁷ S/m → ρ = 1/(5.96×10⁷) = 1.68×10⁻⁸ Ω·m. Perfect reciprocal.
Fundamental physics: current flow opposed by material structure. Inverse relationship emerges from Ohm's law; no true exception known.
Conductivity for materials science (measure of electron mobility). Resistivity for circuit design (calculate wire losses). Choose based on context.
Metals: conductivity decreases with T (atomic vibrations scatter electrons). Semiconductors: conductivity increases with T (more mobile charge carriers).
SI units: σ in S/m, ρ in Ω·m. Older units: σ in mho/cm, ρ in Ω·cm. 1 S/m = 10 mho/cm. Always specify units.
Theoretically never (infinite resistance). Practical insulators have σ ~10⁻¹⁸ S/m (nearly infinite ρ). Perfect insulators don't exist in practice.
Adding impurities increases conductivity dramatically (millions of times). p-doping (holes) and n-doping (electrons) fine-tune conductivity.
State where σ → ∞, ρ → 0 (perfect conductor) below critical temperature. Electrons pair (Cooper pairs), zero resistance flow.
Crystalline defects, atomic disorder increase scattering. Alloys less conductive than pure metals. Brass (Cu+Zn) less conductive than pure copper.
Conductivity-resistivity conversions are essential for material selection, electrical design, semiconductor engineering, and characterizing conducting properties of materials.
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