SI Unit of Resistivity — Ohm-Metre (Ω·m)

The relationship between resistance and resistivity is:

R = ρ × L / A

Where: • R = resistance (in ohms, Ω) • ρ = resistivity (in Ω·m) • L = length of the conductor (in metres, m) • A = cross-sectional area (in m²)

Rearranging for ρ: ρ = R × A / L

SI unit of ρ = (unit of R × unit of A) / unit of L = (Ω × m²) / m = Ω·m

So the SI unit of resistivity is ohm-metre (Ω·m).

Physical meaning: The resistivity of a material equals the resistance of a cube of that material with side length 1 metre, measured across opposite faces. A higher resistivity means the material resists current more strongly.

Resistivity (ρ) is defined as the resistance offered by a conductor of unit length and unit cross-sectional area.

For Class 10: Resistivity is a property of the material, not of the object. Two wires of the same material (e.g., both copper) have the same resistivity, regardless of their length or thickness. But their resistance will differ based on their dimensions.

Formula connections: • R = ρL/A → resistance increases with length and decreases with area • ρ = RA/L → resistivity is material-specific

Temperature dependence: • Metals: resistivity increases with temperature (more thermal vibration of atoms impedes electron flow) • Semiconductors: resistivity decreases with temperature (more charge carriers generated) • Insulators: resistivity very high, largely temperature-independent at room temperature

Dimensional formula: [ρ] = [R][A]/[L] = (ML²T⁻³A⁻²)(L²)/(L) = ML³T⁻³A⁻²

Material | Resistivity (Ω·m) | Category Silver | 1.6 × 10⁻⁸ | Best conductor Copper | 1.7 × 10⁻⁸ | Excellent conductor (used in wires) Gold | 2.4 × 10⁻⁸ | Conductor (used in contacts) Aluminium | 2.8 × 10⁻⁸ | Conductor (used in overhead lines) Tungsten | 5.6 × 10⁻⁸ | Conductor (used in bulb filaments) Nichrome | 1.0 × 10⁻⁶ | High resistivity metal (used in heating elements) Germanium | 0.46 | Semiconductor Silicon | ~640 | Semiconductor Glass | 10¹⁰ – 10¹⁴ | Insulator Rubber | 10¹³ – 10¹⁶ | Insulator Ebonite | 10¹⁵ – 10¹⁷ | Excellent insulator

Key observations: • Silver has the lowest resistivity → best conductor, but expensive • Copper is used in electrical wiring due to its low cost and low resistivity • Nichrome is used in heating elements (electric irons, geysers) because of its high resistivity and high melting point • Semiconductors have intermediate resistivity between conductors and insulators

Property | Resistance (R) | Resistivity (ρ) Definition | Opposition to current in a specific conductor | Intrinsic material property — opposition per unit dimensions SI unit | Ohm (Ω) | Ohm-metre (Ω·m) Depends on | Length, area, material, temperature | Material and temperature only Formula | R = ρL/A | ρ = RA/L Changes with shape/size? | Yes | No

Example: Two copper wires: • Wire 1: length 1 m, area 1 mm² → R = 1.7 × 10⁻⁸ × 1 / 10⁻⁶ = 0.017 Ω • Wire 2: length 2 m, area 1 mm² → R = 0.034 Ω (double the resistance) • Both have the same resistivity: 1.7 × 10⁻⁸ Ω·m (property of copper, not the wire)