26.4: Resistivity
When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The current density that results depends on the electrical field and the properties of the material. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as:
where σ is the electrical conductivity and is represented by (Ω·m)−1. Electrical conductivity is analogous to thermal conductivity and is a measure of a material’s ability to conduct or transmit electricity. Conductors have a higher electrical conductivity than insulators. Conductivity is an intrinsic property of a material. Another intrinsic property of a material is its resistivity, or electrical resistivity. The resistivity of a material is a measure of how strongly a material opposes the flow of electrical current. Resistivity can be stated as the reciprocal of electrical conductivity and is represented by the Greek letter rho, ρ. The unit of resistivity in SI units is the ohm-meter. Resistivity can also be defined as the ratio of the electrical field and the current density. The greater the resistivity, the larger the field needed to produce a given current density. The lower the resistivity, the larger the current density produced by a given electrical field. As listed in Table 1, good conductors show high conductivity and low resistivity, whereas good insulators show low conductivity and high resistivity.
Table 1: Lists resistivity and conductivity values for various materials.
| Materials | Conductivity, σ ( Ω · m)−1 |
Resistivity, ρ ( Ω · m) |
Temperature Coefficient, α (°C)−1 |
| Silver | 6.29 × 107 | 1.59 × 10−8 | 0.0038 |
| Copper | 5.95 × 107 | 1.68 × 10−8 | 0.0039 |
| Gold | 4.10 × 107 | 2.44 × 10−8 | 0.0034 |
| Aluminum | 3.77 × 107 | 2.65 × 10−8 | 0.0039 |
| Tungsten | 1.79 × 107 | 5.60 × 10−8 | 0.0045 |
| Carbon (pure) | 2.86 × 10−6 | 3.50 × 10−5 | −0.0005 |
| Silicon | 0.1 − 2300 | −0.07 | |
| Amber | 2.00 × 10−15 | 5 × 1014 | |
| Glass | 10−9 − 10−14 | 109 − 1014 | |
| Lucite | <10−13 | >1013 |
