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Resistivity

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Electrical resistivity is an intrinsic property of a material, describing how effectively it resists the flow of charges.

Resistivity is the reciprocal of electrical conductivity and can be defined in terms of the electrical field and the current density. The SI unit of resistivity is the ohm-meter.

Good conductors have a high conductivity but a low resistivity, whereas good insulators have a low conductivity but a high resistivity.

Temperature influences the resistivity of some materials. In many materials, the dependence is approximately linear and can be modeled using a linear equation where ρ is the resistivity of the material at a temperature, α is the temperature coefficient of the material, and ρ₀ is the resistivity at room temperature.

The resistivity of some materials, such as copper, increases as temperature increases; in others, like carbon, resistivity decreases as temperature increases.

In semiconductors, the temperature coefficient is negative, implying that resistivity decreases as temperature increases.

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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:

Ohm's Law, current density equation, J=σE, symbol, electromagnetism concept

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

Transcript

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