13.3.4 Resistivity

A cylindrical carbon wire has length L, cross-sectional area A and resistance R. How do the dimensions of the wire affect its resistance?

If we double the length of the wire, it is like connecting two of them in series. The resistance will be doubled. So we conclude that R\propto L. If we double the area of the wire, it is like connecting two of them in parallel. The resistance will be halved. So we conclude R\propto \frac{1}{A}.

Hence we write

R=\rho \frac{L}{A}

The constant of proportionality r (pronounced rho) is called the resistivity. It is an intrinsic property of the material which is related to the mobile carrier concentration and the atomic structure of the material. Resistivity is also dependent on the temperature the material is at.

Tabulated below are the resistivity of some common materials. I am always amazed by the orders of magnitude difference between the resistivity of copper and glass.

MaterialCategoryResistivity at 20°C / \text{ }\!\!\Omega\!\!\text{ }.\text{m}
CopperConductor1.7\times {{10}^{{-8}}}
Carbon (graphite)Conductor3.5\times {{10}^{{-5}}}
WaterConductor2 to 200
SiliconSemiconductor6.4\times {{10}^{2}}
Skin (dry)Insulator3\times {{10}^{4}}
GlassInsulator1010 to 1014

Concept Test

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