3.7 Resistivity of Various Materials

The materials are classified as conductors, semiconductors, and insulators depending on their resistivities, in an increasing order of their values. Metals have low resistivities in the range of \(10^{-8} \Omega m\) to \(10^{-6} \Omega m\). At the other end are insulators like ceramic, rubber, and plastics having resistivities \(10^{18}\) times greater than metals or more. In between the two are the semiconductors. These, however, have resistivities characteristically decreasing with a rise in temperature. The resistivities of semiconductors can be decreased by adding a small amount of suitable impurities which we will study in semiconductors for electronic devices chapter.

Electrical resistivity is the reciprocal of electrical conductivity. It is the measure of the ability of a material to oppose the flow of current.

• Metals are good conductors of electricity. Hence, they have low resistivity.
• The insulators like rubber, glass, graphite, plastics, etc. have very high resistivity when compared to the metallic conductors.
• The third type is the semiconductor which comes in between the conductors and insulators. Their resistivity decreases with the increase in temperature and is also affected by the presence of impurities in them.

The table below lists the electrical resistivity of several conductors, semiconductors, and insulators.

\(
\begin{array}{|l|l|}
\hline \text { Material } & \text { Resistivity } \rho \text { (ohm m) } \\
\hline \text { Silver } & 1.59 \times 10^{-8} \\
\hline \text { Copper } & 1.68 \times 10^{-8} \\
\hline \text { Copper, Annealed } & 1.72 \times 10^{-8} \\
\hline \text { Aluminium } & 2.65 \times 10^{-8} \\
\hline \text { Tungsten } & 5.6 \times 10^{-8} \\
\hline \text { Iron } & 9.71 \times 10^{-8} \\
\hline \text { Platinum } & 10.6 \times 10^{-8} \\
\hline \text { Manganin } & 48.2 \times 10^{-8} \\
\hline \text { Lead } & 22 \times 10^{-8} \\
\hline \text { Mercury } & 98 \times 10^{-8} \\
\hline \text { Nichrome (Ni.Fe.Cr) } & 100 \times 10^{-8} \\
\hline \text { Constantan } & 49 \times 10^{-8} \\
\hline \text { Carbon }^* \text { (graphite) } & 3-60 \times 10^{-5} \\
\hline \text { Germanium }^* & 1-500 \times 10^{-3} \\
\hline \text { Silicon }^* & 0.1-60 \\
\hline \text { Glass } & 1-10000 \times 10^9 \\
\hline \text { Quartz (fused) } & 7.5 \times 10^{17} \\
\hline \text { Hard rubber } & 1-100 \times 10^{13} \\
\hline
\end{array}
\)

Resistivity Formula

Materials having electric field and current density will have the following resistivity formula:
\(
\rho=\frac{E}{J}
\)
Where,
\(\rho\) is the resistivity of the material in \(\Omega . m\)
\(E\) is the magnitude of the electric field in \(V.m ^{-1}\)
\(J\) is the magnitude of current density in \(A.m^2\)

Conductors with a uniform cross-section and uniform flow of electric current will have the following resistivity formula:
\(
\rho=R \frac{A}{l}
\)
Where,
\(\rho\) is the resistivity of the material in \(\Omega . m\)
\(R\) is the electrical resistance of uniform cross-sectional material in \(\Omega\)
\(l\) is the length of a piece of material in \(m\)
\(A\) is the cross-sectional area of the material in \(m ^2\)

Resistivity Dimension

Following is the unit of resistivity: In  CGS unitit is \(\Omega . cm\) and in SI unit it is \(\Omega . m\)

Dimension of resistivity : \(M ^1 L^3 T^{-3} A^{-2}\)