Question

Define resistivity of a material? How are materials classified on the basis of resistivity?

Answer 1

Concept Used: Resistance and resistivity

Step 1: Definition of resistivity:

Resistivity is the measure of opposition to the flow of current through a conductor ( i.e., resistance) per unit length and per unit cross-sectional area under a specified temperature. It is denoted by $\rho$.

Step 2: Formula for resistivity:

.$\mathrm{Resistivity}\mathrm{\rho }=\mathrm{R}\frac{\mathrm{A}}{l}$ (ohm-metre)

where, $\mathrm{R}$ = electrical resistance of the uniform cross-sectional (ohm)

$\mathrm{A}$= Area of cross section of the material (m²)

$l$= length of the material (m)

Step 3: Derivation of SI unit of resistivity using the formula:

SI unit of resistance is ohm $\left(\Omega \right)$

SI unit of length is meter $\left(\mathrm{m}\right)$

SI unit of cross-sectional area is metre² $\left({\mathrm{m}}^2\right)$

Substituting SI units in the formula,

$$\begin{gathered} \mathrm{Resistivity}\mathrm{\rho }=\mathrm{ohm}\left(\mathrm{\Omega }\right)\times \frac{{\mathrm{metre}}^2\left({\mathrm{m}}^2\right)}{\mathrm{metre}\left(\mathrm{m}\right)} \\ \mathrm{Resistivity}\mathrm{\rho }=\mathrm{ohm}·\mathrm{metre}\left(\mathrm{\Omega }·\mathrm{m}\right) \end{gathered}$$

The SI unit of resistivity $\rho$ is ohm-meter ($\mathrm{\Omega }·\mathrm{m}$)

Step 4: Classification of materials based on resistivity:

Resistivity varies from material to material. Based on their resistivity the materials are classified into three types. They are

• Conductors
• Insulators
• Semiconductors

Step 5: Explanation of the types of materials based on resistivity:

Conductors:

Materials having low resistivity allow the electric charge or electric current to flow through it, called conductors. In conductors, the resistivity increases with an increase in temperature: Examples of conductors are Gold, Silver, Copper, Iron, etc.

Insulators:

Materials having high resistivity do not allow the electric charge or electric current to flow through it, called Insulators. In insulators, the resistivity decreases with an increase in temperature: Examples of insulators are rubber, glass, plastics, etc.

Semiconductors

Semiconductor materials are materials that have moderate resistivity between conductor and insulator. In semiconductors, the resistivity decreases with an increase in temperature.

Examples of semiconductors are silicon, Germanium, Nichrome, etc.