Question

Define specific resistance and state its SI unit.

Answer 1

Hint: The specific resistance of a material is an inherent characteristic property of the material. Its mathematical formula can be written in terms of a body of some resistance and its length and cross sectional area. Its SI unit can be found out by using the SI units of resistance, length and cross sectional area in the proper formula.

Formula used:
$\rho =R\dfrac{A}{l}$

Complete step-by-step solution -
As explained in the hint, the specific resistance or resistivity of a material is defined as the resistance of a body of unit length and cross sectional area made of that material. It is a constant characteristic property of the material.
Hence, mathematically, it is expressed as,
$\rho =R\dfrac{A}{l}$ ---(1)
where $\rho $ is the specific resistance of the material of which a resistor of resistance $R$, length $l$ and cross sectional area $A$ is made.
The SI unit of specific resistance can be found by plugging in the SI units of the quantities in the right hand side of equation (1).
Hence, let us proceed to do that.
The SI unit of resistance is Ohm $\left( \Omega \right)$.
The SI unit of length is metre $\left( m \right)$.
The SI unit of cross sectional area is metre-squared $\left( {{m}^{2}} \right)$.
Therefore putting these values in (1), we get,
$\text{SI unit of specific resistance = }\Omega \times \dfrac{{{m}^{2}}}{m}=\Omega .m$
Hence, the SI unit of specific resistance is Ohm-metre $\left( \Omega .m \right)$.

Note: Students must remember that the specific resistance of a material changes with temperature. In metals, the specific resistance increases with increase in temperature and hence, metals are said to have a positive temperature coefficient of resistivity. On the other hand, the specific resistance of semiconductors decreases with increase in temperature. Hence, semiconductors are said to have a negative temperature coefficient of resistivity. This is a very important point and many questions are made based upon this concept.