Question

Is resistivity directly proportional to the resistance?

Answer 1

Resistance is defined as the obstruction or blockage of the flow of electric current. Resistivity is defined as the resistance per unit cross-sectional area to unit length. We will find their proportionality from their respective equations.

Complete step-by-step solution:
Resistance is defined as the ability to obstruct or block the flow of electric current. Its unit is $ohm$. It is expressed by $\Omega$.
Resistance is denoted by $R$.
Resistivity is the resistance per unit cross-sectional area to unit length. Resistivity is a property of the material. A high resistive material is the one that does not allow the flow of electrons or electricity through themselves freely. Its unit is $ohm.m$. It is denoted by $\rho$.
The expression of resistivity is $\rho = \dfrac{{RA}}{l}$ where $R =$ resistance, $A =$ area of cross-section and $l =$ length.
From the expression it is clear that,
$\rho \propto R$ if $\dfrac{l}{A}$ is constant.
Additional information: The resistivity of an exceedingly good electrical conductor, such as hard-drawn copper, at ${20^ \circ }{\text{ }}C$ is$1.77 \times {10^{ - 8}}{\text{ }}ohm - meter$, or 1.77 × 10-6. At the other extreme, electrical insulators have resistivities in the range${10^{12}} - {10^{20}}{\text{ }}ohm - meters$.
Like resistivity, there is also conductivity which is the reciprocal of resistivity. Conductivity refers to the ability of a material to conduct current. It is expressed as $\sigma = \dfrac{1}{\rho }$.

Note: The value of resistivity depends on the temperature of the material. Tabulations of resistivities usually list values at ${20^ \circ }{\text{ }}C$. Resistivity of metallic conductors generally increases with a rise in temperature but resistivity of semiconductors, such as carbon and silicon, generally decreases with rise in temperature.