Question

The dimensional formula for resistivity of conductor is

A. $\left[ {M{L^2}{T^{ - 2}}{A^{ - 2}}} \right]$

B. $\left[ {M{L^3}{T^{ - 3}}{A^{ - 2}}} \right]$

C. $\left[ {M{L^{ - 2}}{T^{ - 2}}{A^2}} \right]$

D. $\left[ {M{L^2}{T^{ - 2}}{A^{ - 3}}} \right]$

Answer 1

Hint: First we have to know what resistivity is:
Resistivity is an electrical opposition of a conductor of unit cross-sectional area and unit length. A trademark property of every material, resistivity is helpful in contrasting different materials based on their capacity to channel electric flows. High resistivity means poor conductors.
Now we have to know the formula for resistivity to find the dimension.

Complete step by step answer:
Resistance, usually symbolised by the Greek letter $\rho $, is quantitatively equivalent to the resistance $R$ of a specimen, such as wire, compounded by its cross-section area $A$, and divided by its length $l$; $\rho = \dfrac{{RA}}{l}$. The resistance unit is ohm.
In the meter-kilogram-second (mks) framework, the proportion of area in square meters to length in meters rearranges to simply meters. Accordingly, in the meter-kilogram-second framework, the unit of resistivity is ohm-meter. In the event that lengths are estimated in centimetres, resistivity might be communicated in units of ohm-centimetre.
The estimation of resistivity relies additionally upon the temperature of the material; arrangements of resistivities ordinarily list values at 20° C. Resistivity of metallic conduits by and large increments with a rise in temperature; however resistivity of semiconductors, for example, carbon and silicon, for the most part lowers with temperature rise.
Good electrical conductors have high conductivity and low resistance. Good insulators or dielectrics have high resistance and low conductivity. Semiconductors have intermediate values for each of them.
The formula for resistivity is:
Resistivity = $\dfrac{{\text{resistance}} \times {\text{area}}}{\text{length}}$
$
   = \dfrac{{M{L^2}{T^{ - 3}}{A^{ - 2}} \times {L^2}}}{L} \\
   = \left[ {M{L^3}{T^{ - 3}}{A^{ - 2}}} \right] \\
$

Hence, option B is correct.

Note:When using the formula of resistivity we must pay attention to the unit and convert it to any standard form otherwise our result may be wrong.