Question

The electrical resistance R of a conductor of length $I$ and area of cross section a is given by $R = \frac{\rho l}{a}$ where $‘\rho’$ is the electrical resistivity. What is the dimensional formula for electrical conductivity ‘\sigma’ which is reciprocal of resistivity?

• A. $\left[M^{-1}L^{-3}T^{3}A^{2}\right]$
• B. $\left[ML^{-3}T^{3}A^{2}\right]$
• C. $\left[ML^{3}T^{-3}A^{-2}\right]$
• D. $\left[M^{-2}L^{3}T^{2}A^{-1}\right]$

Answer 1

Answer: (A)

Dimensional formula for electrical resistivity, $\rho = \left[ML^{3}T^{-3}A^{-2}\right]$
Dimensional formula for electrical conductivity, $\sigma = \frac{1}{\rho}$ is $\left[M^{-1}L^{-3}T^{3}A^{2}\right]$