The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by…
The electrical resistance $R$ of a conductor of length $l$ 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?
$\left[M^{-1} L^{-3} T^3 A^2\right]$
$\left[M L^{-3} T^{-3} A^2\right]$
$\left[M L^3 T^{-3} A^{-2}\right]$
$\left[M^{-2} L^3 T^2 A^{-1}\right]$
Solution
Dimensional formula for electrical resistivity, $\rho=\left[\mathrm{ML}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-2}\right]$ Dimensional formula for electrical conductivity, $\sigma=\frac{1}{\rho}$ is $\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^3 \mathrm{~A}^2\right]$