Question

The electrical conductivity,s is given by $\sigma =\frac{n{e}^2.T}{2m}$ where $n$ is equal to number of free electrons per cubic meter. $C$ is charge on electron $T$ is relaxation time and $m$ is mass of electron. The dimensional formula for $\sigma$ is :

• A. $M^{-1}{L}^{-3}{T}^3{A}^2$
• B. $M^1{L}^{-3}{T}^3{A}^2$
• C. $M^{-1}{L}^{-3}{T}^3{A}^{-2}$
• D. $M^{-1}{L}^{-2}{T}^3{A}^{-2}$

Answer 1

Answer: (A)

$M^{-1}{L}^{-3}{T}^3{A}^2$

$n=\frac{no.offree{e}^{-}}{m^3}=M^0{L}^{-3}{T}^0$
$e=A^1{T}^1$
$T=T^1$
$M=M^1$
$\sigma =\frac{n{e}^{2}T}{2m}=\frac{\left(L^{-3}\right)\left(I^2{T}^2\right)T^1}{2\left(M^1\right)}=M^{-1}{L}^{-3}{A}^2{T}^3$