Question

Dimensions of ohm are same as (where $h$ is Planck's constant and $e$ is charge)

• A. $\frac{h}{e}$
• B. $\frac{h^2}{e}$
• C. $\frac{h}{e^2}$
• D. $\frac{h^2}{e^2}$

Answer 1

Answer: (C)

$\left[\frac{h}{e^2}\right]=\frac{\left[M{L}^2{T}^{-1}\right]}{{\left[AT\right]}^2}=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
[Resistance] $=\frac{\text{[Potential difference]}}{\text{[Current]}}$
$=\frac{\left[M{L}^2{T}^{-3}{A}^{-1}\right]}{\left[A\right]}=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
The $SI$ unit of resistance is ohm
Therefore, the dimensions of ohm are same as that of $\frac{h}{e^2}$