Question

$[M{L}^3{T}^{-3}{A}^{-2}]$ is the dimensional formula of

• A. resistance
• B. resistivity
• C. conductance
• D. conductivity

Answer 1

Answer: (B)

Resistances $=\frac{\text{Potential difference}}{\text{Current}}$
$=\frac{\left[M{L}^2{T}^{-3}{A}^{-1}\right]}{\left[A\right]}=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
Resistivity $=\frac{\text{Resistance × Area}}{\text{Length}}$
$=\frac{\left[M{L}^2{T}^{-3}{A}^{-2}\left[L^2\right]\right]}{\left[L\right]}=\left[M{L}^3{T}^{-3}{A}^{-2}\right]$
Conductance $=\frac{1}{\text{Resistivity}}=\left[M^{-1}{L}^{-3}{T}^3{A}^2\right]$
$\therefore \left[M{L}^3{T}^{-3}{A}^{-2}\right]$ is the dimensional formula of resistivity.