Question

The dimensions of electrical conductivity are,

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

Answer 1

The correct option is A

$\left[M^{-1}{L}^{-3}{T}^3{A}^2\right]$

Step 1: Given data

A material's electrical conductivity, or capacity to carry a current, is a measure of how much electrical current it can transport.

Dimension of electric conductivity$=\left[M^{-1}{L}^{-2}{T}^3{A}^2\right]$

Step 2: Concept Used

Use the formula of the electrical conductivity:

Therefore the electrical conductivity$=\frac{1}{R}$

Know that, $R=\frac{V}{I}$, where $R=$resistance, $V=$potential difference, and $I=$current

Now the electrical conductivity, $\frac{1}{R}=\frac{I}{V}$

Therefore the dimension of $V=\frac{W}{Q}$, where $W=$work, and $Q=$charge.

$\begin{array}{rcl}V& =& \frac{\left[M{L}^2{T}^{-2}\right]}{\left[IT\right]}\\ & =& \left[M{L}^2{T}^{-3}{I}^{-1}\right]\end{array}$

Step 3: Calculation

Therefore the dimension of electrical conductivity will be,

$\begin{array}{rcl}\frac{I}{V}& =& \frac{\left[I\right]}{\left[M{L}^2{T}^{-3}{I}^{-1}\right]}\\ & =& \left[M^{-1}{L}^{-2}{T}^3{I}^2\right]\end{array}$

Therefore the dimension of the electrical conductivity is, $\left[M^{-1}{L}^{-2}{T}^3{A}^2\right]$.

Hence, the correct option is (B).