Question

The dimensional formula for inductance is,

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

Answer 1

The correct option is A

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

Solution :

Step 1: Given that :

The formula of the inductance$L=\frac{\mu N^{2}A}{l}$, here $L$ is the inductance,$\mu$ permeability, $N$ number of turns in coil, $A$area encircled by coil, $l$ and length of the coil.

Step 2: Formula used:

The dimension of inductance

$$\begin{gathered} L=\frac{\mu N^{2}A}{l} \\ \left[L\right]=\frac{\left[M{L}^2{T}^{-3}\right]}{\left[A^2{T}^{-1}\right]} \\ \left[L\right]=\left[M{L}^2{T}^{-2}{A}^{-2}\right] \end{gathered}$$

Therefore the dimension of inductance is $\left[M{L}^2{T}^{-2}{A}^{-2}\right]$.

Hence, the correct option is A.