Question

The dimensional formula for inductance is:

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

Answer 1

The correct option is A $\left[M^1{L}^2{T}^{-2}{A}^{-2}\right]$

We know that energy stored in an inductor $=\frac{1}{2}L{I}^2$

Hence, dimensions of $\frac{1}{2}L{I}^2$ are that of energy.

$⟹$ Dimensions of $\frac{1}{2}L{I}^2=\left[M^1{L}^2{T}^{-2}\right]$

$⟹$ Dimensions of $L=\left[M^1{L}^2{T}^{-2}{A}^{-2}\right]$