Question

The dimensions of the coefficient of self-inductance are

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

Answer 1

Answer: (A)

Energy $U=\frac{1}{2}L{I}^2$
$\Rightarrow L=\frac{2U}{I^2}$
$\therefore \left[L\right]=\frac{\left[U\right]}{{\left[I\right]}^2}=\frac{\left[M{L}^2{T}^{-2}\right]}{{\left[A\right]}^2}=\left[M{L}^2{T}^{-2}{A}^{-2}\right]$