A

The unit of self-inductance, denoted as $L$, can be derived from the energy stored in an inductor given by the formula $U = \frac{1}{2} L i^2$, where $U$ is energy, $L$ is self-inductance, and $i$ is current.
If we rearrange this formula, we find:
$$ L = \frac{2U}{i^2} $$
The SI unit of energy ($U$) is the joule (J), and the SI unit of current ($i$) is the ampere (A). Therefore, substituting the units, we get:
$$ [L] = \frac{2 \text{ joules}}{\text{ amperes}^2} = \frac{2 \text{ kg m}^2 / s^2}{A^2} = \frac{\text{ kg m}^2}{\text{s}^2 \text{ A}^2} $$
This leads us to conclude that the units of self-inductance can be expressed as henrys (H), where 1 H = 1 \( \frac{\text{kg m}^2}{\text{s}^2 A^2} \). Thus, the correct representation of a unit of self-inductance involves a basic combination of fundamental SI units, illustrated in Option A.