C

Step 1: The inductance (L) of a coil is defined by the relationship between the induced voltage (V) across the coil and the rate of change of current (I) through it. The mathematical expression is given by:
$$ V = L \cdot \frac{dI}{dt} $$
Step 2: Rearranging this formula to express inductance gives us:
$$ L = \frac{V}{\frac{dI}{dt}} $$
Step 3: Here, $$ V $$ is in volts and $$ \frac{dI}{dt} $$ is in amperes per second. Thus, the units can be expressed as:
$$ \text{Unit of } L = \frac{\text{Volt}}{\text{Ampere/Second}} = \text{Volt} \cdot \frac{\text{Second}}{\text{Ampere}} $$
Hence, we can convert this to:
$$ L = \frac{\text{Volt} \cdot \text{Second}}{\text{Ampere}} $$
Therefore, the unit of inductance is Volt-Second/Ampere, which corresponds to Option C: Volt-sec/ampere.