What is the unit of inductance?

The correct option is Volt-sec/ampere.

To understand why this is the correct unit of inductance, we can derive it from the fundamental electromagnetic relationship that defines self-inductance ($L$).

The induced voltage ($v$) across an inductor is proportional to the rate of change of current ($i$) flowing through it. This relationship is mathematically expressed by Faraday's law of induction in terms of inductance as:
$v=L\frac{di/dt}{}$

To find the unit of inductance ($L$), we can rearrange the formula to solve for $L$:
$L=\frac{v}{di/dt}=v·\frac{dt}{di}$

Now, let's substitute the standard SI units for the variables on the right-hand side of the equation:
- The unit of voltage ($v$) is Volt.
- The unit of time ($t$) is second.
- The unit of current ($i$) is ampere.

Substituting these units into our rearranged formula gives:
$\text{Unit of Inductance}=\frac{\text{Volt}·\text{second}}{\text{ampere}}$

This is commonly written as Volt-sec/ampere (which is equivalent to the Henry, the standard SI unit of inductance).