The SI unit of inductance, the henry can be written as

Step 1: Use the magnetic flux relation.

The magnetic flux $\Phi$ is proportional to the current $I$.

$$\Phi = L I$$ $$L = \frac{\Phi}{I}$$ $$[L] = \frac{\text{weber}}{\text{ampere}}$$

Step 2: Use the induced electromotive force relation.

The induced electromotive force $e$ is related to the rate of change of current.

$$e = -L \frac{dI}{dt}$$ $$L = \frac{|e|}{\left|\frac{dI}{dt}\right|}$$ $$[L] = \frac{\text{volt} \cdot \text{second}}{\text{ampere}}$$

Step 3: Use the stored magnetic energy relation.

The energy $U$ stored in an inductor depends on the current.

$$U = \frac{1}{2} L I^{2}$$ $$L = \frac{2U}{I^{2}}$$ $$[L] = \frac{\text{joule}}{\text{ampere}^{2}}$$

Step 4: Use the $RL$ circuit time constant relation.

The time constant $\tau$ of a series $RL$ circuit depends on resistance $R$ and inductance $L$.

$$\tau = \frac{L}{R}$$ $$L = R \tau$$ $$[L] = \text{ohm} \cdot \text{second}$$

Step 5: Compare the units.

All four derived units represent the henry ($\text{H}$).

$$1 \text{ H} = \frac{\text{weber}}{\text{ampere}} = \frac{\text{volt} \cdot \text{second}}{\text{ampere}} = \frac{\text{joule}}{\text{ampere}^{2}} = \text{ohm} \cdot \text{second}$$

Answer: The henry ($\text{H}$) can be written as $\dfrac{\text{weber}}{\text{ampere}}$, $\dfrac{\text{volt} \cdot \text{second}}{\text{ampere}}$, $\dfrac{\text{joule}}{\text{ampere}^{2}}$, or $\text{ohm} \cdot \text{second}$.