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

Options

A. weber/ampere
B. volt-second/ampere
C. `J/A^(2)`
D. ohm-second

Explanation

To determine the SI unit of inductance, which is the henry (H), we can express it in different forms based on the relationships involving magnetic flux, current, and energy. Let's analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Inductance**:
- Inductance (L) is defined as the ratio of magnetic flux (Φ) linked with a circuit to the current (I) flowing through it. The formula is:
\[ L = \frac{\Phi}{I} \]

2. **Option A: Weber per Ampere**:
- The unit of magnetic flux (Φ) is the weber (Wb). Therefore, substituting the units into the formula:
\[ L = \frac{\text{Wb}}{\text{A}} \quad \text{(where A is ampere)} \]
- Thus, option A can be expressed as:
\[ 1 \, \text{H} = 1 \, \text{Wb/A} \]
- **Conclusion**: Option A is correct.

3. **Option B: Volt Second per Ampere**:
- The electromotive force (EMF) induced in a circuit can be expressed as:
\[ \text{EMF} = -L \frac{dI}{dt} \]
- Rearranging gives:
\[ L = -\frac{\text{EMF}}{dI/dt} \]
- The unit of EMF is volt (V), and \(dI/dt\) has units of A/s. Thus:
\[ L = \frac{\text{V} \cdot \text{s}}{\text{A}} \quad \text{(where s is seconds)} \]
- **Conclusion**: Option B is also correct.

4. **Option C: Joule per Ampere Square**:
- The energy (U) stored in an inductor is given by:
\[ U = \frac{1}{2} L I^2 \]
- Rearranging gives:
\[ L = \frac{2U}{I^2} \]
- The unit of energy (U) is joules (J), and \(I^2\) has units of A². Therefore:
\[ L = \frac{\text{J}}{\text{A}^2} \]
- **Conclusion**: Option C is correct.

5. **Option D: Ohm Second**:
- Inductance can also be related to resistance (R) and time (T):
\[ L = R \cdot T \]
- The unit of resistance is ohms (Ω), and time is in seconds (s), thus:
\[ L = \text{Ω} \cdot \text{s} \]
- **Conclusion**: Option D is correct.

### Final Conclusion:
All four options (A, B, C, and D) are valid representations of the SI unit of inductance, henry (H).