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

Options

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

Explanation

To find the SI unit of inductance, the henry (H), we can analyze the relationship between magnetic flux, current, and inductance. Here’s a step-by-step solution:

### Step 1: Understand the definition of inductance
Inductance (L) is defined as the ratio of magnetic flux (Φ) linked with a coil to the current (I) flowing through it. Mathematically, this can be expressed as:
\[ L = \frac{\Phi}{I} \]

### Step 2: Identify the SI units involved
- The SI unit of magnetic flux (Φ) is the weber (Wb).
- The SI unit of current (I) is the ampere (A).

### Step 3: Substitute the units into the formula
Using the definition of inductance, we can express the unit of inductance as:
\[ \text{Unit of } L = \frac{\text{Unit of } \Phi}{\text{Unit of } I} = \frac{\text{Wb}}{\text{A}} \]

### Step 4: Analyze other options
Now, let’s analyze the other options provided in the question:
1. **Volt-second per ampere (V·s/A)**:
- We know that 1 V = 1 W/A = 1 J/C. Therefore,
\[ \text{V·s} = \text{J} \]
- Thus,
\[ \text{V·s/A} = \frac{\text{J}}{\text{C}} \]
- Since 1 C = 1 A·s, this simplifies to:
\[ \text{V·s/A} = \frac{\text{J}}{\text{A·s}} = \text{Wb/A} \]
- Hence, this is equivalent to Wb/A.

2. **Joule per ampere squared (J/A²)**:
- Using Joule’s law, we can express this as:
\[ \text{J/A²} = \frac{\text{Energy}}{\text{Current}^2} \]
- This can also be related back to the units of inductance.

3. **Resistance times time (R·T)**:
- Resistance (R) has units of ohms (Ω), which can be expressed as V/A. Thus:
\[ R·T = \text{(V/A)}·\text{s} \]
- This also simplifies down to units that relate back to Wb/A.

### Step 5: Conclusion
Since all the derived units from the options can be shown to be equivalent to Wb/A, we conclude that:
- The SI unit of inductance, the henry, can indeed be expressed in multiple forms:
1. Weber per ampere (Wb/A)
2. Volt-second per ampere (V·s/A)
3. Joule per ampere squared (J/A²)
4. Resistance times time (R·T)

Thus, all options are correct.