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

Answer

To determine the SI unit of inductance, known as the henry (H), we can analyze each of the options provided in the question.

### Step-by-Step Solution:

1. **Understanding Inductance**:
- Inductance (L) is defined as the ratio of magnetic flux linkage to the current flowing through the coil. Mathematically, it can be expressed as:
\[ L = \frac{\Phi}{I} \]
where \( \Phi \) is the magnetic flux in webers (Wb) and \( I \) is the current in amperes (A).

2. **Analyzing the First Option (Weber per Ampere)**:
- From the definition of inductance:
\[ L = \frac{\Phi}{I} \implies L = \frac{\text{Wb}}{\text{A}} \]
- Thus, the first option, Weber per Ampere (Wb/A), is indeed a valid representation of henry.

3. **Analyzing the Second Option (Volt Second per Ampere)**:
- The electromotive force (EMF) is related to inductance by the equation:
\[ E = -L \frac{dI}{dt} \]
- Rearranging gives:
\[ L = \frac{E \cdot dt}{dI} \]
- The unit of EMF (E) is volts (V), the unit of time (dt) is seconds (s), and the unit of current change (dI) is amperes (A). Therefore:
\[ L = \frac{\text{V} \cdot \text{s}}{\text{A}} \implies L = \text{V s/A} \]
- This confirms that the second option, Volt Second per Ampere (V·s/A), is also a valid representation of henry.

4. **Analyzing the Third Option (Joule per Ampere Square)**:
- The energy stored in an inductor can be expressed as:
\[ U = \frac{1}{2} L I^2 \]
- Rearranging gives:
\[ L = \frac{2U}{I^2} \]
- The unit of energy (U) is joules (J), and the unit of current squared (I²) is amperes squared (A²). Thus:
\[ L = \frac{\text{J}}{\text{A}^2} \implies L = \text{J/A}^2 \]
- This means that the third option, Joule per Ampere Square (J/A²), is also a valid representation of henry.

5. **Analyzing the Fourth Option (Ohm per Second)**:
- The relationship between inductance, resistance (R), and time (t) can be expressed as:
\[ L = R \cdot t \]
- The unit of resistance (R) is ohms (Ω), and the unit of time (t) is seconds (s). Therefore:
\[ L = \text{Ω} \cdot \text{s} \]
- This confirms that the fourth option, Ohm per Second (Ω·s), is also a valid representation of henry.

### Conclusion:
All four options (Weber per Ampere, Volt Second per Ampere, Joule per Ampere Square, and Ohm per Second) can be expressed as the unit of inductance, henry (H).