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

Options

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

Explanation

To find the SI unit of inductance, which is the henry (H), we can derive it step by step from the definitions of magnetic flux and current.

### Step-by-Step Solution:

1. **Understanding Inductance**:
- Inductance (L) is a property of an electrical circuit that opposes changes in current. It is defined in terms of the magnetic flux (Φ) linked with the circuit and the current (I) flowing through it.

2. **Formula for Inductance**:
- The relationship between magnetic flux and inductance can be expressed as:
\[ \Phi = L \cdot I \]
- Rearranging this gives us:
\[ L = \frac{\Phi}{I} \]

3. **Units of Magnetic Flux and Current**:
- The unit of magnetic flux (Φ) is the weber (Wb).
- The unit of current (I) is the ampere (A).

4. **Substituting Units into the Inductance Formula**:
- Substituting the units into the formula for inductance:
\[ L = \frac{\text{Wb}}{\text{A}} \]
- Therefore, we can express the unit of inductance (henry) as:
\[ 1 \text{ H} = 1 \frac{\text{Wb}}{\text{A}} \]

5. **Alternative Expressions for Inductance**:
- We can also derive the unit of inductance using the relationship with induced electromotive force (emf):
\[ E = L \frac{dI}{dt} \]
- Rearranging gives:
\[ L = \frac{E}{\frac{dI}{dt}} \]
- The unit of emf (E) is the volt (V), which can also be expressed as:
\[ 1 \text{ V} = 1 \frac{\text{J}}{\text{s}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^3} \]
- Thus, substituting this into the inductance formula gives:
\[ L = \frac{\text{V}}{\text{A}} \cdot \text{s} = \frac{\text{J/s}}{\text{A}} \cdot \text{s} = \frac{\text{J}}{\text{A} \cdot \text{s}} = \frac{\text{kg} \cdot \text{m}^2}{\text{s}^2 \cdot \text{A}} \]

6. **Final Result**:
- Therefore, we conclude that the SI unit of inductance, the henry, can be expressed in multiple ways:
\[ 1 \text{ H} = 1 \frac{\text{Wb}}{\text{A}} = 1 \frac{\text{V} \cdot \text{s}}{\text{A}} = 1 \frac{\text{J}}{\text{A} \cdot \text{s}} = 1 \frac{\text{kg} \cdot \text{m}^2}{\text{s}^2 \cdot \text{A}} \]