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 follow these steps:

### Step-by-Step Solution:

1. **Definition of Henry**:
The henry (H) is defined as the amount of inductance in a circuit where a change in current of one ampere per second induces an electromotive force (EMF) of one volt.
\[ 1 \, \text{H} = \frac{1 \, \text{V}}{1 \, \text{A/s}} \]

2. **Using the Formula for Induced EMF**:
The formula for induced EMF (E) in terms of inductance (L) and the rate of change of current (di/dt) is given by:
\[ E = L \frac{di}{dt} \]
Rearranging this gives:
\[ L = \frac{E}{\frac{di}{dt}} \]

3. **Substituting Units**:
Substituting the units into the equation:
- EMF (E) is measured in volts (V).
- Current (I) is measured in amperes (A).
- Time (t) is measured in seconds (s).
Thus, we have:
\[ L = \frac{\text{V}}{\text{A/s}} = \text{V} \cdot \frac{\text{s}}{\text{A}} = \text{V} \cdot \text{s} \cdot \text{A}^{-1} \]

4. **Expressing Volt in Terms of Ohm**:
We know that:
\[ \text{V} = \text{I} \cdot \text{R} \]
where R is resistance measured in ohms (Ω). Therefore, substituting this into our equation gives:
\[ L = \frac{\text{I} \cdot \text{R} \cdot \text{s}}{\text{A}} = \text{R} \cdot \text{s} \]
Since the unit of current (I) is in amperes, we can simplify this to:
\[ L = \text{Ω} \cdot \text{s} \]

5. **Using Magnetic Flux**:
The inductance can also be expressed in terms of magnetic flux (Φ) and current (I):
\[ L = \frac{\Phi}{I} \]
Here, magnetic flux is measured in webers (Wb). Thus, we can express L as:
\[ L = \frac{\text{Wb}}{\text{A}} \]

6. **Energy Stored in Inductance**:
The energy (U) stored in an inductor is given by:
\[ U = \frac{1}{2} L I^2 \]
Rearranging gives:
\[ L = \frac{2U}{I^2} \]
Since energy is measured in joules (J), we have:
\[ L = \frac{2 \, \text{J}}{\text{A}^2} \]

7. **Final Summary of Units**:
From the above steps, we can summarize that the henry (H) can be expressed in various forms:
- \( \text{H} = \text{V} \cdot \text{s} \cdot \text{A}^{-1} \)
- \( \text{H} = \text{Ω} \cdot \text{s} \)
- \( \text{H} = \frac{\text{Wb}}{\text{A}} \)
- \( \text{H} = \frac{\text{J}}{\text{A}^2} \)