Unit of self inductance is

Options

A. `("Newton-second")/("Coulomb"xx"Ampere")`
B. `("Joule"//"Coulomb"xx"Second")/("Ampere")`
C. `("Volt"xx"metre")/("Coulomb")`
D. `("Newton"xx"metre")/("Ampere")`

Answer

To determine the unit of self-inductance, we can start from the definition and formula related to self-inductance. The self-inductance \( L \) is defined in terms of the induced electromotive force (EMF) when the current through a coil changes.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The self-inductance \( L \) is defined by the equation:
\[ \text{EMF} = -L \frac{dI}{dt} \]
where:
- EMF is the induced electromotive force,
- \( I \) is the current,
- \( t \) is time.

2. **Rearranging the Formula**:
We can rearrange this equation to express \( L \):
\[ L = -\frac{\text{EMF}}{dI/dt} \]
Since we are interested in the unit of \( L \), we can ignore the negative sign as it indicates direction.

3. **Identifying Units**:
- The unit of EMF (voltage) is volts (V).
- The unit of current \( I \) is amperes (A).
- The unit of time \( t \) is seconds (s).

4. **Substituting Units**:
Now substituting the units into the equation:
\[ L = \frac{\text{Volts}}{\text{Amperes/Seconds}} = \frac{\text{Volts} \cdot \text{Seconds}}{\text{Amperes}} \]

5. **Expressing Volts in Basic Units**:
We know that:
\[ 1 \text{ Volt} = 1 \frac{\text{Joule}}{\text{Coulomb}} = 1 \frac{\text{Newton} \cdot \text{meter}}{\text{Coulomb}} \]
Thus, substituting this into our expression for \( L \):
\[ L = \frac{\text{Newton} \cdot \text{meter} \cdot \text{Seconds}}{\text{Amperes} \cdot \text{Coulomb}} \]

6. **Final Unit of Self-Inductance**:
Since \( 1 \text{ Coulomb} = 1 \text{ Ampere} \cdot \text{Second} \), we can simplify:
\[ L = \frac{\text{Newton} \cdot \text{meter} \cdot \text{Seconds}}{\text{Amperes} \cdot \text{(Amperes} \cdot \text{Seconds)}} = \frac{\text{Newton} \cdot \text{meter}}{\text{Amperes}^2} \]
Therefore, the unit of self-inductance is:
\[ \text{Henry (H)} = \text{Newton} \cdot \text{meter} \cdot \text{Seconds}^{-2} \cdot \text{Amperes}^{-2} \]

### Conclusion:
The unit of self-inductance is the **Henry (H)**.