Self inductance of a soleniod can be increased by

Options

A. increasing the current passing through the solenoid
B. decreasing the current passing through the solenoid
C. inserting an iron core in the solenoid
D. increasing number of turns per unit length

Answer

To determine how the self-inductance of a solenoid can be increased, we need to analyze the factors that influence it. The self-inductance \( L \) of a solenoid is given by the formula:

\[ L = \frac{n^2 \mu_0 A l}{l} \]

Where:
- \( n \) = number of turns per unit length
- \( \mu_0 \) = permeability of free space
- \( A \) = cross-sectional area of the solenoid
- \( l \) = length of the solenoid

### Step-by-Step Solution:

1. **Understanding Self-Inductance**:
Self-inductance is a property of a coil (or solenoid) that quantifies how much electromotive force (emf) is induced in the coil when the current through it changes.

2. **Identifying the Formula**:
The self-inductance \( L \) of a solenoid can be expressed as:
\[ L = \frac{n^2 \mu_0 A l}{l} \]
This shows that \( L \) depends on \( n \), \( \mu_0 \), \( A \), and \( l \).

3. **Analyzing Each Factor**:
- **Increasing Current**: The self-inductance \( L \) does not depend on the current \( I \). Thus, increasing or decreasing the current does not affect the self-inductance.
- **Inserting an Iron Core**: Inserting an iron core increases the permeability \( \mu \) of the solenoid. Since \( \mu = \mu_0 \mu_r \) (where \( \mu_r \) is the relative permeability), increasing \( \mu \) will increase \( L \).
- **Increasing Number of Turns**: Increasing the number of turns per unit length \( n \) increases \( L \) since \( L \) is proportional to \( n^2 \).
- **Changing Length**: The length \( l \) of the solenoid is in the denominator, so increasing the length will decrease \( L \).

4. **Conclusion**:
From the analysis, we conclude that the self-inductance of a solenoid can be increased by:
- Inserting an iron core (increasing permeability).
- Increasing the number of turns per unit length.

### Final Answer:
The self-inductance of a solenoid can be increased by:
- Inserting an iron core.
- Increasing the number of turns per unit length.