If number of turns in a coil is quadrupled, then self-inductance will be:

Options

A. doubled
B. four times
C. remains the same
D. sixteen times

Explanation

To solve the problem, we need to understand the relationship between the self-inductance \( L \) of a coil and the number of turns \( n \) in that coil. The self-inductance is given by the formula:

\[ L \propto n^2 \]

This means that the self-inductance \( L \) is directly proportional to the square of the number of turns \( n \).

### Step-by-Step Solution:

1. **Identify the Initial Number of Turns**:
Let the initial number of turns in the coil be \( n \).

2. **Quadruple the Number of Turns**:
If the number of turns is quadrupled, the new number of turns becomes:
\[ n' = 4n \]

3. **Express the Relationship of Self-Inductance**:
Since self-inductance is proportional to the square of the number of turns, we can write:
\[ L \propto n^2 \]

4. **Calculate the New Self-Inductance**:
The new self-inductance \( L' \) when the number of turns is \( n' \) can be expressed as:
\[ L' \propto (n')^2 = (4n)^2 = 16n^2 \]

5. **Relate the New Self-Inductance to the Old**:
Since \( L \propto n^2 \), we can represent the old self-inductance as \( L = k n^2 \) for some constant \( k \). Then:
\[ L' = k (4n)^2 = k \cdot 16n^2 = 16L \]

6. **Conclusion**:
Therefore, the new self-inductance \( L' \) is:
\[ L' = 16L \]
This means that if the number of turns in a coil is quadrupled, the self-inductance will be **16 times** the original self-inductance.

### Final Answer:
The self-inductance will be **16 times** the original self-inductance.