If `'N'` is the number of turns in a coil, the value of self inductance varies as

Options

A. `N^(0)`
B. N
C. `N^(2)`
D. `N^(-2)`

Explanation

To determine how the self-inductance \( L \) of a coil varies with the number of turns \( N \), we can follow these steps:

### Step 1: Understand the Concept of Self-Inductance
Self-inductance is a property of a coil (or inductor) that quantifies its ability to induce an electromotive force (EMF) in itself due to a change in current. The self-inductance depends on the physical characteristics of the coil, including the number of turns.

### Step 2: Recall the Formula for Self-Inductance
The self-inductance \( L \) of a solenoid (a type of coil) can be expressed by the formula:
\[ L = \mu_0 \frac{N^2 A}{l} \]
where:
- \( L \) is the self-inductance,
- \( \mu_0 \) is the permeability of free space,
- \( N \) is the number of turns,
- \( A \) is the cross-sectional area of the coil, and
- \( l \) is the length of the coil.

### Step 3: Analyze the Relationship
From the formula, we can see that self-inductance \( L \) is proportional to the square of the number of turns \( N \):
\[ L \propto N^2 \]
This indicates that if the number of turns in the coil increases, the self-inductance increases with the square of that number.

### Step 4: Conclusion
Thus, the value of self-inductance varies as \( N^2 \).

### Final Answer
The self-inductance \( L \) varies as \( N^2 \).

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