Which of the following graphs represent the correct variation of inductive reactance `X_(L)` with frequency `upsilon`?

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of inductive reactance \( X_L \) with frequency \( \nu \), we can follow these steps:

### Step 1: Understand the formula for inductive reactance
The inductive reactance \( X_L \) in a purely inductive circuit is given by the formula:
\[ X_L = 2 \pi f L \]
where:
- \( X_L \) is the inductive reactance,
- \( f \) is the frequency,
- \( L \) is the inductance.

### Step 2: Analyze the relationship between \( X_L \) and \( f \)
From the formula, we can see that \( X_L \) is directly proportional to the frequency \( f \). This means that as the frequency increases, the inductive reactance also increases linearly.

### Step 3: Identify the type of graph
Since \( X_L \) is directly proportional to \( f \), the relationship can be represented as:
\[ X_L \propto f \]
This implies that if we were to plot \( X_L \) on the y-axis and \( f \) on the x-axis, the graph would be a straight line passing through the origin.

### Step 4: Compare with the given options
Now, we need to look at the provided graphs and identify which one represents a linear relationship. The correct graph will show a straight line indicating that \( X_L \) increases linearly with \( f \).

### Step 5: Conclusion
Upon examining the options, we find that **Option B** represents the correct variation of inductive reactance \( X_L \) with frequency \( \nu \) as it shows a linear relationship.

### Summary of the Solution
The inductive reactance \( X_L \) varies linearly with frequency \( f \), and the correct graph representing this relationship is **Option B**.

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