In pure inductive circuit, the curves between frequency `f` and reciprocal of inductive reactance `1//X_(L)` is

Options

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Answer

To solve the question regarding the relationship between frequency \( f \) and the reciprocal of inductive reactance \( \frac{1}{X_L} \) in a pure inductive circuit, we can follow these steps:

### Step 1: Understand Inductive Reactance
Inductive reactance \( X_L \) is given by the formula:
\[ X_L = \omega L \]
where \( \omega = 2\pi f \) is the angular frequency and \( L \) is the inductance.

### Step 2: Substitute Angular Frequency
Substituting \( \omega \) into the equation for \( X_L \):
\[ X_L = 2\pi f L \]

### Step 3: Find the Reciprocal of Inductive Reactance
We need to find \( \frac{1}{X_L} \):
\[ \frac{1}{X_L} = \frac{1}{2\pi f L} \]

### Step 4: Analyze the Relationship
From the equation \( \frac{1}{X_L} = \frac{1}{2\pi L} \cdot \frac{1}{f} \), we can see that:
\[ \frac{1}{X_L} \propto \frac{1}{f} \]
This indicates that \( \frac{1}{X_L} \) is inversely proportional to the frequency \( f \).

### Step 5: Determine the Graphical Representation
The relationship \( \frac{1}{X_L} \propto \frac{1}{f} \) suggests that if we plot \( \frac{1}{X_L} \) against \( f \), the graph will be a hyperbola. This is because as \( f \) increases, \( \frac{1}{X_L} \) decreases, and vice versa.

### Step 6: Identify the Correct Option
Given the options provided, we can conclude that the correct graph representing the relationship between frequency \( f \) and \( \frac{1}{X_L} \) is the one that shows a hyperbolic curve.

### Final Answer
The correct option is the one that depicts a hyperbola.

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