Identify the graph which correctly reperesents the variation of capacitive reactance `X_C` with frequency

Options

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Explanation

To determine the variation of capacitive reactance \( X_C \) with frequency \( f \), we start by analyzing the relationship between these two quantities.

### Step-by-Step Solution:

1. **Understand the Formula for Capacitive Reactance**:
The formula for capacitive reactance is given by:
\[ X_C = \frac{1}{2 \pi f C} \]
where \( X_C \) is the capacitive reactance, \( f \) is the frequency, and \( C \) is the capacitance.

2. **Identify the Relationship**:
From the formula, we can see that \( X_C \) is inversely proportional to the frequency \( f \). This means:
\[ X_C \propto \frac{1}{f} \]
As the frequency increases, the capacitive reactance decreases, and vice versa.

3. **Graphical Representation**:
Since \( X_C \) decreases as \( f \) increases, the graph of \( X_C \) versus \( f \) will not be a straight line. Instead, it will be a hyperbolic curve. Specifically, it will be a rectangular hyperbola.

4. **Characteristics of the Graph**:
- The graph will approach the axes but never touch them, indicating that as frequency approaches zero, \( X_C \) approaches infinity, and as frequency approaches infinity, \( X_C \) approaches zero.
- The shape of the graph will be such that it is in the first quadrant, with \( X_C \) on the y-axis and \( f \) on the x-axis.

5. **Conclusion**:
The correct graph that represents the variation of capacitive reactance \( X_C \) with frequency \( f \) is a rectangular hyperbola.