Which of the following curves correctly represent the variation of capacitve reactance (`underset(C )(X)`) with frequency (f) ?

Options

A.
B.
C.
D.

Answer

To determine the correct curve representing the variation of capacitive reactance (Xc) with frequency (f), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Capacitive Reactance**:
The capacitive reactance (Xc) is given by the formula:
\[ X_c = \frac{1}{\omega C} \]
where \(\omega\) is the angular frequency.

2. **Relate Angular Frequency to Frequency**:
The angular frequency \(\omega\) can be expressed in terms of frequency (f) as:
\[ \omega = 2\pi f \]
Substituting this into the formula for Xc gives:
\[ X_c = \frac{1}{2\pi f C} \]

3. **Analyze the Relationship**:
From the equation \(X_c = \frac{1}{2\pi f C}\), we can see that Xc is inversely proportional to frequency (f). This means that as frequency increases, the capacitive reactance decreases.

4. **Graphical Representation**:
The relationship \(X_c \propto \frac{1}{f}\) indicates that the graph of Xc versus f will be a rectangular hyperbola. This is because the product of Xc and f remains constant for a given capacitance C.

5. **Identify the Correct Curve**:
Among the given options, we need to find the one that represents a hyperbolic curve that decreases as frequency increases. Based on the analysis, option C is the correct representation.

### Final Answer:
The correct curve that represents the variation of capacitive reactance (Xc) with frequency (f) is **option C**.