With increase in frequency of an `AC` supply, the capacitive reactance:

Options

A. varies inversely with frequency
B. varies directly with frequency
C. varies directly as square of frequeny
D. remains constant

Answer

To solve the question regarding the relationship between capacitive reactance and the frequency of an AC supply, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Capacitive Reactance**:
Capacitive reactance (denoted as \(X_C\)) is the opposition that a capacitor offers to the flow of alternating current (AC). It is a measure of how much the capacitor resists the change in voltage.

2. **Identify the Formula**:
The formula for capacitive reactance is given by:
\[ X_C = \frac{1}{\omega C} \]
where:
- \(X_C\) is the capacitive reactance,
- \(\omega\) is the angular frequency of the AC supply, and
- \(C\) is the capacitance of the capacitor.

3. **Relate Angular Frequency to Frequency**:
The angular frequency \(\omega\) is related to the frequency \(f\) by the equation:
\[ \omega = 2\pi f \]
Therefore, as frequency \(f\) increases, \(\omega\) also increases.

4. **Analyze the Relationship**:
From the formula \(X_C = \frac{1}{\omega C}\), we can see that:
- If \(C\) (capacitance) is constant, then \(X_C\) is inversely proportional to \(\omega\).
- As frequency \(f\) (and thus \(\omega\)) increases, \(X_C\) decreases.

5. **Conclusion**:
Therefore, with an increase in the frequency of the AC supply, the capacitive reactance \(X_C\) decreases. This means that capacitive reactance varies inversely with frequency.

### Final Answer:
The capacitive reactance decreases with an increase in frequency of the AC supply.