Find capacitive reactance of a capacitor connected to a dc source.

Answer

To find the capacitive reactance of a capacitor connected to a DC source, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Capacitive Reactance**:
- Capacitive reactance (Xc) is a measure of a capacitor's opposition to alternating current (AC). It is given by the formula:
\[ X_c = \frac{1}{\omega C} \]
where \( \omega \) is the angular frequency and \( C \) is the capacitance.

2. **Identify the Frequency of a DC Source**:
- A direct current (DC) source has a constant voltage over time, which means that the frequency (f) is zero. Therefore, we can state:
\[ f = 0 \]

3. **Relate Angular Frequency to Frequency**:
- The angular frequency \( \omega \) is related to frequency by the formula:
\[ \omega = 2 \pi f \]
Substituting \( f = 0 \) into this equation gives:
\[ \omega = 2 \pi \times 0 = 0 \]

4. **Substitute Values into the Capacitive Reactance Formula**:
- Now, substituting \( \omega = 0 \) into the capacitive reactance formula:
\[ X_c = \frac{1}{0 \cdot C} \]
This results in:
\[ X_c = \frac{1}{0} \]

5. **Conclusion**:
- Since division by zero is undefined, we conclude that the capacitive reactance of a capacitor connected to a DC source is infinite:
\[ X_c = \infty \]

### Final Answer:
The capacitive reactance of a capacitor connected to a DC source is infinite.

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