Question

An ac source is connected to a capacitor C. Due to decrease in its operating frequency:

• A. capacitive reactance remains constant
• B. capacitive reactance decreases
• C. displacement current increases
• D. displacement current decreases

Answer 1

The Correct Option is D

To solve this problem, we need to understand the behavior of a capacitor in an AC circuit, focusing on how it interacts with frequency changes.

Concept Explanation:

The capacitive reactance \(X_C\) of a capacitor in an AC circuit is given by the formula:

\(X_C = \frac{1}{2\pi f C}\)

Where:

• \(X_C\) is the capacitive reactance.
• \(f\) is the frequency of the AC source.
• \(C\) is the capacitance.

Effect of Frequency Decrease:

1. From the formula \(X_C = \frac{1}{2\pi f C}\), it is clear that capacitive reactance \(X_C\) is inversely proportional to the frequency \(f\).
2. Therefore, if the frequency of the AC source decreases, the capacitive reactance \(X_C\) increases.

Analysis of Displacement Current:

The displacement current \(I_d\) is related to the capacitive reactance and the applied voltage \(V\):

\(I_d = \frac{V}{X_C}\)

1. Since \(X_C\) increases as frequency decreases, the displacement current \(I_d\) must decrease as it is inversely proportional to \(X_C\).

Conclusion:

The correct answer is: displacement current decreases. The decrease in operating frequency causes the capacitive reactance to increase, resulting in a decrease in displacement current.