Question

A 30 μF capacitor is connected to a 240 V, 50 Hz source. If the frequency of the source is changed from 50 Hz to 200 Hz, the capacitive reactance of the capacitor will

• A. increase by a factor of two.
• B. increase by a factor of four.
• C. decrease by a factor of four.
• D. decrease by a factor of two.

Hint:

The capacitive reactance decreases with an increase in frequency, and is inversely proportional to both the frequency and capacitance.

Answer 1

The Correct Option is C

Step 1: Understanding capacitive reactance.
The capacitive reactance (\( X_C \)) is given by the formula: \[ X_C = \frac{1}{2 \pi f C} \] where \( f \) is the frequency of the source, and \( C \) is the capacitance.

Step 2: Analyzing the change in frequency.
If the frequency is increased from 50 Hz to 200 Hz, the capacitive reactance will decrease because it is inversely proportional to the frequency. Specifically, if the frequency quadruples, the reactance will decrease by a factor of four.

Step 3: Conclusion.
The correct answer is (C) decrease by a factor of four, as the capacitive reactance is inversely proportional to frequency.