Question

A capacitor of capacitance \( C \) has reactance \( X \) in an AC circuit. If the capacitance and the frequency of the applied voltage are doubled, the new reactance will become:

• A. 4X
• B. 2X
• C. \(\frac{X{2\)
• D. \(\frac{X{4\)

Hint:

The capacitive reactance is inversely proportional to both capacitance and frequency. Doubling both will decrease the reactance by a factor of 4.

Answer 1

The Correct Option is D

The capacitive reactance \( X \) is given by the formula: \[ X = \frac{1}{2 \pi f C} \] Where:
- \( f \) is the frequency of the applied voltage,
- \( C \) is the capacitance of the capacitor. Now, if the capacitance and the frequency are doubled, the new reactance \( X' \) will be: \[ X' = \frac{1}{2 \pi (2f) (2C)} = \frac{1}{2 \pi f C \cdot 4} \] \[ X' = \frac{X}{4} \] Therefore, the new reactance will be \( \frac{X}{4} \).