Question

In a capacitive circuit, the reactance of capacitor at frequency \( f \) is \( X_C \). What will be its reactance at frequency \( 2f \)?

• A. \( \frac{X_C}{2} \)
• B. \( \frac{X_C}{4} \)
• C. \( \frac{X_C}{8} \)
• D. \( X_C \)

Hint:

The reactance of a capacitor is inversely proportional to the frequency. When the frequency is doubled, the reactance is reduced by a factor of 4.

Answer 1

The Correct Option is B

Step 1: Understanding capacitive reactance.
The reactance \( X_C \) of a capacitor is given by the formula: \[ X_C = \frac{1}{2 \pi f C} \] where \( f \) is the frequency and \( C \) is the capacitance.
Step 2: Calculating reactance at frequency \( 2f \).
When the frequency is doubled, the reactance becomes: \[ X_C' = \frac{1}{2 \pi (2f) C} = \frac{X_C}{4} \] Step 3: Conclusion.
Thus, the reactance at frequency \( 2f \) is \( \frac{X_C}{4} \), which is option (B).