Question

Capacitive reactance of a capacitor in an AC circuit is 6 k\(\Omega\). If the same capacitor is connected to an AC source of double the frequency, find the new capacitive reactance.

• A. 6 k\(\Omega\)
• B. 3 k\(\Omega\)
• C. 1.5 k\(\Omega\)
• D. 8.5 k\(\Omega\)

Hint:

Capacitive reactance varies inversely with frequency: \(X_C \propto 1/f\). Doubling frequency halves reactance.

Answer 1

The Correct Option is B

Step 1: Use the inverse proportionality directly.
Since $X_C = \dfrac{1}{2\pi f C}$, for the same capacitor $X_C \propto \dfrac{1}{f}$.
Step 2: Apply the doubling.
Doubling $f$ simply halves $X_C$, no need to recompute anything from scratch:
\[ X_{C2} = \frac{X_{C1}}{2} = \frac{6}{2} = 3\ \text{k}\Omega \]
\[ \boxed{3\ \text{k}\Omega} \]