Question

The reactance of a capacitor is \(\mathrm{X}_{\mathrm{C}}\). If the frequency and the capacitance are doubled, then the new reactance will be

• A. \(\frac{X_{C}}{2}\)
• B. \(\mathrm{X}_{\mathrm{C}}\)
• C. \(\frac{X_{C}}{4}\)
• D. \(2X_{C}\)

Hint:

Capacitive reactance is inversely proportional to both frequency and capacitance.

Answer 1

The Correct Option is C

Step 1: Proportionality
$X_C\propto \dfrac{1}{fC}$.

Step 2: Substitute factors
$\dfrac{X_C'}{X_C}=\dfrac{fC}{(2f)(2C)}=\dfrac{1}{4}$.

Step 3: Result
So $X_C'=\dfrac{X_C}{4}$, option (C).

Final Answer:
The reactance becomes $X_C/4$. \[ \boxed{\text{(C) }\dfrac{X_{C}}{4}} \]