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
The reactance of a capacitor is \(\mathrm{X}_{\mathrm{C}}\). If the frequency and the capacitance are doubled, then the new reactance will be
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Capacitive reactance is inversely proportional to both frequency and capacitance.
Updated On: Nov 13, 2026
- \(\frac{X_{C}}{2}\)
- \(\mathrm{X}_{\mathrm{C}}\)
- \(\frac{X_{C}}{4}\)
- \(2X_{C}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Capacitive reactance is \(X_C=\dfrac{1}{2\pi f C}\).
Step 2: Apply the change
New frequency is \(2f\) and new capacitance is \(2C\).
Step 3: Calculation
\(X_C'=\dfrac{1}{2\pi(2f)(2C)}=\dfrac{1}{4}\cdot\dfrac{1}{2\pi fC}=\dfrac{X_C}{4}\).
Step 4: Compare the options
This is option (C).
Final Answer:
The new reactance is one fourth of the original. \[ \boxed{\text{(C) }\dfrac{X_{C}}{4}} \]
Capacitive reactance is \(X_C=\dfrac{1}{2\pi f C}\).
Step 2: Apply the change
New frequency is \(2f\) and new capacitance is \(2C\).
Step 3: Calculation
\(X_C'=\dfrac{1}{2\pi(2f)(2C)}=\dfrac{1}{4}\cdot\dfrac{1}{2\pi fC}=\dfrac{X_C}{4}\).
Step 4: Compare the options
This is option (C).
Final Answer:
The new reactance is one fourth of the original. \[ \boxed{\text{(C) }\dfrac{X_{C}}{4}} \]
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