Q104 / 150 · MHT CET 2025 (25 Apr Shift 1) · Physics

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
    $\mathrm{X}_{\mathrm{c}}$
  • Correct answer
    C
    $\frac{X_C}{4}$
  • D
    $2 \mathrm{X}_{\mathrm{c}}$

Solution

The capacitive reactance is defined by $X_C = \frac{1}{2\pi f C}$.

When both frequency and capacitance are doubled, the new reactance becomes $X_{C2} = \frac{1}{2\pi (2f) (2C)} = \frac{1}{4} \cdot \frac{1}{2\pi f C} = \frac{X_C}{4}$.

Final answer: $\frac{X_C}{4}$

Hence, the correct answer is option: 'C'.

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