Q145 / 150 · MHT CET 2026 (15 April Shift 1) · Physics

Determine the frequency for which a $10\,\mu\text{F}$ capacitor has a reactance of $2 \times 10^{-3}\,\Omega$.

  • Correct answer
    A
    $\dfrac{25}{\pi}$ MHz
  • B
    $\dfrac{20}{\pi}$ MHz
  • C
    $2 \times 10^{-3}$ MHz
  • D
    $10\pi$ MHz

Solution

The capacitive reactance is given by the formula:

$X_C = \dfrac{1}{2\pi f C}$

Rearranging for frequency $f$:

$f = \dfrac{1}{2\pi X_C C}$

Substituting the given values $X_C = 2 \times 10^{-3} \, \Omega$ and $C = 10 \, \mu\text{F} = 10 \times 10^{-6} \, \text{F}$:

$f = \dfrac{1}{2\pi \times (2 \times 10^{-3}) \times (10 \times 10^{-6})}$

$f = \dfrac{1}{4\pi \times 10^{-8}}$

$f = \dfrac{10^8}{4\pi}$

$f = \dfrac{100 \times 10^6}{4\pi}$

$f = \dfrac{25}{\pi} \times 10^6 \, \text{Hz}$

$f = \dfrac{25}{\pi} \, \text{MHz}$

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

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