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MHT CET · Physics · Alternating Current

The frequency for which a \(5 \mu \mathrm{F}\) capacitor has a reactance of \(\frac{1}{1000} \Omega\) is given by

  1. A \(\frac{1}{1000} \mathrm{~Hz}\)
  2. B \(1000 \mathrm{~Hz}\)
  3. C \(\frac{100}{\pi} \mathrm{MHz}\)
  4. D \(\frac{1000}{\pi} \mathrm{Hz}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{100}{\pi} \mathrm{MHz}\)

Step-by-step Solution

Detailed explanation

Concept: reactance of capacitor is
\(X_c=\frac{1}{\omega c}=\frac{1}{2 \pi f C}\)
Given \(X_c=10^{-3} \Omega, C=5 \times 10^{-6} \mathrm{~F}\)
\(\begin{aligned}
& \therefore 10^{-3} \Omega=\frac{1}{2 \pi \mathrm{f}\left(5 \times 10^{-6}\right)} \\
& \Rightarrow \mathrm{f}=\frac{1}{10 \pi \times 10^{-9}} \mathrm{~Hz}=\frac{10^8}{\pi} \mathrm{Hz}=\frac{100}{\pi} \mathrm{MHz}
\end{aligned}\)