Question

A capacitor of \(10\mu F\) has reactance \(2\times 10^{-3}\Omega\). The corresponding frequency is

• A. \(\frac{25}{\pi }MHz\)
• B. \(\frac{25}{\pi }Hz\)
• C. \(2.5\) MHz
• D. \(\frac{2.5}{\pi }MHz\)

Hint:

Capacitive reactance is inversely proportional to frequency and capacitance, so rearrange the reactance formula to get the frequency.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
The reactance of a capacitor is \(X_C=\dfrac{1}{2\pi fC}\).
We are given \(C\) and \(X_C\), so we can find the frequency \(f\).

Step 2: Rearrange the Formula
\(f=\dfrac{1}{2\pi C X_C}\)

Step 3: Calculation
\(C=10\times10^{-6}\,\text{F}=10^{-5}\,\text{F}\) and \(X_C=2\times10^{-3}\,\Omega\).
\(f=\dfrac{1}{2\pi\times10^{-5}\times2\times10^{-3}}=\dfrac{1}{4\pi\times10^{-8}}\)
\(f=\dfrac{25\times10^{5}}{\pi}\times10=\dfrac{25}{\pi}\times10^{6}\,\text{Hz}\)

Step 4: Compare the options
\(\dfrac{25}{\pi}\times10^{6}\,\text{Hz}=\dfrac{25}{\pi}\,\text{MHz}\), which matches option (A).

Final Answer:
The corresponding frequency is \(\dfrac{25}{\pi}\) MHz. \[ \boxed{\text{(A) }\dfrac{25}{\pi}\text{ MHz}} \]