Question

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

• A. \(\frac{25}{π}\) MHz
• B. \(\frac{20}{π}\) MHz
• C. \(2\times 10^{-3}\) MHz
• D. \(10π\) MHz

Hint:

Use f = 1/(2 pi C X).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The capacitive reactance is \(X_C=\dfrac1{2\pi fC}\).

Step 2: Rearrange:
\[ f=\frac1{2\pi CX_C} \]

Step 3: Substitute:
\[ f=\frac1{2\pi\times10\times10^{-6}\times2\times10^{-3}}=\frac1{4\pi\times10^{-8}}=\frac{10^8}{4\pi}\ \text{Hz} \]

Step 4: Convert:
\(\dfrac{10^8}{4\pi}=\dfrac{25\times10^6}{\pi}\) Hz \(=\dfrac{25}{\pi}\) MHz. Option (A).

Final Answer:
The frequency is 25/pi MHz. \[ \boxed{\frac{25}{\pi}\ \text{MHz}} \]