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: Formula First
Use $X_C=\dfrac{1}{\omega C}$ with $\omega=2\pi f$, so $\omega=\dfrac{1}{X_C C}$.

Step 2: Find the Angular Frequency
$\omega=\dfrac{1}{2\times10^{-3}\times10^{-5}}=5\times10^{7}\,\text{rad/s}$

Step 3: Convert to Frequency
$f=\dfrac{\omega}{2\pi}=\dfrac{5\times10^{7}}{2\pi}=\dfrac{2.5\times10^{7}}{\pi}\,\text{Hz}=\dfrac{25}{\pi}\,\text{MHz}$, which is option (A).

Final Answer:
The frequency works out to $\dfrac{25}{\pi}$ MHz. \[ \boxed{\text{(A) }\dfrac{25}{\pi}\text{ MHz}} \]