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: Angular frequency:
$X_C=\dfrac1{\omega C}$, so $\omega=\dfrac1{CX_C}=\dfrac1{10^{-5}\times2\times10^{-3}}=5\times10^7$ rad/s.

Step 2: Frequency:
$f=\dfrac\omega{2\pi}=\dfrac{5\times10^7}{2\pi}=\dfrac{2.5\times10^7}\pi$ Hz.

Step 3: Convert:
$\dfrac{25}{\pi}$ MHz. Option (A).

Final Answer:
omega is 5 times 10^7 rad/s. \[ \boxed{A} \]