Question

The frequency for which $5\mu F$ capacitor has a reactance of $10,000\Omega$ is

• A. $\left(100/\pi \right)$ cycles per second
• B. $\left(10/\pi \right)$ cycles per second
• C. $200$ cycles per second
• D. $5,000$ cycles per second

Answer 1

The correct option is B $\left(10/\pi \right)$ cycles per second

$=5\times {10}^{-6}f$

$x_c=10000\Omega$

$x_c=\frac{1}{W_C}$

$\Rightarrow w=\frac{1}{c\times x_c}=\frac{1}{5\times {10}^{-6}\times 10000}$

$=\frac{{10}^6}{5\times {10}^4}=\frac{100}{5}=20rad/\sec$

$\Rightarrow 2\pi f=20rad/\sec$

$\Rightarrow f=\frac{10}{\pi }cycles/\sec$

Hence,

option $\left(B\right)$ is correct answer.