The frequency for which a 5,mu F capacitor ha | vedclass

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Question

(A) The capacitive reactance $X_C$ is given by the formula $X_C = \frac{1}{2\pi 
u C}$.Given $X_C = \frac{1}{1000}\,\Omega$ and $C = 5\,\mu F = 5 	i

Vedclass · Accepted Answer

$\frac{100}{\pi}\,MHz$

Vedclass · Answer

(A) The capacitive reactance $X_C$ is given by the formula $X_C = \frac{1}{2\pi 
u C}$.Given $X_C = \frac{1}{1000}\,\Omega$ and $C = 5\,\mu F = 5 	imes 10^{-6}\,F$.Substituting the values into the formula:$\frac{1}{1000} = \frac{1}{2\pi 	imes 
u 	imes 5 	imes 10^{-6}}$$2\pi 	imes 
u 	imes 5 	imes 10^{-6} = 1000$$10\pi 	imes 
u 	imes 10^{-6} = 10^3$$
u = \frac{10^3}{10\pi 	imes 10^{-6}} = \frac{10^2}{\pi 	imes 10^{-6}} = \frac{10^8}{\pi}\,Hz$.Converting to $MHz$ $(1\,MHz = 10^6\,Hz)$:$
u = \frac{10^8}{\pi} 	imes 10^{-6}\,MHz = \frac{100}{\pi}\,MHz$.

The frequency for which a $5\,\mu F$ capacitor has a reactance of $\frac{1}{1000}\,\Omega$ is given by

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