Determine the frequency for which a 10 muF ca | vedclass

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Question

(A) The capacitive reactance $X_C$ is given by the formula: $X_C = \frac{1}{2\pi f C}$.Given values are $C = 10 \mu F = 10 	imes 10^{-6} F = 10^{-5}

Vedclass · Accepted Answer

$\frac{25}{\pi}$ MHz

Vedclass · Answer

(A) The capacitive reactance $X_C$ is given by the formula: $X_C = \frac{1}{2\pi f C}$.Given values are $C = 10 \mu F = 10 	imes 10^{-6} F = 10^{-5} F$ and $X_C = 2 	imes 10^{-3} \Omega$.Rearranging the formula to solve for frequency $f$: $f = \frac{1}{2\pi X_C C}$.Substituting the values: $f = \frac{1}{2 	imes \pi 	imes (2 	imes 10^{-3}) 	imes 10^{-5}}$.$f = \frac{1}{4 	imes \pi 	imes 10^{-8}} = \frac{10^8}{4\pi} = \frac{100 	imes 10^6}{4\pi} = \frac{25}{\pi} 	imes 10^6$ Hz.Since $10^6$ Hz = $1$ MHz, the frequency is $\frac{25}{\pi}$ MHz.

Determine the frequency for which a $10$ $\mu$$F$ capacitor has a reactance of $2 \times 10^{-3} \Omega$.

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