Capacitive reactance of a capacitor in an AC | vedclass

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(B) The capacitive reactance $X_C$ of a capacitor is given by the formula $X_C = \frac{1}{2 \pi f C}$,where $f$ is the frequency of the $AC$ source an

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$3 \ k\Omega$

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(B) The capacitive reactance $X_C$ of a capacitor is given by the formula $X_C = \frac{1}{2 \pi f C}$,where $f$ is the frequency of the $AC$ source and $C$ is the capacitance.From this relation,we can see that $X_C \propto \frac{1}{f}$.Let the initial frequency be $f_1$ and the initial reactance be $X_{C1} = 6 \ k\Omega$.Let the new frequency be $f_2 = 2f_1$.The new reactance $X_{C2}$ is given by the ratio:$\frac{X_{C2}}{X_{C1}} = \frac{f_1}{f_2} = \frac{f_1}{2f_1} = \frac{1}{2}$.Therefore,$X_{C2} = \frac{X_{C1}}{2} = \frac{6 \ k\Omega}{2} = 3 \ k\Omega$.

Capacitive reactance of a capacitor in an $AC$ circuit is $6 \ k\Omega$. If the same capacitor is connected to an $AC$ source of double the frequency,the capacitive reactance will become

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