Capacitive reactance of a capacitor in an AC | vedclass

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

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$1.5 \ k\Omega$

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(A) The capacitive reactance $X_C$ of a capacitor is given by the formula: $X_C = \frac{1}{2 \pi f C}$.Here,$f$ is the frequency of the $AC$ source and $C$ is the capacitance.From the formula,it is clear that $X_C \propto \frac{1}{f}$.Given,initial capacitive reactance $X_{C1} = 3 \ k\Omega$ at frequency $f_1 = f$.When the frequency is doubled,$f_2 = 2f$.The new capacitive reactance $X_{C2}$ will be: $X_{C2} = \frac{1}{2 \pi (2f) C} = \frac{1}{2} 	imes \left( \frac{1}{2 \pi f C} ight) = \frac{X_{C1}}{2}$.Substituting the value: $X_{C2} = \frac{3 \ k\Omega}{2} = 1.5 \ k\Omega$.

Capacitive reactance of a capacitor in an $AC$ circuit is $3 \ k\Omega$. If this capacitor is connected to a new $AC$ source of double frequency,the capacitive reactance will become:

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