An inductance of 1, mH,a capacitor of 10, mu | vedclass

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(D) Given that the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$,so $X_L = X_C = X$.We know that $X_L = \omega L$ and $X_C = \f

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$10$

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(D) Given that the inductive reactance $X_L$ is equal to the capacitive reactance $X_C$,so $X_L = X_C = X$.We know that $X_L = \omega L$ and $X_C = \frac{1}{\omega C}$.Since $X_L = X_C$,we have $\omega L = \frac{1}{\omega C}$,which implies $\omega^2 = \frac{1}{LC}$.Substituting the given values: $L = 1\, mH = 10^{-3}\, H$ and $C = 10\, \mu F = 10 	imes 10^{-6}\, F = 10^{-5}\, F$.$\omega^2 = \frac{1}{10^{-3} 	imes 10^{-5}} = \frac{1}{10^{-8}} = 10^8$.Therefore,$\omega = \sqrt{10^8} = 10^4\, rad/s$.The reactance $X$ is given by $X = \omega L = 10^4 	imes 10^{-3} = 10\, \Omega$.

An inductance of $1\, mH$,a capacitor of $10\, \mu F$,and a resistance of $50\, \Omega$ are connected in series. The reactances of the inductor and the capacitor are the same. The reactance of either of them will be........$\Omega$.

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