An inductance of 2 text{ mH},a capacitor of 2 | vedclass

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(D) Given:Inductance $L = 2 	ext{ mH} = 2 	imes 10^{-3} 	ext{ H}$Capacitance $C = 20 \mu	ext{F} = 20 	imes 10^{-6} 	ext{ F}$Resistance $R = 50 \

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$10$

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(D) Given:Inductance $L = 2 	ext{ mH} = 2 	imes 10^{-3} 	ext{ H}$Capacitance $C = 20 \mu	ext{F} = 20 	imes 10^{-6} 	ext{ F}$Resistance $R = 50 \Omega$Condition for resonance: Inductive reactance $X_L$ equals capacitive reactance $X_C$.$X_L = X_C = \omega L = \frac{1}{\omega C}$From this,$\omega^2 = \frac{1}{LC}$.$\omega = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{2 	imes 10^{-3} 	imes 20 	imes 10^{-6}}} = \frac{1}{\sqrt{40 	imes 10^{-9}}} = \frac{1}{\sqrt{4 	imes 10^{-8}}} = \frac{1}{2 	imes 10^{-4}} = 0.5 	imes 10^4 = 5000 	ext{ rad/s}$.Now,calculate the reactance $X_L = \omega L$:$X_L = 5000 	imes 2 	imes 10^{-3} = 10 \Omega$.Therefore,the reactance of either component is $10 \Omega$.

An inductance of $2 \text{ mH}$,a capacitor of $20 \mu\text{F}$,and a resistance of $50 \Omega$ are connected in series to an $A.C.$ source. The reactance of the inductor and the capacitor are the same. The reactance of either of them will be: (in $\Omega$)

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