An AC circuit consists of an inductor of indu | vedclass

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(A) The current in an $LCR$ or $LC$ series circuit is maximum at the condition of resonance.At resonance,the inductive reactance equals the capacitive

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$500 \, rad/s$

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(A) The current in an $LCR$ or $LC$ series circuit is maximum at the condition of resonance.At resonance,the inductive reactance equals the capacitive reactance,i.e.,$X_L = X_C$.This implies $\omega L = \frac{1}{\omega C}$,which gives the resonant angular frequency $\omega_0 = \frac{1}{\sqrt{LC}}$.Given: $L = 0.5 \, H$ and $C = 8 	imes 10^{-6} \, F$.Substituting the values: $\omega_0 = \frac{1}{\sqrt{0.5 	imes 8 	imes 10^{-6}}} = \frac{1}{\sqrt{4 	imes 10^{-6}}}$.$\omega_0 = \frac{1}{2 	imes 10^{-3}} = \frac{1000}{2} = 500 \, rad/s$.

An $AC$ circuit consists of an inductor of inductance $0.5 \, H$ and a capacitor of capacitance $8 \, \mu F$ in series. The current in the circuit is maximum when the angular frequency of the $AC$ source is

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