For the series LCR circuit shown in the figur | vedclass

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(B) The resonance frequency $\omega_0$ of a series $LCR$ circuit is given by $\omega_0 = \frac{1}{\sqrt{LC}}$.Given: $L = 8 \, mH = 8 	imes 10^{-3} \

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$2500 \, rad \cdot s^{-1}$ and $5 \, A$

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(B) The resonance frequency $\omega_0$ of a series $LCR$ circuit is given by $\omega_0 = \frac{1}{\sqrt{LC}}$.Given: $L = 8 \, mH = 8 	imes 10^{-3} \, H$,$C = 20 \, \mu F = 20 	imes 10^{-6} \, F$,and $R = 44 \, \Omega$.$\omega_0 = \frac{1}{\sqrt{8 	imes 10^{-3} 	imes 20 	imes 10^{-6}}} = \frac{1}{\sqrt{160 	imes 10^{-9}}} = \frac{1}{\sqrt{16 	imes 10^{-8}}} = \frac{1}{4 	imes 10^{-4}} = 0.25 	imes 10^4 = 2500 \, rad \cdot s^{-1}$.At resonance,the impedance $Z = R$. The amplitude of the current $I_0$ is given by $I_0 = \frac{V_0}{Z} = \frac{V_0}{R}$.Assuming the given voltage $220 \, V$ is the peak voltage $V_0$,$I_0 = \frac{220}{44} = 5 \, A$.Thus,the resonance frequency is $2500 \, rad \cdot s^{-1}$ and the current amplitude is $5 \, A$.

For the series $LCR$ circuit shown in the figure,what is the resonance frequency and the amplitude of the current at the resonating frequency?

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