A series R-L-C circuit consists of an 8.0 Ome | vedclass

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(B) Given: $R = 8.0\ \Omega$,$C = 5.0\ \mu F = 5.0 	imes 10^{-6}\ F$,$L = 50.0\ mH = 50.0 	imes 10^{-3}\ H$.Resonance frequency $\omega_0 = \frac{1}

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$57$

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(B) Given: $R = 8.0\ \Omega$,$C = 5.0\ \mu F = 5.0 	imes 10^{-6}\ F$,$L = 50.0\ mH = 50.0 	imes 10^{-3}\ H$.Resonance frequency $\omega_0 = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{50 	imes 10^{-3} 	imes 5 	imes 10^{-6}}} = \frac{1}{\sqrt{250 	imes 10^{-9}}} = \frac{1}{\sqrt{2.5 	imes 10^{-7}}} = 2000\ rad/s$.The operating frequency is $\omega = \frac{1}{2} \omega_0 = 1000\ rad/s$.Inductive reactance $X_L = \omega L = 1000 	imes 50 	imes 10^{-3} = 50\ \Omega$.Capacitive reactance $X_C = \frac{1}{\omega C} = \frac{1}{1000 	imes 5 	imes 10^{-6}} = \frac{1}{0.005} = 200\ \Omega$.Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{8^2 + (50 - 200)^2} = \sqrt{64 + (-150)^2} = \sqrt{64 + 22500} = \sqrt{22564} \approx 150.21\ \Omega$.$I_{rms} = \frac{V_{rms}}{Z} = \frac{400}{150.21} \approx 2.663\ A$.Power $P = I_{rms}^2 R = (2.663)^2 	imes 8 \approx 7.09 	imes 8 \approx 56.72\ W$.Rounding to the nearest integer,$P \approx 57\ W$.

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