Find the peak current and resonant frequency | vedclass

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(A) Given: $L = 100 \, mH = 0.1 \, H$,$C = 100 \, \mu F = 10^{-4} \, F$,$R = 120 \, \Omega$,$V = 30 \sin(100t) \, V$.From the voltage equation,peak vo

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$0.2 \, A$ and $50 \, Hz$

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(A) Given: $L = 100 \, mH = 0.1 \, H$,$C = 100 \, \mu F = 10^{-4} \, F$,$R = 120 \, \Omega$,$V = 30 \sin(100t) \, V$.From the voltage equation,peak voltage $V_0 = 30 \, V$ and angular frequency $\omega = 100 \, rad/s$.Inductive reactance $X_L = \omega L = 100 	imes 0.1 = 10 \, \Omega$.Capacitive reactance $X_C = \frac{1}{\omega C} = \frac{1}{100 	imes 10^{-4}} = \frac{1}{0.01} = 100 \, \Omega$.Impedance $Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{120^2 + (10 - 100)^2} = \sqrt{120^2 + (-90)^2} = \sqrt{14400 + 8100} = \sqrt{22500} = 150 \, \Omega$.Peak current $I_0 = \frac{V_0}{Z} = \frac{30}{150} = 0.2 \, A$.Resonant frequency $f_r = \frac{1}{2\pi \sqrt{LC}} = \frac{1}{2\pi \sqrt{0.1 	imes 10^{-4}}} = \frac{1}{2\pi \sqrt{10^{-5}}} = \frac{1}{2\pi 	imes 10^{-2.5}} \approx \frac{1}{2 	imes 3.14 	imes 0.00316} \approx 50.3 \, Hz \approx 50 \, Hz$.

Find the peak current and resonant frequency of the following circuit (as shown in the figure).

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