If a resistance of 100, Omega,an inductance o | vedclass

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(C) The impedance $Z$ of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given: $R = 100\, \Omega$,$L = 0.5\, H$,$C = 10 	imes 1

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$189.72\, \Omega$

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(C) The impedance $Z$ of an $LCR$ series circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Given: $R = 100\, \Omega$,$L = 0.5\, H$,$C = 10 	imes 10^{-6}\, F$,and $f = 50\, Hz$.Angular frequency $\omega = 2\pi f = 2 	imes \pi 	imes 50 = 100\pi\, rad/s$.Inductive reactance $X_L = \omega L = 100\pi 	imes 0.5 = 50\pi \approx 157.08\, \Omega$.Capacitive reactance $X_C = \frac{1}{\omega C} = \frac{1}{100\pi 	imes 10 	imes 10^{-6}} = \frac{1}{10^{-3}\pi} = \frac{1000}{\pi} \approx 318.31\, \Omega$.Now,$Z = \sqrt{100^2 + (157.08 - 318.31)^2} = \sqrt{10000 + (-161.23)^2} = \sqrt{10000 + 25995.11} = \sqrt{35995.11} \approx 189.72\, \Omega$.

If a resistance of $100\, \Omega$,an inductance of $0.5\, H$,and a capacitance of $10 \times 10^{-6}\, F$ are connected in series to a $50\, Hz$ $AC$ supply,then the impedance is:

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