In a series LCR circuit,operated with an ac o | vedclass

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(B) In a series $LCR$ circuit,the impedance $Z$ is the vector sum of resistance $R$ and the net reactance $X = X_L - X_C$.The inductive reactance is g

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${\left[ {{R^2} + {{\left( {L\omega - \frac{1}{{C\omega }}} \right)}^2}} \right]^{1/2}}$

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(B) In a series $LCR$ circuit,the impedance $Z$ is the vector sum of resistance $R$ and the net reactance $X = X_L - X_C$.The inductive reactance is given by $X_L = L\omega$.The capacitive reactance is given by $X_C = \frac{1}{C\omega}$.The total impedance $Z$ is calculated using the formula:$Z = \sqrt{R^2 + (X_L - X_C)^2}$Substituting the values of $X_L$ and $X_C$ into the formula:$Z = \sqrt{R^2 + \left(L\omega - \frac{1}{C\omega}\right)^2}$This can be written as:$Z = \left[R^2 + \left(L\omega - \frac{1}{C\omega}\right)^2\right]^{1/2}$

In a series $LCR$ circuit,operated with an $ac$ of angular frequency $\omega$,the total impedance is

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