Mathematical Analysis of L-C Series Circuit : Let us consider, a circuit containing inductor $L$ capacitor $C$ and these are connected in series. If an alternating voltage source is applied across it then the resultant voltage of the L-C circuit $V=V_{L} - V_{C} \qquad(1)$ We know that: $V_{L} = iX_{L}$ $V_{C} = iX_{C}$ So from equation $(1)$ $V= iX_{L} - iX_{C} $ $V=i \left(X_{L} - X_{C} \right) $ $\frac{V}{i}=\left(X_{L} - X_{C} \right) $ $Z=\left(X_{L} - X_{C} \right) \qquad(2)$ Where $Z \rightarrow$ Impedance of L-C circuit. $X_{L} \rightarrow$ Inductive Reactance which has value $\omega L$ $X_{C} \rightarrow$ Capacitive Reactance which has value $\frac{1}{\omega C}$ So from equation $(2)$, we get $Z=\left( \omega L - \frac{1}{\omega C} \right) \qquad(3)$ The phase of resultant voltage: The phase of resultant voltage from current is $90^{\circ}$ as shown in the figure above. The Impedance and Phase at Re

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