The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why ?

Z_{LR} = \(\sqrt{R^{2}+X_{\mathrm{L}}^{2}}\), where X_{L} is the reactance of the inductor.

When a capacitor of capacitance C is added in series with L and R, the impedance,

Z_{LCR} = \(\sqrt{R^{2}+\left(X_{\mathrm{L}}-X_{\mathrm{C}}\right)^{2}}\) because in the case of an inductor the current lags behind the voltage by a phase angle of \(\frac{\pi}{2}\) rad while in the case of a capacitor the current leads the voltage by a phase angle of \(\frac{\pi}{2}\) rad. The decrease in net reactance decreases the total impedance (Z_{LCR} < Z_{LR}).