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The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why ?
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For an LR circuit, the impedance,
ZLR = \(\sqrt{R^{2}+X_{\mathrm{L}}^{2}}\), where XL is the reactance of the inductor.
When a capacitor of capacitance C is added in series with L and R, the impedance,
ZLCR = \(\sqrt{R^{2}+\left(X_{\mathrm{L}}-X_{\mathrm{C}}\right)^{2}}\) 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 (ZLCR < ZLR).

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