A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the source, explaining the nature of its variation.

Phasor Diagram for a series LCR circuit is shown in the attached figure.From definition of impedance,For inductor,VL=IXL=IωLFor capacitance,VC=IXC=IωCFor resistance,VR=IRFrom the phasor diagram,Vs²=VR²+(VL−VC)²(IZ)²=(IR)²+(IωL−IωC)²Z=√R²+(ωL−1ωC)²Variation of current in the circuit on the variation of applied frequency is shown in the attached figure.Current is given as:I=VsZAt resonance, impedance is minimum and hence, current is maximum as shown in the plot.For frequencies smaller than the resonant frequencies,VC>VL and hence circuit is capacitive.For frequencies greater than the resonant frequencies,VL>VC and hence circuit is inductive.