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.
Suppose a resistance R, inductance L and capacitance C connected in series.
An alternating source of voltage V = Vo sin 
t is applied across it. Since all the components are connected in series, the current flowing through all is same.
Voltage across resistance R is VR, voltage across inductance L is VL and voltage across capacitance C is VC.
VR and (VC -VL) are mutually perpendicular and the phase difference between them is 90°.
From the figure above, we have 
and
The phase difference between current and voltage is given by,
From the graph, we can see that with increase in frequency, current first increases and then decreases. At resonant frequency, current amplitude is maximum.
