Obtain an expression for Impedance and current in series LCR circuit. Deduce an expression for the resonating frequency of an LCR series resonating circuit.

Draw the approximate vector diagrams of currents in the circuits shown in the figure. The voltage applied across the points $A$ and $B$ is assumed to be sinusoidal; the parameters of each circuit are so chosen that the total current $I_0$ lags in phase behind the external voltage by an angle $\mathrm{\phi }$.