What is a serial resonant circuit?

A series resonant circuit is one in which the inductive and capacitive reactance are equal in magnitude. Since the signs of the vectors of their reactance are opposite, they cancel and so leave only the resistance of the series circuit at the resonant frequency. Because reactance of a capacitor is inversely related to frequency, and the reactance of an inductor is directly related to frequency, this happens at a particular frequency dependent on the values of capacitance and inductance.

You see, when you apply a sine wave to an inductor, the current lags behind the voltage by 90 degrees. Or you may look at it as the voltage leading the current by 90 degrees.

But when a sine wave is applied to a capacitor, the reverse is true. Current leads voltage by 90 degrees. Or voltage lags behind current by 90 degrees.

Put a capacitor and inductor in series and input a sine wave of current at the frequency at which both have the same amount of reactance. Current is equal in magnitude and phase everywhere in a series circuit. Voltage dropped across the inductor is 90 degrees ahead of the current, while voltage dropped across the capacitor is 90 degrees behind the current. This puts the voltage drops 180 degrees out of phase with each other. Because the applied frequency is the one at which the reactance of each component is equal in magnitude, the voltage drops are also equal in magnitude so they sum to zero volts.

Zero volts at any current is zero ohms (Ohm's law, R = E/I). In the real world, both parts have resistance or a series resistor may be part of the design. But the end result is that impedance of the series circuit is lowest at the resonant frequency.