By hvhipot 
Series resonance in AC circuits
Since all three components are connected in series, the same current flows through them.
This is represented by horizontal phasor.
Due to the fact that the resistor current and voltage are in phase, the resistor voltage is displayed on the same phasor.
For capacitor C, current I leads voltage V by 90 degrees.
For inductor L, voltage V leads current I by 90 degrees.
If the voltage across the capacitor is equal to the voltage across the coil, their effects will cancel out due to their phase difference of 180 degrees, and we will only be affected by the resistance.
Z = R
The current and voltage in the circuit will be in phase.
I = V / R
All of these occur when capacitive reactance equals inductive reactance.
Due to the fact that the capacitance reactance decreases with increasing frequency, while the inductance reactance decreases with decreasing frequency, there must exist a frequency equal to them.
This is called the resonant frequency.
Series resonant circuits have low impedance.