Define quality factor of resonance in series LCR circuit. What is its SI unit?

Hint: In case of DC circuit if there is resistor we can measure using an ohmmeter but if there are capacitors and inductors in the AC circuit we can’t measure the obstruction for the flow of current hence there comes a term reactance and it depends on source angular frequency too. Quality factor is the ratio.
Formula used:
$\eqalign{
  & {X_C} = \dfrac{1}{{\omega C}} \cr
  & {X_L} = \omega L \cr} $

Complete answer:
Quality factor is nothing but in a series LCR circuit the ratio of voltage drop across inductor or capacitor to the voltage drop across the resistor gives the quality factor. As the name suggests it is the series circuit means the current flow will be the same throughout the circuit. Incase of resistors we use the term resistance but incase of capacitors and inductors we use reactance. Where reactance of the capacitor is given by ${X_C} = \dfrac{1}{{\omega C}}$ and the reactance of the inductor is given by ${X_L} = \omega L$ where $\omega $ is the frequency of the source and L and C are the inductance and capacitance respectively. Let us assume that ‘i’ amount of current is passing through the circuit then voltage drop across the resistor and across the capacitor and across the inductor will be given by
$\eqalign{
  & {V_R} = iR \cr
  & {V_C} = i{X_C} = i \times \dfrac{1}{{\omega C}} \cr
  & {V_L} = i{X_L} = i \times \omega L \cr} $
Where R is the resistance and hence we have quality factor as
$\dfrac{{{V_C}}}{{{V_R}}} = \dfrac{{{V_L}}}{{{V_R}}}$
Here we have voltage across the capacitor and inductor equal because at resonance conditions they will be equal.
Hence quality factor will be $\dfrac{{{V_C}}}{{{V_R}}} = \dfrac{{{V_L}}}{{{V_R}}} = \dfrac{{i{X_L}}}{{iR}} = \dfrac{{i{X_C}}}{{iR}} = \dfrac{{{X_L}}}{R} = \dfrac{{{X_C}}}{R} = \dfrac{1}{R}\sqrt {\dfrac{L}{C}} $

Note:
Since it was clearly mentioned that the quality factor is ratio it is obvious that it has no units. Coming to resonance we use resonance in mechanics like when frequency to two objects become equal then those two will be in resonance but there when voltages between capacitor and inductor become equal then those two will be in resonance.