Why is the quality factor Q equal to the capacitor current divided by source current?

[sanazy24]

Homework Statement

i have a problem about RCL parallel circuit .
when we have a RCl circuit with applied sinsusoid currnet ,we make all parameters in circuit as complex number i mean make them phasors.
i study this formula in my book and i do not know how too proove it.
why quality factor in this circuit is the ratio of capacitor or indoctor current to applied current?

Homework Equations

Q=I(c)/I(s)=I(l)/I(s)

The Attempt at a Solution

with the help of impedence and I(C)=V/X(c) and I(s)=V/Z

 

[ehild]

Was it a series or parallel RLC circuit?

How did you define the quality factor?

What did exactly your book say about the quality factor being equal to the ratio of currents?
ehild