Quality Factors
The Q of an inductor or capacitor is the ratio of its reactance to its resistance.
Example 01
A inductor and a resistor in series
\[Q = \frac{\omega L}{R}\]Example 02
A capacitor and a resistor in series
\[Q = \frac{1}{\omega CR}\]In general \(Q\) will depend on frequency \(\omega\)
Example 03
Four elements \(L, R_L, C, R_C\) in series, at the resonant frequency \(\omega_0\)
\[Q = \frac{\omega_0 L}{R_L + R_C} = \frac{1}{\omega_0 C (R_L + R_C)}\]