Q factor is equal to ____. (a) (ωr L)/(R) (b) (1)/(R)√((L)/(C)) (c) (XL)/(R) (d) All the above

Question 114 of 132

Q. Q factor is equal to ________.

(a)

\dfrac{\omega_r L}{R}

(b)

\dfrac{1}{R}\sqrt{\dfrac{L}{C}}

(c)

\dfrac{X_L}{R}

(d) All the above

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The three listed expressions for Q factor are all mathematically equivalent forms of the same quantity, related through $\omega_r=1/\sqrt{LC}$ .

Working

The quality factor (Q factor) of a series RLC circuit at resonance is defined as

$Q=\dfrac{\omega_rL}{R}$

where $\omega_r=\dfrac1{\sqrt{LC}}$ is the resonant angular frequency.

Since $X_L=\omega_rL$ at resonance:

$Q=\dfrac{X_L}{R}$

Also substituting $\omega_r=1/\sqrt{LC}$ into $Q=\omega_rL/R$ : …

Q.Q factor is equal to ________.