In an L-C-R series AC circuit, if ω0 is the resonant angular frequency, then the quality factor (Q-factor) is given by

Question

In an L-C-R series AC circuit, if ω0 is the resonant angular frequency, then the quality factor (Q-factor) is given by (A)  ω0 L/C (B)  (1/R) √ ( L/ C)  (C)  ω0 C/R (D)  L/ ω0 R

Tardigrade Admin · Accepted Answer

Quality factor Q=(XL/R)=(ω0L/R) At resonance ω0=(1/√LC) ∴ Q=(L/R)×(1/√LC)=(1/R)√(L/C)

Q. In an L-C-R series AC circuit, if $ω_{0}$ is the resonant angular frequency, then the quality factor (Q-factor) is given by

$ω_{0} L / C$

$(1/ R) \frac{L}{C}$

$ω_{0} C / R$

$L / ω_{0} R$

$L / CR$

Quality factor
$Q = \frac{X _{L}}{R} = \frac{ω _{0} L}{R}$
At resonance
$ω_{0} = \frac{1}{L C}$
$∴ Q = \frac{L}{R} \times \frac{1}{L C} = \frac{1}{R} \frac{L}{C}$

Q. In an L-C-R series AC circuit, if ω0​ is the resonant angular frequency, then the quality factor (Q-factor) is given by

ω0​L/C

(1/R)CL​​

ω0​C/R

L/ω0​R

L/CR

Quality factor Q=RXL​​=Rω0​L​ At resonance ω0​=LC​1​ ∴Q=RL​×LC​1​=R1​CL​​