What happens to the quality factor of a series LCR circuit if its inductance is made four times and its resistance is halved?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → It becomes four times.
The quality factor of a series LCR circuit is \( Q=\omega_0L/R \), where the resonant angular frequency is \( \omega_0=1/\sqrt{LC} \). In terms of \( L \), \( C \) and \( R \), the quality factor is:
\( \begin{aligned} Q &= \frac{\omega_0L}{R} \\ &= \frac{1}{R}\sqrt{\frac{L}{C}} \end{aligned} \)
With the inductance made \( 4L \) and the resistance made \( R/2 \), the new quality factor is:
\( \begin{aligned} Q' &= \frac{1}{R/2}\sqrt{\frac{4L}{C}} \\ &= 2\times2\times\frac{1}{R}\sqrt{\frac{L}{C}} \\ &= 4Q \end{aligned} \)