Question

In a series $LCR$ resonant circuit, the quality factor is measured as $100$. If the inductance is increased by two-fold and resistance is decreased by two-fold, then the quality factor after this change will be equal to ________. $($up to two decimal places$)$.

Answer 1

We know that,
Quality factor, $Q=\frac{{\omega }_{o}L}{R}=\sqrt{\frac{1}{LC}}\times \frac{L}{R}=\frac{\sqrt{L}}{R\sqrt{C}}$

$\Rightarrow Q=100$ $[$Given$]$

If the inductance is increased by two-fold and resistance is decreased by two-fold, then the quality factor after this change,

$Q^{{}^{\prime }}=\frac{\sqrt{\left(2L\right)}}{\left(R/2\right)\sqrt{C}}=2\sqrt{2}\times \frac{\sqrt{L}}{R\sqrt{C}}$

$\Rightarrow Q^{{}^{\prime }}=2\sqrt{2}\times 100=282.84$