Physics - EMI/AC Question with Solution | TestHub

The resonance frequency of a series LCR circuit is given by ${\omega }_0=\frac{1}{\sqrt{LC}}$. Since L and C remain unchanged, the resonance frequency ${\omega }_0$ also remains unchanged. The quality factor (Q-factor) of a series LCR circuit is given by $Q=\frac{{\omega }_{0}L}{R}$ or $Q=\frac{1}{R}\sqrt{\frac{L}{C}}$.

If the resistance R is doubled (R' = 2R) and L, C, and ${\omega }_0$ remain unchanged, the new Q-factor will be $Q^{\prime }=\frac{{\omega }_{0}L}{2R}=\frac{1}{2}\left(\frac{{\omega }_{0}L}{R}\right)=\frac{Q}{2}$. Therefore, the resonance frequency remains unchanged, and the Q-factor is halved.