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 ______

The quality factor of a series LCR resonant circuit is given by $$Q = \frac{\omega_0 L}{R} = \frac{1}{R}\sqrt{\frac{L}{C}}$$, where $$\omega_0 = \frac{1}{\sqrt{LC}}$$ is the resonant angular frequency.

Initially, $$Q = 100 = \frac{1}{R}\sqrt{\frac{L}{C}}$$.

When the inductance is increased by two fold ($$L' = 2L$$) and the resistance is decreased by two fold ($$R' = R/2$$), the new quality factor becomes:

$$Q' = \frac{1}{R'}\sqrt{\frac{L'}{C}} = \frac{1}{R/2}\sqrt{\frac{2L}{C}} = \frac{2}{R} \cdot \sqrt{2} \cdot \sqrt{\frac{L}{C}} = 2\sqrt{2} \cdot Q$$

$$Q' = 2\sqrt{2} \times 100 = 200\sqrt{2} \approx \mathbf{282.84}$$