Question

Quality factor of a series LCR circuit decreases from $3$ to $2$. Resonant frequency is $600Hz$. Change in band width is

• A. Zero
• B. $100Hz$ increase
• C. $100Hz$ decrease
• D. $300Hz$ increase

Answer 1

The correct option is B $100Hz$ increase

Band width $\beta =\frac{w_r}{Q}$

where $w_o=600$ Hz is the resonant frequency and $Q$ is the quality factor.

So, band width increases if quality factor decreases.

Initial band width ${\beta }_1=\frac{w_o}{Q_1}$

$\therefore$ ${\beta }_1=\frac{600}{3}=200$ Hz

Final band width ${\beta }_2=\frac{w_o}{Q_2}$

$\therefore$ ${\beta }_1=\frac{600}{2}=300$ Hz

Thus increase in band width $\Delta \beta ={\beta }_2-{\beta }_1$

$⟹$ $\Delta \beta =300-200=100$ Hz