Question

A series LCR circuit has R = 5 $\Omega$, L = 40 mH and C = 1 $\mu$F, the bandwidth of the circuit is:

• A. 10 Hz
• B. 20 Hz
• C. 30 Hz
• D. 40 Hz

Answer 1

The correct option is B 20 Hz

Resonant angular frequency ${\omega }_r=\frac{1}{\sqrt{LC}}$ ....(i}
Quality factor $Q=\frac{Resonantangularfrequency}{Bandwith}$

Bandwidth = ${\nu }_2-{\nu }_1=\frac{{\nu }_r}{Q}$ .....(ii)
where ${\nu }_r=resonantfrequency=\frac{1}{2\pi \sqrt{LC}}$
Q = quality factor.
Also, Q = $\frac{{\omega }_{r}L}{R}$

$\therefore {\nu }_2-{\nu }_1=\frac{{\nu }_{r}R}{2\pi {\nu }_{r}L}=\frac{R}{2\pi L}$ ( Using (i) and(ii))

${\nu }_2-{\nu }_1=\frac{R}{2\pi L}=\frac{5}{2\pi \times 40\times {10}^{-3}}=20Hz$