Question

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

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

Answer 1

Answer: (B)

Resonant angular frequency ${\omega }_r=\frac{1}{\sqrt{LC}}...\left(i\right)$
Quality factor $Q=\frac{Resonantangularfrequency}{Bandwidth}$
Bandwidth $={\upsilon }_2-{\upsilon }_1=\frac{{\upsilon }_r}{Q}...\left(ii\right)$
where ${\upsilon }_r=$ resonant frequency $=\frac{1}{2\pi \sqrt{LC}}$
Also, $Q=\frac{{\omega }_{r}L}{R}$
$\therefore {\upsilon }_2-{\upsilon }_1=\frac{{\upsilon }_{r}R}{2\pi {\upsilon }_{r}L}=\frac{R}{2\pi L}$ (Using (i) and (ii))
${\upsilon }_2-{\upsilon }_1=\frac{R}{2\pi L}$
$=\frac{5}{2\pi \times 40\times 10^{-3}}$
$=20Hz$