Question

Which of the following combinations should be selected for better tuning of an $L-C-R$ circuit used for communication?

• A. $R=25\Omega ,L=2.5H,C=45\mu F$
• B. $R=20\Omega ,L=1.5H,C=35\mu F$
• C. $R=15\Omega ,L=3.5H,C=30\mu F$
• D. $R=25\Omega ,L=1.5H,C=45\mu F$

Answer 1

The correct option is C $R=15\Omega ,L=3.5H,C=30\mu F$

Quality factor of an $L-C-R$ circuit is given by,
$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$
So, checking each options one by one, we have
$Q_1=\frac{1}{20}\sqrt{\frac{1.5}{35\times {10}^{-6}}}=50\times \sqrt{\frac{3}{70}}=10.35$

$Q_2=\frac{1}{25}\times \sqrt{\frac{2.5}{45\times {10}^{-6}}}=40\times \sqrt{\frac{5}{90}}=9.43$

$Q_3=\frac{1}{15}\sqrt{\frac{3.5}{30\times {10}^{-6}}}=\frac{100}{15}\sqrt{\frac{35}{3}}=22.77$

$Q_4=\frac{1}{25}\times \sqrt{\frac{1.5}{45\times {10}^{-6}}}=\frac{40}{\sqrt{30}}=7.30$

Clearly $Q_3$ is maximum out of $Q_1,Q_2,Q_3$ and $Q_4$.
Hence, option $\left(c\right)$ should be selected for better tuning of an $L-C-R$ circuit.