Question

Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?

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

Answer 1

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

Formula used:

$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$

Tuning of an LCR circuit depends on quality factor of the circuit.

Tuning will be better when quality factor of the circuit is high. For $Q$ to be high, $R$ should be low, $L$ should be high, and $C$ should be low.

As we know, quality factor of an LCR circuit is given by:

$Q=\frac{1}{R}\sqrt{\frac{L}{C}}$


$Q_1=\frac{1}{20}\sqrt{\frac{1.5}{35\times {10}^{-6}}}=50\times \sqrt{\frac{3}{70}}=10.35$


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


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


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

From the above observation $Q_3$ is maximum.

Final Answer: Option (c)