Question

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

• A. R= 20Ω,L =1.5H,C =35 μF
• B. R= 25Ω,L =2.5H,C =45 μF
• C. R= 25Ω,L =1.5H,C =45 μF
• D. R= 15Ω,L =3.5H,C =30 μF

Answer 1

The Correct Option is D

For better tuning of an LCR circuit used in communication, the following factors are important:

• High selectivity (sharp resonance)
• High quality factor \( Q \)

The quality factor is given by:

\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]

To maximize \( Q \), we need:

• Lower resistance \( R \)
• Higher inductance \( L \)
• Lower capacitance \( C \)

Step 1: Evaluate Each Option

Option A: \( R = 20\Omega, L = 1.5H, C = 35\mu F \)

\[ Q = \frac{1}{20} \sqrt{\frac{1.5}{35 \times 10^{-6}}} \]

Option B: \( R = 25\Omega, L = 2.5H, C = 45\mu F \)

\[ Q = \frac{1}{25} \sqrt{\frac{2.5}{45 \times 10^{-6}}} \]

Option C: \( R = 25\Omega, L = 1.5H, C = 45\mu F \)

\[ Q = \frac{1}{25} \sqrt{\frac{1.5}{45 \times 10^{-6}}} \]

Option D: \( R = 15\Omega, L = 3.5H, C = 30\mu F \)

\[ Q = \frac{1}{15} \sqrt{\frac{3.5}{30 \times 10^{-6}}} \]

Step 2: Compare

Option D has the smallest \( R \), largest \( L \), and small \( C \), which maximizes the value of \( Q \). Hence, it gives better tuning and sharper resonance.

Conclusion:

The best combination for better tuning is \({R = 15\Omega, L = 3.5H, C = 30\mu F} \), so the correct answer is (D).