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).

Answer 2

The resonance frequency \( f_0 \) of an LCR circuit is given by the formula:

\(f_0 = \frac{1}{2\pi\sqrt{LC}}\)

For an LCR circuit to have better tuning, we need to select the components (R, L, C) in such a way that it provides an optimal resonance frequency for communication circuits. Typically, the ideal resonance frequency for communication should be in the range that ensures efficient signal transmission with minimal losses.

Considerations for Better Tuning:

• Resistance (R): The resistance should be as low as possible for better tuning and less energy dissipation.
• Inductance (L) and Capacitance (C): The values of L and C should be chosen such that the resonance frequency \( f_0 \) is suitable for communication. The combination must satisfy the resonance condition with the proper frequency range.

Calculation for Each Option:

After comparing each combination for suitable resonance frequency using the formula \( f_0 = \frac{1}{2\pi\sqrt{LC}} \), it was found that:

• For option (A), the resonance frequency is not optimal for communication.
• For option (B), the resonance frequency is too high.
• For option (C), although the resistance is reasonable, the values of L and C do not provide the best tuning.
• For option (D), the combination of low resistance \( R = 15Ω \), high inductance \( L = 3.5H \), and moderate capacitance \( C = 30μF \) gives the most appropriate resonance frequency suitable for communication applications.

Thus, the correct combination for better tuning is option (D): R = 15Ω, L = 3.5H, C = 30μF.