To determine the best combination for better tuning of an LCR circuit used for communication, we need to analyze the quality factor (Q) of the circuit. The quality factor is given by the formula:
\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]
Where:
- \( Q \) is the quality factor,
- \( R \) is the resistance,
- \( L \) is the inductance, and
- \( C \) is the capacitance.
### Step-by-Step Solution:
1. **Understand the Quality Factor**:
The quality factor \( Q \) indicates how well the circuit can be tuned. A higher \( Q \) means better tuning.
2. **Analyze the Formula**:
From the formula \( Q = \frac{1}{R} \sqrt{\frac{L}{C}} \), we can deduce:
- \( Q \) is inversely proportional to \( R \) (lower resistance is better).
- \( Q \) is directly proportional to \( L \) (higher inductance is better).
- \( Q \) is inversely proportional to \( C \) (lower capacitance is better).
3. **Select Parameters for Better Tuning**:
- To achieve a high quality factor, we need:
- Low resistance \( R \)
- High inductance \( L \)
- Low capacitance \( C \)
4. **Evaluate Given Options**:
Suppose we have four options with different values of \( R \), \( L \), and \( C \). We will compare them based on the criteria established:
- Identify the option with the highest inductance \( L \).
- Identify the option with the lowest capacitance \( C \).
- Identify the option with the lowest resistance \( R \).
5. **Determine the Best Combination**:
After evaluating the options:
- If option A has \( L = 3.5 \, H \), \( R = 15 \, \Omega \), and \( C = 30 \, \mu F \),
- Compare with other options to ensure it has the highest inductance and lowest capacitance and resistance.
6. **Conclusion**:
The best combination for better tuning of the LCR circuit is the one with the highest inductance, lowest capacitance, and lowest resistance. Based on the analysis, option C (with \( L = 3.5 \, H \), \( R = 15 \, \Omega \), and \( C = 30 \, \mu F \)) is the correct answer.
### Final Answer:
Option C is the best combination for better tuning of the LCR circuit.
