Which of the following combination should be selected for better tuning of a L.C.R circuit used for communication?

Options

A. R = 25 ohm, L = 1.5H, C = 45 microF
B. R = 25 ohm, L = 1.5H, C = 35 microF
C. R = 25 ohm, L = 2.5H, C = 45 microF
D. R = 25 ohm, L = 3.5H, C = 30- microF

Answer

To determine which combination should be selected for better tuning of an L.C.R circuit used for communication, we need to analyze the quality factor (Q) of the circuit. The quality factor is a measure of the selectivity of the circuit, which is its ability to respond to a specific frequency while discriminating against other frequencies.

### Step-by-Step Solution:

1. **Understand the Quality Factor (Q)**:
The quality factor (Q) is defined as:
\[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \]
where \(R\) is the resistance, \(L\) is the inductance, and \(C\) is the capacitance of the circuit.

2. **Identify the Relationship**:
From the formula, we can see that:
- \(Q\) is directly proportional to \(\sqrt{L}\) (inductance) and inversely proportional to \(\sqrt{C}\) (capacitance).
- To maximize \(Q\) (and thus improve selectivity), we want \(L\) to be large and \(C\) to be small.

3. **Evaluate the Options**:
We need to evaluate the given options based on the values of \(L\) and \(C\) provided in each option. Since the resistance \(R\) is the same for all options, we will focus on \(L\) and \(C\).

4. **Calculate Q for Each Option**:
For each option, we will calculate the quality factor \(Q\):
- **Option A**: Calculate \(Q_A\)
- **Option B**: Calculate \(Q_B\)
- **Option C**: Calculate \(Q_C\)
- **Option D**: Calculate \(Q_D\)

5. **Compare the Values**:
After calculating \(Q\) for all options, we compare the values:
- \(Q_A = 7.3\)
- \(Q_B = 8.28\)
- \(Q_C = 9.43\)
- \(Q_D = 13.67\)

6. **Select the Best Option**:
The option with the highest \(Q\) value indicates the best tuning for the L.C.R circuit. In this case, **Option D** with \(Q = 13.67\) is the best choice.

### Conclusion:
The best combination for better tuning of an L.C.R circuit used for communication is **Option D**.

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