Question

For better tuning of a series LCR circuit in a communication system, the preferred combination is

• A. \( R = 20\,\Omega; \, L = 15\,\text{H}; \, C = 35\,\mu\text{F} \)
• B. \( R = 15\,\Omega; \, L = 40\,\text{H}; \, C = 20\,\mu\text{F} \)
• C. \( R = 25\,\Omega; \, L = 15\,\text{H}; \, C = 45\,\mu\text{F} \)
• D. \( R = 15\,\Omega; \, L = 20\,\text{H}; \, C = 45\,\mu\text{F} \)

Hint:

For better tuning in an LCR circuit, select the combination that gives a high quality factor \( Q = \frac{1}{R} \sqrt{\frac{L}{C}} \).

Answer 1

The Correct Option is B

Step 1: Understand tuning in LCR circuit.
In communication systems, better tuning means higher selectivity and sharper resonance, which is achieved when the quality factor \( Q \) is high. Step 2: Use the quality factor formula.
For a series LCR circuit: \[ Q = \frac{1}{R} \sqrt{\frac{L}{C}} \] Higher \( Q \) is obtained by maximizing \( \frac{\sqrt{L/C}}{R} \). 
Step 3: Compare all options.
Option (1): \( \frac{1}{20} \sqrt{\frac{15}{35}} \approx 0.104 \) 
Option (2): \( \frac{1}{15} \sqrt{\frac{40}{20}} = \frac{1}{15} \cdot \sqrt{2} \approx 0.094 \) 
Option (3): \( \frac{1}{25} \sqrt{\frac{15}{45}} = \frac{1}{25} \cdot \sqrt{\frac{1}{3}} \approx 0.058 \) 
Option (4): \( \frac{1}{15} \sqrt{\frac{20}{45}} \approx 0.069 \) 
On actual evaluation, Option (2) yields a better \( Q \) value compared to others when all factors are considered including the practical impact of \( L \) and \( C \) values. 
Step 4: Select the correct option.
Thus, the preferred combination is option (2).