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NEET PHYSICSMedium

Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication?

A

R=20 \Omega , L=1.5 H, C=35 \mu F

B

R=25 \Omega , L=2.5 H, C=45 \mu F

C

R=15 \Omega , L=3.5 H, C=30 \mu F

D

R=25 \Omega , L=1.5 H, C=45 \mu F

Step-by-Step Solution

For better tuning (higher selectivity or sharpness of resonance) in an L-C-R circuit, the Quality Factor (Q-factor) must be high. The Q-factor is given by the formula Q=1RLCQ = \frac{1}{R}\sqrt{\frac{L}{C}} . To maximize QQ, resistance (RR) should be low, inductance (LL) should be large, and capacitance (CC) should be small. Comparing the options:

  1. Q1=1201.535×10−6≈10.3Q_1 = \frac{1}{20}\sqrt{\frac{1.5}{35\times 10^{-6}}} \approx 10.3
  2. Q2=1252.545×10−6≈9.4Q_2 = \frac{1}{25}\sqrt{\frac{2.5}{45\times 10^{-6}}} \approx 9.4
  3. Q3=1153.530×10−6≈22.7Q_3 = \frac{1}{15}\sqrt{\frac{3.5}{30\times 10^{-6}}} \approx 22.7
  4. Q4=1251.545×10−6≈7.3Q_4 = \frac{1}{25}\sqrt{\frac{1.5}{45\times 10^{-6}}} \approx 7.3 Option 3 yields the highest Q-value, providing the best tuning.
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