Which combination is to be selected for better tuning of an LCR serie…

The correct answer is Option (3) → \( R = 15\,\Omega,\ L = 3.5\,\mathrm{H},\ C = 30\,\mu\mathrm{F} \)

Good tuning needs a sharp resonance, so that the circuit picks one frequency and rejects its neighbours. The sharpness is measured by the quality factor; the larger \( Q \), the better the tuning.

    \( \displaystyle Q = \frac{1}{R}\sqrt{\frac{L}{C}} \)

Option (1):

    \( \displaystyle Q = \frac{1}{20}\sqrt{\frac{1.5}{35\times10^{-6}}} = \frac{207}{20} \approx 10.4 \)

Option (2):

    \( \displaystyle Q = \frac{1}{25}\sqrt{\frac{2.5}{45\times10^{-6}}} = \frac{236}{25} \approx 9.4 \)

Option (3):

    \( \displaystyle Q = \frac{1}{15}\sqrt{\frac{3.5}{30\times10^{-6}}} = \frac{342}{15} \approx 22.8 \)

Option (4):

    \( \displaystyle Q = \frac{1}{15}\sqrt{\frac{1.5}{45\times10^{-6}}} = \frac{183}{15} \approx 12.2 \)

Option (3) has the highest quality factor, so it gives the sharpest resonance.

Shortcut: A small \( R \) and a large \( L/C \) both raise \( Q \). Options (3) and (4) share the smallest \( R = 15\,\Omega \), and Option (3) has the larger \( L \) with the smaller \( C \), so it wins without full working.

Note: A similar question was also asked in CUET (UG) 2023 on 23-05-2023 (Slot 3).