Which of the following combination should be selected for better tuni…

The correct answer is Option (3) → R = 10 Ω, L = 5.0 H, C = 25 μF

The sharpness of tuning of a series LCR circuit at resonance is measured by its quality factor; the larger the Q, the sharper the tuning and the better the circuit separates one station from its neighbours.

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

Evaluating for each option:

    Option 1: \( \displaystyle \frac{1}{30}\sqrt{\frac{2.5}{45\times10^{-6}}} \approx 7.9 \)

    Option 2: \( \displaystyle \frac{1}{25}\sqrt{\frac{3.5}{30\times10^{-6}}} \approx 13.7 \)

    Option 3: \( \displaystyle \frac{1}{10}\sqrt{\frac{5.0}{25\times10^{-6}}} \approx 44.7 \)

    Option 4: \( \displaystyle \frac{1}{20}\sqrt{\frac{1.5}{35\times10^{-6}}} \approx 10.4 \)

Option 3 has the largest Q.

Shortcut: Q rises with L, falls with C and falls with R. Option 3 has the smallest R (10 Ω), the largest L (5.0 H) and the smallest C (25 μF) at the same time, so it has the largest Q without any calculation.