Rankers Physics

Alternating Current: Practice Problem & Solution

23. Which of the following combinations should be selected for better tuning of an L-C-R circuit used for communication? (2016 - II)
$ R = 15 \Omega, L = 3.5 H, C = 30 \mu F $
$ R = 25 \Omega, L = 1.5 H, C = 45 \mu F $
$ R = 20 \Omega, L = 1.5 H, C = 35 \mu F $
$ R = 25 \Omega, L = 2.5 H, C = 45 \mu F $

Solution Explained:

To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:

For better tuning of an L-C-R circuit, the quality factor $Q = \frac{1}{R}\sqrt{\frac{L}{C}}$ must be as high as possible.
For option a, $Q = \frac{1}{15}\sqrt{\frac{3.5}{30 \times 10^{-6}}} \approx 22.7$.
For options b, c, and d, $Q$ is approximately $7.3$, $10.4$, and $9.4$ respectively.
Therefore, the combination in option a has the highest Q-factor.

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