Question
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.
$$R = 25\,\Omega ,L = 1.5\,H,C = 45\mu F$$
Answer :
$$R = 15\,\Omega ,L = 3.5\,H,C = 30\mu F$$
Solution :
Key Idea
For better tuning, peak of current growth must be sharp. This is ensured by a high value of quality factor $$Q.$$
Now, quality factor is given by $$Q = \frac{1}{R}\sqrt {\frac{L}{C}} $$
From the given options, highest value of $$Q$$ is associated with $$R = 15\,\Omega ,L = 3.5\,H,C = 30\mu F$$