Question

A series resonant circuit consists of an inductor 'L' and capacitor 'C' which produces resonant frequency 'f'. If 'L' is increased by '2L' and 'C' is changed to '9C' the resonant frequency will be

• A. \(\frac{f}{3}\)
• B. \(\frac{f}{2}\)
• C. \(\frac{f}{2\sqrt{2}}\)
• D. \(\frac{f}{3\sqrt{3}}\)

Hint:

Resonant frequency f = 1 / (2 pi sqrt(LC)).

Answer 1

The Correct Option is D

Step 1: Product LC
Originally $LC$. Now $(3L)(9C) = 27LC$.

Step 2: Frequency
$f \propto (LC)^{-1/2}$, so $f' = f/\sqrt{27}$.

Step 3: Simplify
$\sqrt{27} = 3\sqrt3$. Option (D).

Final Answer:
Option (D). \[ \boxed{\frac{f}{3\sqrt{3}}} \]