Question

The LC series resonant circuit produces a resonant frequency '\(f\)'. If L is tripled and 'C' is increased by 3C, the resonant frequency will be

• A. \(\frac{f}{3}\)
• B. \(\frac{f}{2\sqrt{3}}\)
• C. \(6f\)
• D. \(\frac{f}{3\sqrt{2}}\)

Hint:

\(f=\dfrac{1}{2\pi\sqrt{LC}}\); here \(L\to3L\) and \(C\to C+3C=4C\).

Answer 1

The Correct Option is B

Step 1: Use proportionality
$f\propto\dfrac{1}{\sqrt{LC}}$. The product $LC$ is multiplied by $3\times4=12$.

Step 2: Compute
So $f$ is divided by $\sqrt{12}=2\sqrt3$, option (B).

Final Answer:
The frequency becomes $f/(2\sqrt3)$, option (B). \[ \boxed{\dfrac{f}{2\sqrt3}} \]