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: Understanding the Concept
The resonant frequency of an LC circuit is \(f=\dfrac{1}{2\pi\sqrt{LC}}\).

Step 2: Key Formula or Approach
New inductance \(3L\). The capacitance is increased by \(3C\), so it becomes \(C+3C=4C\).

Step 3: Detailed Explanation
\[ f'=\frac{1}{2\pi\sqrt{3L\cdot4C}}=\frac{1}{2\pi\sqrt{12\,LC}}=\frac{f}{\sqrt{12}}=\frac{f}{2\sqrt3} \]

Final Answer:
The new frequency is \(\frac{f}{2\sqrt3}\), option (B). \[ \boxed{\dfrac{f}{2\sqrt3}\ \text{(B)}} \]