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

Step 2: New values
L is increased by 2L, so the new inductance is \(L + 2L = 3L\). The capacitance becomes \(9C\).
\[ f' = \frac{1}{2\pi\sqrt{3L \cdot 9C}} = \frac{1}{2\pi\sqrt{27LC}} = \frac{f}{\sqrt{27}} = \frac{f}{3\sqrt3} \]
This is option (D).

Final Answer:
The new resonant frequency is \(\dfrac{f}{3\sqrt3}\), option (D). \[ \boxed{\frac{f}{3\sqrt{3}}} \]