Question

In an \(LC\) circuit, angular frequency at resonance is \(\omega\). The new angular frequency when inductance is made four times and capacitance is made eight times is

• A. \(\frac{\omega}{2\sqrt{2}}\)
• B. \(\frac{\omega}{4\sqrt{2}}\)
• C. \(\frac{\omega}{4}\)
• D. \(\frac{\omega}{\sqrt{2}}\)

Hint:

Resonant frequency is inversely proportional to the square root of the product of L and C.

Answer 1

The Correct Option is B

Step 1: Formula
The resonant angular frequency is given by $\omega = \frac{1}{\sqrt{LC}}$.

Step 2: Analysis
New inductance $L' = 4L$ and new capacitance $C' = 8C$.
$\omega' = \frac{1}{\sqrt{L'C'}} = \frac{1}{\sqrt{4L \times 8C}}$.

Step 3: Calculation
$\omega' = \frac{1}{\sqrt{32LC}} = \frac{1}{4\sqrt{2} \cdot \sqrt{LC}}$.
$\omega' = \frac{\omega}{4\sqrt{2}}$.
Final Answer: (B)