Question

The frequency at resonance for the circuit is

• A. $\frac{1}{4\pi\sqrt{LC}}$
• B. $\frac{1}{2\pi\sqrt{LC}}$
• C. $\frac{1}{\pi\sqrt{LC}}$
• D. $\frac{2}{\pi\sqrt{LC}}$

Hint:

Parallel inductors and series capacitors both reduce the equivalent values.

Answer 1

The Correct Option is C

Step 1: Analysis
The circuit shows two inductors $L$ in parallel and two capacitors $C$ in series.
- $L_{\text{eq}} = L/2$
- $C_{\text{eq}} = C/2$

Step 2: Formula
Resonant frequency $f = \frac{1}{2\pi\sqrt{L_{\text{eq}} C_{\text{eq}}}}$.

Step 3: Calculation
$f = \frac{1}{2\pi\sqrt{(L/2)(C/2)}} = \frac{1}{2\pi\sqrt{LC/4}}$
$f = \frac{1}{2\pi (1/2) \sqrt{LC}} = \frac{1}{\pi\sqrt{LC}}$.

Step 4: Conclusion
Hence, the frequency is $\frac{1}{\pi\sqrt{LC}}$. Final Answer: (C)