Question

In resonance condition, the frequency of L-C circuit is

• A. \( \frac{1}{2\pi} \sqrt{\frac{1}{LC}} \)
• B. \( 2\pi \sqrt{\frac{1}{LC}} \)
• C. \( 2\pi \sqrt{LC} \)
• D. \( \frac{1}{2\pi} \sqrt{LC} \)

Hint:

Resonance frequency is crucial in L-C circuits for efficient energy transfer, and it is inversely proportional to the square root of the product of L and C.

Answer 1

The Correct Option is A

Step 1: Formula for resonance frequency in an L-C circuit.
The resonance frequency of an L-C circuit is given by the formula: \[ f = \frac{1}{2\pi \sqrt{LC}} \] where \( L \) is the inductance and \( C \) is the capacitance. This frequency occurs when the inductive reactance equals the capacitive reactance.
Step 2: Conclusion.
Thus, the correct expression for the resonance frequency is \( \frac{1}{2\pi} \sqrt{\frac{1}{LC}} \).
\[ \boxed{\frac{1}{2\pi} \sqrt{\frac{1}{LC}}} \]