At resonant frequency

Options

A. `omega = sqrt ((L)/(C))`
B. `omega = (1)/( sqrt( LC))`
C. `omega = sqrt (LC)`
D. None of these

Explanation

To solve the question regarding the resonant frequency in an RLC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Resonance in RLC Circuit**:
At the resonant frequency, the inductive reactance (XL) is equal to the capacitive reactance (XC). This is a fundamental property of RLC circuits.

2. **Expressing Inductive and Capacitive Reactance**:
- The inductive reactance (XL) is given by the formula:
\[ X_L = \omega L \]
- The capacitive reactance (XC) is given by the formula:
\[ X_C = \frac{1}{\omega C} \]

3. **Setting Inductive Reactance Equal to Capacitive Reactance**:
At resonance, we set these two reactances equal to each other:
\[ \omega L = \frac{1}{\omega C} \]

4. **Cross-Multiplying to Solve for Omega**:
Cross-multiplying gives:
\[ \omega^2 = \frac{1}{LC} \]

5. **Taking the Square Root**:
Taking the square root of both sides, we find:
\[ \omega = \frac{1}{\sqrt{LC}} \]

6. **Identifying the Correct Option**:
From the options provided:
- \( \omega = \sqrt{\frac{L}{C}} \)
- \( \omega = \frac{1}{\sqrt{LC}} \)
- \( \omega = \sqrt{LC} \)
- None of these.

The correct answer is:
\[ \omega = \frac{1}{\sqrt{LC}} \]

### Conclusion:
Thus, the correct option is the second one: \( \omega = \frac{1}{\sqrt{LC}} \).

---