Assertion: At frequency greater than resonance frequency circuit is inductive in nature.
Reason: `X_(L) propto omega`

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we need to evaluate the assertion and the reason provided:

**Assertion:** At frequency greater than resonance frequency, the circuit is inductive in nature.

**Reason:** \( X_L \propto \omega \)

### Step-by-Step Solution:

1. **Understanding Resonance Frequency:**
- The resonance frequency (\( f_0 \)) in an RLC circuit is given by the formula:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
- At this frequency, the inductive reactance (\( X_L \)) and capacitive reactance (\( X_C \)) are equal, leading to a purely resistive impedance.

2. **Behavior of Reactances:**
- Inductive reactance is given by:
\[ X_L = \omega L \]
- Capacitive reactance is given by:
\[ X_C = \frac{1}{\omega C} \]
- Here, \( \omega \) is the angular frequency, which is related to the frequency \( f \) by \( \omega = 2\pi f \).

3. **Analyzing Frequencies Greater than Resonance:**
- When the frequency is increased beyond the resonance frequency (\( f > f_0 \)), the following occurs:
- \( X_L \) increases because it is directly proportional to \( \omega \).
- \( X_C \) decreases because it is inversely proportional to \( \omega \).

4. **Conclusion on Circuit Nature:**
- Since \( X_L \) increases and \( X_C \) decreases, the inductive reactance becomes greater than the capacitive reactance:
\[ X_L > X_C \]
- This means the circuit behaves inductively, as the net reactance is positive, leading to an overall inductive nature.

5. **Evaluating the Assertion and Reason:**
- The assertion is true: at frequencies greater than the resonance frequency, the circuit is indeed inductive.
- The reason is also true: \( X_L \) is proportional to \( \omega \), which explains why the circuit becomes inductive as frequency increases.

6. **Final Conclusion:**
- Both the assertion and reason are correct, and the reason correctly explains the assertion.

### Final Answer:
Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.

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