In the non-resonant circuit, what will be the nature of the circuit for frequencies heigher than the resonant frequency?

Options

A. Resistive
B. Capacitive
C. inductance
D. None of these

Explanation

To determine the nature of a non-resonant circuit for frequencies higher than the resonant frequency, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circuit**:
- We are dealing with an LCR (Inductor-Capacitor-Resistor) circuit. The components involved are a resistor (R), an inductor (L), and a capacitor (C).

2. **Identifying Resonant Frequency**:
- The resonant frequency (ω_R) is the frequency at which the inductive reactance (ωL) and capacitive reactance (1/ωC) are equal. At this frequency, the circuit behaves like a purely resistive circuit.

3. **Analyzing Frequencies Above Resonant Frequency**:
- When the frequency (ω) is greater than the resonant frequency (ω > ω_R), we need to analyze the behavior of the circuit.
- The inductive reactance (X_L = ωL) increases with frequency, while the capacitive reactance (X_C = 1/ωC) decreases with frequency.

4. **Comparing Reactances**:
- For ω > ω_R:
- X_L (inductive reactance) becomes larger because it is directly proportional to ω.
- X_C (capacitive reactance) becomes smaller because it is inversely proportional to ω.

5. **Conclusion on Circuit Nature**:
- Since the inductive reactance (X_L) dominates over the capacitive reactance (X_C) when ω > ω_R, the circuit behaves more like an inductive circuit.
- Therefore, in a non-resonant circuit with frequencies higher than the resonant frequency, the nature of the circuit is inductive.

### Final Answer:
The nature of the circuit for frequencies higher than the resonant frequency in a non-resonant circuit is **inductive**.

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