The current graph for resonance in LC circuit is

Options

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Answer

To solve the question regarding the current graph for resonance in an LC circuit, we can break down the solution into clear steps:

### Step 1: Understand the LC Circuit
An LC circuit consists of an inductor (L) and a capacitor (C) connected together. The behavior of the circuit is characterized by its natural frequency, which is given by the formula:
\[ \omega_0 = \frac{1}{\sqrt{LC}} \]
where \(\omega_0\) is the angular frequency at which resonance occurs.

### Step 2: Define Resonance Condition
At resonance, the inductive reactance (\(X_L\)) equals the capacitive reactance (\(X_C\)):
\[ X_L = X_C \]
This leads to the condition where the impedance (\(Z\)) of the circuit becomes zero, allowing maximum current to flow through the circuit.

### Step 3: Analyze Current Behavior
As the frequency of the applied AC signal approaches the natural frequency (\(\omega_0\)), the impedance of the circuit approaches zero. According to Ohm's Law:
\[ I = \frac{E}{Z} \]
where \(I\) is the current, \(E\) is the voltage, and \(Z\) is the impedance. When \(Z\) approaches zero, the current (\(I\)) approaches infinity:
\[ I \to \infty \quad \text{as} \quad Z \to 0 \]

### Step 4: Graphical Representation
In a graph of current versus frequency, the current will show a peak at the natural frequency (\(\omega_0\)). This peak represents the resonance condition where the current is maximized. The graph typically resembles a sharp peak at the frequency corresponding to the natural frequency of the LC circuit.

### Step 5: Identify the Correct Graph
Given the options, we need to identify the graph that shows a peak at the natural frequency. The correct graph will depict the current rising sharply as it approaches the natural frequency and then falling off as the frequency moves away from \(\omega_0\).

### Conclusion
The correct answer is the graph that shows the current peaking at the natural frequency of the LC circuit.

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