In a LCR oscillatory circuit find the energy stored in inductor at resonance. If voltage of source is 10 V and resistance is `10Omega and inductance = 1H.

Options

A. 0.5 J
B. 2 J
C. 4 J
D. 10 J

Explanation

To solve the problem of finding the energy stored in the inductor at resonance in an LCR oscillatory circuit, we can follow these steps:

### Step 1: Understand the resonance condition
In an LCR circuit at resonance, the impedance (Z) is equal to the resistance (R). This means that the circuit behaves like a purely resistive circuit.

### Step 2: Identify the given values
- Voltage (V) = 10 V
- Resistance (R) = 10 Ω
- Inductance (L) = 1 H

### Step 3: Calculate the current (I) in the circuit
Using Ohm's Law, the current can be calculated as:
\[ I = \frac{V}{Z} \]
Since the circuit is at resonance, \( Z = R \):
\[ I = \frac{V}{R} = \frac{10 \, \text{V}}{10 \, \Omega} = 1 \, \text{A} \]

### Step 4: Calculate the energy stored in the inductor
The energy (E) stored in an inductor is given by the formula:
\[ E = \frac{1}{2} L I^2 \]
Substituting the values:
\[ E = \frac{1}{2} \times 1 \, \text{H} \times (1 \, \text{A})^2 \]
\[ E = \frac{1}{2} \times 1 \times 1 = 0.5 \, \text{J} \]

### Final Answer
The energy stored in the inductor at resonance is **0.5 Joules**.

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