Choose the correct expression of energy stored in an inductor ?

Options

A. `U =1//2 L I _(0) ^(2)`
B. `U = 1//2 LI _(0)`
C. `U = 1 //3 LI _(0) ^(3)`
D. None of the above

Explanation

To find the correct expression for the energy stored in an inductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**: The energy stored in an inductor is related to the work done to establish the current through it. When current flows through an inductor, it creates a magnetic field, and energy is stored in that magnetic field.

2. **Formula for Energy in an Inductor**: The energy (U) stored in an inductor can be derived from the work done to establish the current. The formula for the energy stored in an inductor is given by:
\[ U = \frac{1}{2} L I^2 \]
where:
- \( U \) = energy stored in the inductor,
- \( L \) = inductance of the inductor,
- \( I \) = current flowing through the inductor.

3. **Identifying the Variables**: In the expression, \( I \) can be represented as \( I_0 \) (the maximum or steady-state current), so we can rewrite the formula as:
\[ U = \frac{1}{2} L I_0^2 \]

4. **Evaluating the Options**: Now, let's evaluate the given options:
- Option 1: \( U = \frac{1}{2} L I_0^2 \) (This matches our derived formula)
- Option 2: \( U = \frac{1}{2} L I_0 \) (This is incorrect)
- Option 3: \( U = \frac{1}{3} L I_0^3 \) (This is incorrect)
- Option 4: None of the above (This is incorrect since we have a correct option)

5. **Conclusion**: The correct expression for the energy stored in an inductor is:
\[ U = \frac{1}{2} L I_0^2 \]
Thus, the correct answer is **Option 1**.