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Choose the correct expression of energy ...

Choose the correct expression of energy stored in an inductor ?

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

Text Solution

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The correct Answer is:
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**.

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: \[ ...
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