What is the formula for the average energy stored in an inductor?

The average energy stored in an inductor is calculated using the formula ( \frac{1}{2} LI^2 ), where ( L ) represents the inductance of the inductor and ( I ) is the current flowing through it. This formula derives from the fundamental principles of electromagnetic energy storage.

When a current flows through an inductor, it generates a magnetic field, and the energy associated with this magnetic field increases with the square of the current. The factor of ( \frac{1}{2} ) in the formula arises from integrating the voltage across the inductor with respect to current, reflecting that the energy increases progressively as the current rises.

Understanding this relationship not only illustrates how inductors function in electronic circuits, particularly in applications involving energy storage and management, such as in power supplies and converters, but also highlights the quadratic dependence on current, indicating that small increases in current can lead to significantly higher stored energy.

The other options relate to different components and energy storage scenarios—capacitance and the energy stored in capacitors or charges—thus are not applicable to inductors.