inductor energy

Question

Energy stored in inductor of inductance L carrying current I?

RankGuru · Accepted Answer

1. **Mechanism**: Work must be done against the self-induced back emf ($\epsilon = -L\frac{di}{dt}$) to establish a current in an inductor. This work is stored as magnetic potential energy.
2. **Differential Work**: $dW = P \cdot dt = (\epsilon i) \cdot dt = (L \frac{di}{dt} \cdot i) \cdot dt = Li \cdot di$.
3. **Integration**: Total energy $U = \int_0^I Li \cdot di = L [\frac{i^2}{2}]_0^I$.
4. **Equation**: **$U = \frac{1}{2} L I^2$**.
5. **Location**: This energy is stored in the **magnetic field** of the inductor.

Rank Guru

inductor energy

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