inductor-energy-is-half-li-squared - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

An inductor energy claim is a checked square-current ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The energy ledger squares current

The stored-energy model uses the checked inductance and current. The previous current is zero in this first ledger.

E=\frac{1}{2}LI^{2}

At fixed current, energy follows inductance

The current stays fixed across the rows, so stored energy moves with inductance.

\begin{array}{c|c|c}L&I&E\\1\ \text{H}&3\ \text{A}&\tfrac{9}{2}\ \text{J}\\2\ \text{H}&3\ \text{A}&9\ \text{J}\\4\ \text{H}&3\ \text{A}&18\ \text{J}\\\end{array}

Stored magnetic energy is one half L I squared

The field geometry is not modeled here; the trusted quantity is the finite energy ledger.

E=\frac{1}{2}LI^{2}=\frac{1}{2}\cdot2\ \text{H}\cdot\left(3\ \text{A}\right)^{2}=9\ \text{J}