inductor-energy-is-half-li-squared - Electronic Circuits XIII & XIV: Power Supplies and Switching Energy Step by Step

An inductor-energy-is-half-L-I-squared scan holds the current fixed and varies the inductance across three rows, checking that stored magnetic energy E = L * I^2 / 2 recomputes row by row. The arithmetic is exact only for the stated inductances, currents, stored energies, and rows in the ideal lossless inductor model. Real inductors add winding resistance, core saturation, core loss, switch loss, current-sense/probe calibration limits, finite precision, and measurement uncertainty.

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}