energy-current-square-three-row-scan - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

The stored-energy square law is scanned with three current rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Energy squares current before multiplying by inductance

The inductor stays fixed. The changing quantity is current, and the energy row uses current squared.

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

Current-square rows make the nonlinear step visible

The current values move evenly, but energy does not. Squaring the current creates the larger jumps.

\begin{array}{c|c|c|c}L&I&I\cdot I&E\\2\ \text{H}&2\ \text{A}&4&4\ \text{J}\\2\ \text{H}&4\ \text{A}&16&16\ \text{J}\\2\ \text{H}&6\ \text{A}&36&36\ \text{J}\\\end{array}

The checked energy row carries the square-current result

The accepted energy label is generated from the same inductance and current shown in the diagram.

E=\frac{1}{2}\cdot2\ \text{H}\cdot\left(4\ \text{A}\right)^{2}=16\ \text{J}