double-current-quadruples-energy - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

Changing only current exposes the square in the energy law. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Current is the squared variable

The inductance stays at 2 H. Changing current changes stored energy by the square.

E\propto I^{2}\quad\text{when }L\text{ is fixed}

Energy grows by the square of current

The rows show why a doubled current stores four times as much energy in the same inductor.

\begin{array}{c|c|c}L&I&E\\2\ \text{H}&1\ \text{A}&1\ \text{J}\\2\ \text{H}&3\ \text{A}&9\ \text{J}\\2\ \text{H}&6\ \text{A}&36\ \text{J}\\\end{array}

Doubling current quadruples the stored energy

The inductor is unchanged. The current is squared before the energy is computed.

3\ \text{A}\rightarrow9\ \text{J}\quad;\quad6\ \text{A}\rightarrow36\ \text{J}