work-energy-closure-three-row-scan - Electronic Circuits XIV: Inductors and Switching Energy Step by Step

Ramp source work is checked against stored-energy increase. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Ramp work has to match stored-energy increase

Each row builds a ramp endpoint, then cites that endpoint in the energy and work checks.

W=V I_{\text{avg}}\Delta t=\Delta E

The source-work rows close against stored energy

Voltage changes the endpoint current. The average-current work ledger still lands on the same energy increase.

\begin{array}{c|c|c|c|c}V&I_f&I_{\text{avg}}&W&\Delta E\\2\ \text{V}&1\ \text{A}&\tfrac{1}{2}\ \text{A}&1\ \text{J}&1\ \text{J}\\4\ \text{V}&2\ \text{A}&1\ \text{A}&4\ \text{J}&4\ \text{J}\\6\ \text{V}&3\ \text{A}&\tfrac{3}{2}\ \text{A}&9\ \text{J}&9\ \text{J}\\\end{array}

The accepted row binds ramp, work, and stored energy

The work value is accepted only because the ramp endpoint and energy increase agree.

W=6\ \text{V}\cdot\tfrac{3}{2}\ \text{A}\cdot1\ \text{s}=9\ \text{J}=\Delta E