References / Physics and formulas

Pulse completeness from the L over R time constant

Established physics
When resistance and inductance are known, the report shows how completely each pulse builds up current, using the coil's electrical time constant.
Where it appears in the report: Engineering Details, Design and Engineering Guidance

The evidence

In a resistor-inductor circuit, the current rises toward its full value on a time constant equal to inductance divided by resistance. It reaches about 95 percent of the build-up at three time constants and about 99 percent at five. The report checks each pulse width against these standard points to judge whether the pulse is sufficient, marginal, or cut short.
How coil current builds up over the L over R time constantA rising curve showing coil current building toward its final value. It reaches about 63 percent of final after one time constant, 95 percent after three, and 99 percent after five. A pulse is essentially complete by about three time constants.100%63%1τ (63%)3τ (95%)5τ (99%)pulse essentially completeTime (multiples of the L/R time constant τ)Current built up (% of final)© 2026 Gauss Labs
Coil current does not switch on instantly; it builds up along this curve, set by the coil's L/R time constant. It reaches about 63% of full after one time constant, 95% after three, and 99% after five. If the pulse is at least about three time constants long, the current has essentially finished building, so the pulse is complete.

Primary sources

  • Standard resistor-inductor (RL) circuit result; any introductory electromagnetics or circuits text.