Ada Audits the Coil and Stall-Current Physics
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Ada Audits the Coil and Stall-Current Physics
A 12 V motor whose windings measure 2 ohms draws 6 A at stall but settles to 1.5 A once 9 V of back-EMF builds — a 4× inrush — while a 20 mH coil at 0.5 A quietly stores 2.5 mJ. Those figures look reassuringly small on the page. This audit re-derives the stored-energy, stall-current, and back-EMF numbers and asks whether a supply sized for the tidy 1.5 A running current can survive the 6 A startup surge, and whether that stored energy has anywhere safe to go.
Companion to the chapter The Output Side of IoT — every number here comes from that chapter.
Protection is not an accessory — it is arithmetic. Three equations decide whether the switch and supply survive: stored coil energy ½LI², Ohm's-law stall current V/R, and the back-EMF that reins it in. Every number below is one this chapter already stated.
1. A coil stores energy in its magnetic field.
With 20 mH (0.020 H) carrying 0.5 A:
2. Before back-EMF builds, the motor is just its winding resistance.
A 12 V motor with 2 Ω windings, at the instant of startup or a stall, obeys plain Ohm's law:
3. Once spinning, back-EMF opposes the supply.
At 9 V of back-EMF only the difference drives current, so the surge is several times the running draw:
| Physical quantity | Arithmetic shown | Result |
| Stored coil energy (½LI²) | 0.5 × 0.020 × 0.5² | 0.0025 J (2.5 mJ) |
| Stall / startup current (V / R) | 12 / 2 | 6 A surge |
| Running current (back-EMF 9 V) | (12 − 9) / 2 | 1.5 A |
| Inrush ratio (surge ÷ running) | 6 / 1.5 | 4× |
| Solenoid valve power | 12 × 0.5 | 6 W |
What this means for your design: 2.5 mJ sounds negligible until it has nowhere to go — open the switch with no flyback diode, snubber, or TVS and the coil forces that energy into a fast voltage spike that can punch through the driver transistor. And a supply sized for the tidy 1.5 A running current will collapse under the 6 A startup surge, four times higher, browning out the controller. Size the driver and supply to the stall current, and give every inductive load a safe path for its stored energy.
Every number above is taken from the chapter’s own examples and re-derived step by step.