Ada Audits the Coil and Contact Numbers

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Ada Audits the Coil and Contact Numbers

The chapter switches off a 100 mH relay coil carrying 80 mA and the induced kick reaches 8000 V — enough to punch straight through a transistor rated for 60 V. The same page separates the contacts of a 50 mH vacuum-motor winding at 8 A and derates that inductive load up to a 20 A relay. This audit re-derives each coil, arc, and derating figure and asks whether the identical GPIO command can be electrically safe or unsafe depending only on the driver, flyback path, and contact rating.

Companion to the chapter Relays and Solenoids — every number here comes from that chapter.

— driver current, stored energy, arc stress, and derating, ~4 minutes

A relay or solenoid is a magnetic energy device before it is a software output. The mathematics checks current, energy, and contact stress; the physics explains why the driver, clamp, and relay rating must be selected from the switch-off case, not the GPIO command.

The chapter's values

Use only values already introduced in this chapter: a 5 V relay coil at 80 mA, the 100 mH flyback example, the 50 mH vacuum-motor winding switched from 8 A in 5 ms, the 120 V supply case, and the inductive-load derating example.

power = voltage x current; stored_energy = 0.5 x L x I^2; kickback_voltage = L x (current / switch_time); required_rating = load_current / derating_factor

The worked checks

Check	Arithmetic	Review meaning
GPIO overload	5 V x 0.080 A = 0.40 W	An 80 mA coil is a power load; the GPIO should command a driver, not source the coil current.
Stored coil energy	0.5 x 0.100 H x 0.080^2 = 0.00032 J = 0.32 mJ	The flyback path must absorb the magnetic energy every time the coil is released.
Fast switch-off spike	0.100 H x (0.080 A / 0.000001 s) = 8000 V	The chapter's example exceeds a 60 V transistor limit by about 8000 / 60 = 133 times before clamping.
Motor contact spike	0.050 H x (8 A / 0.005 s) = 80 V	The 50 mH winding can add an 80 V inductive kick as contacts separate.
Contact voltage and arc power	120 V + 80 V = 200 V; 200 V x 8 A = 1600 W	The arc concentrates kilowatt-scale instantaneous power at a tiny contact area.
Inductive derating	8 A / 0.4 = 20 A	The 8 A inductive load needs about a 20 A relay under the chapter's 0.4 derating example.

Audit conclusion: the same command can be electrically safe or unsafe depending on the driver, flyback path, load type, and derated contact rating. Record the switch-off path and the load class before approving the relay.

Every number above is taken from the chapter’s own examples and re-derived step by step.