Ada Audits the Driver Power Path

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

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Ada ADA · CALCULATION AUDIT

Ada Audits the Driver Power Path

A greenhouse fan and an irrigation solenoid both run from 12 V, drawing 6 W and 4.8 W, but the number that decides reliability is the 2 A startup surge: pushed through 0.3 Ω of wire and connector resistance it drops 0.6 V, so the load sees only 11.4 V while the wiring itself burns 1.2 W. This audit re-derives each figure with the power law and Ohm’s law and asks whether that 0.6 V sag is trivial, or enough to brown out a marginal 3.3 V controller sharing the same rail.

Companion to the chapter How Actuators Work — every number here comes from that chapter.

— the power law and Ohm's law across the actuator interface, ~4 minutes

Two equations govern every number on this page: the power law P = V × I for how much the load draws, and Ohm's law V = I × R for what the wiring steals on the way. Each value below is one the chapter already gave; I only carry the arithmetic through.

1. Running power is the power law.

The greenhouse fan and the irrigation solenoid both run from 12 V; only their currents differ:

P = V × I  →  fan: 12 × 0.5 = 6 W  |  solenoid: 12 × 0.4 = 4.8 W

2. The wiring is a resistor in series.

At the 2 A startup surge, 0.3 Ω of wire and connector resistance drops voltage before the driver even sees the load, so the load receives less than the nominal 12 V:

Vdrop = I × R = 2 × 0.3 = 0.6 V  →  Vload = 12 − 0.6 = 11.4 V

3. That lost voltage becomes heat, and a held coil spends energy.

The wiring burns I²R, and the solenoid's safe 5 s energize window sets its energy budget:

Quantity Arithmetic shown Result
Fan running power 12 × 0.5 6 W
Solenoid running power 12 × 0.4 4.8 W
Startup wiring drop (Ohm's law) 2 × 0.3 0.6 V
Voltage actually reaching the load 12 − 0.6 11.4 V
Heat burned in the wiring (I²R) 2² × 0.3 1.2 W
Solenoid energy over a 5 s hold 4.8 × 5 24 J

What this means for your design: the 0.6 V startup sag looks trivial, but it lands on the same rail that feeds a 3.3 V regulator, and 0.6 V of ripple during inrush is enough to brown out a marginal controller and reset it. The 1.2 W dissipated in a thin connector is exactly what makes it warm to the touch. Give the load its own supply sized to the startup current, not the running current, and read the 0.6 V as evidence that wiring resistance and inrush — not steady power — decide whether the board resets.

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