Why does a contact get hot?
The bike, after a climb: the pack cable is cool, but the XT60 that joins it to the controller is warm, its nylon browned on one side. On the bench, one lug on the tool pack has browned, not its neighbors; in January, a car battery terminal gets hot while the starter cranks. Same current everywhere, one spot that heats up.
With a multimeter and the load you already have, why does this contact get hot, and how do you prove it without taking anything apart?
Show the answer
The answer
A contact is not a wire: it is a resistor, a few milliohms, and the power P = R I² it dissipates lands on far less than a pinhead. A healthy XT60 runs 0.5 to 1 mΩ per contact; at 20 A it drops 10 to 20 mV and dissipates 0.2 to 0.4 W, enough to feel warm. Worn, at 10 mΩ: 0.2 V and 4 W, enough to soften the nylon. An oxidized lug at 5 mΩ, under 30 A: 0.15 V and 4.5 W. A hot car terminal sits at 5 or 10 mΩ: 1 to 2 V of drop under the starter’s 200 to 400 A, and the starter drags.
The measurement that settles it: the multimeter on millivolts, one probe on each side of the contact, under load; the current from a clamp meter or the pack’s display; R = U / I. Above 20 to 30 mV per contact, at the connector’s rated current, you clean, retighten or replace: around 0.1 V, the contact spots soften (Holm).
Teacher’s note
The question is meant to show that two metals pressed together barely touch: only a few peaks of the surface roughness carry, the rest is oxide and air. The electrons of the whole cable squeeze through those few points: that is contact resistance, made of the real area touching, the oxide covering it, the spring pressure. This is target 7 of outcome 1.1: which movement of charge is hindered, and where.
Why a hot contact makes itself worse: the brass spring relaxes (stress relaxation, then annealing) and grips less; oxide grows faster when hot; copper gains 0.4% per degree; the nylon softens, the contacts drift out of line and bear on fewer peaks. Each effect grows R, hence P, hence temperature: a loop.
Why the ohmmeter sees nothing: its milliamp of test current makes only a microvolt across a milliohm, invisible at a tenth of an ohm; and it reads its own leads and probe tips, 0.1 to 0.5 Ω, a hundred times what you are looking for: its "zero" is the zero of the leads. Under load, the voltmeter draws nothing, the probe tips no longer count, and the load current makes the other two wires of a four-wire measurement: probes on the metal, you read the drop of the contact alone.
The square of the current is target 4 of outcome 1.3: double the current and you quadruple the heat. Two meters of 12 AWG wire also make 10 mΩ and 4 W, but spread out in the air; the contact concentrates them on a few peaks of brass inside nylon: the connector burns before the wire does.
What next?
- 1.1 Charge and its motion: the free electrons, and what hinders them.
- The pencil lead: copper resisting more when hot, measured.
- 6.2 The pack: the lugs and the nickel strip, the same milliohms.
The EGO pack opened
Ten groups, the nickel strips, the BMS.
storyElectricity before Franklin
Before it was something you measure, electricity was a parlour curiosity for two thousand years.
storyThe Leyden jar
If electricity is a fluid, you ought to be able to bottle it.
storyFranklin’s fluid
A multimeter in series shows a number with a sign, and the sign depends on which lead you put on which side.
storyGalvani’s frog
The pack of a cordless drill shows 3.7 V cells.
benchTwo nails in a glass of water
We think water conducts.
benchThe pencil lead and the lighter
We think heat gets in the way of everything that conducts: the hot contact resists more.
benchThe battery in the freezer
We think the cold drains the battery: the flashlight dies in January and comes back to life in the house.
questionWhy does a battery weaken in the cold?
January in New Brunswick, -20 °C.
the crossroads1.1 Charge and its movement
Everything tied to this idea, and the exercises.