Wire Voltage Drop
Round-trip drop over a copper pair: AWG size, one-way length, and load current.
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The engineering
The factor everyone forgets is the 2: current goes out on one conductor and comes home on the other, so a '10-meter run' is 20 meters of copper. Low-voltage systems feel this hardest — the same 1.7 V that vanishes politely in a 120 V feeder is 14% of a 12 V rail, which is why automotive and solar people size wire like they mean it.
This is 20 °C copper; resistance climbs ~0.4%/°C, so a wire at 60 °C in a hot engine bay drops ~16% more than the card says. Common design targets: 3% for building branch circuits (NEC recommendation, not law), 5–10% tolerated in 12 V vehicle wiring for non-critical loads.
Where this math comes from
Georg Ohm published the law in 1827 to widespread indifference and some hostility; it took the telegraph boom to make V = IR the most economically important equation of the century, since every mile of undersized wire was money spent twice.
The war of the currents was a voltage-drop story: Edison's 110 V DC couldn't reach past a mile of practical copper, which is precisely the arithmetic on this card scaled up — and precisely why Tesla and Westinghouse's high-voltage AC transmission won.
- 1827Georg OhmDie galvanische Kette — V = IR.
- 1857Brown & SharpeAWG standardizes the copper in the denominator.
- 1897National Electrical CodeFirst NEC; drop guidance enters wiring practice, circa.
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