Lessons · Electrical · voltage drop over a run
Voltage drop: the wire eats some of the volts on the way
Every foot of wire has resistance, so the far end of a long run sees less voltage than the panel; the drop is estimated with VD = 2 × K × I × L / CM, where K is 12.9 for copper, I is the amps, L the one-way length in feet and CM the wire's circular mils.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A detached workshop 120 feet from the house: the lights dim when the saw starts and the compressor motor runs hot and dies young. Nothing is faulty. The wire was sized for ampacity alone and it is fine for that; it is just too small for the distance. The 3 percent guideline is the difference between a shop that works and one the customer calls you back about.
How to think about it
Write the four numbers down with units before touching the formula: amps, one-way feet, circular mils, and K = 12.9 for copper (21.2 for aluminium). The 2 is for the trip out and back. Divide the drop by the supply voltage for a percentage, and if it is over 3 percent, go up a wire size and do it again.
Worked example
Load 12 A, run 100 ft one way, 12 AWG copper (6530 CM), 120 V supplyThe four knowns, with units.
VD = 2 × 12.9 × 12 × 100 / 6530The formula with the numbers in. Top: 2 × 12.9 × 12 × 100 = 30960.
VD = 30960 / 6530 = 4.74 VThe far end sees 120 − 4.74 = 115.3 V.
4.74 / 120 = 0.0395 = 3.95 %Over the 3 percent guideline. Not a code violation on its own; a shop that will not work well.
On 10 AWG (10380 CM): VD = 30960 / 10380 = 2.98 V = 2.5 %One size up brings it under. Same breaker, same load, more copper.
Your turn
A 30 A load, 90 ft one way, on 8 AWG copper (16510 circular mils). Write the formula with the numbers in.
VD = 2 × 12.9 × 30 × 90 /
Solve one, graded on the server
The trap
Using the round-trip length. L is the one-way distance; the 2 in the formula already sends the current out and back. Doubling it again makes every run look twice as bad and puts 6 AWG on a garden shed.