# Wire Voltage Drop Calculation for DC

#### tvist21

Joined Jun 11, 2021
7
I am trying to find a clear explanation on how to calculate how much of a voltage drop there is for a given lead length.

If I am powering a 24V light that requires 0.5A using a 24Vdc power supply, how much of a voltage drop is there if I'm using 22AWG (0.33mm^2) copper wire for 100 meters? Google says copper has a resistivity of 1.68e-8.

I'm not sure why their calculation is using 0.017 rather than 1.68e-8.

Can someone give me an intuitive explanation and relate it to ohms law?

#### BobTPH

Joined Jun 5, 2013
3,658
Look up the resistance per meter of 22 ga wire, then use Ohm’s law.

Bob

#### LesJones

Joined Jan 8, 2017
3,490
The resistivity value of 1.68 x 10^-8 is the resistance of a piece of copper 1 metre long and 1 square metre in cross section.
So it is more convenient to have the resistance of a a 1 metre length of copper with a cross sectional area of 1 square mm.
A there are 1000 mm in a metre. So there are 1000000 sq mm in a square metre.
So the resistance per metre of 1 sq mm is 1000000 (10^6) times the resistance of of 1 metre with a cross section of 1 square metre.
So the resistance of 1 metre of copper with a cross section of 1 square mm is 1.68 x 10^-8 x 10^6 = 1.68 x 10^-2
0.0168.
The 0.017 is just 0.0168 rounded to 3 decimal places.
This difference will make very little difference to your calculations.
Don't forget that if the cable run is 100 metres there will be 200 metres of conducter.

Les.

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• #### Ian0

Joined Aug 7, 2020
3,232
Resistance = (length * Resistivity) / Cross sectional area
Convert everything to standard form before you work it out otherwise you're almost certain to get the decimal point in the wrong place

ρ=1.7*10^-8Ωm for copper
Don't forget that 0.3mm^2 is 0.3*10^-6 m^2

Easy to remember that 1mm^2 cable is 17mΩ/m
Also, don't forget that it varies with temperature, so ρ=1.7*10^-8Ωm is probably accurate enough.

#### MisterBill2

Joined Jan 23, 2018
9,267
To make the discussion more interesting, there is also a difference in resistiivity between hard drawn and soft drawn and different alloys of "copper" wire. So really, if you need to be exact, you need to start with the resistance per length of the size and type of wire that you are using, and then multiply that value by the length involved. And as mentioned, for a power connection, there is a voltage drop in both power conductors.
And, as mentioned, some data gives the bulk resistivity of copper, while other references use the resistance per length of a specific wire size. (same theory but much different units).
Or you can use the current capacity tables for wire, but beware that they may be based on the temperature rise and not the voltage drop.