## NEC Voltage Drop

## NEC Voltage Drop

(OP)

I am a structural engineer tasked with finding the maximum wire run length for a simple modular building. The panel has 120v receps with the branch load rating of 900 Watts. So, I'm working with 7.5 amps. I am allowed 2% voltage drop on the branch circuit (ASHRAE requirement I believe). Googling has allowed me to find my answer, but the equation isn't sitting right with me and in the interest of getting a better understanding, I have some questions.

First, the voltage drop equation using the circular mils approach is fairly easy if you don't consider units in the equation:

VD = 2*Length*Load*K / CM

Therefore Length= VD*CM/(2*Load*K)= 2.4*6530/(2*7.5*12.9) =

Where:

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

First, the voltage drop equation using the circular mils approach is fairly easy if you don't consider units in the equation:

VD = 2*Length*Load*K / CM

Therefore Length= VD*CM/(2*Load*K)= 2.4*6530/(2*7.5*12.9) =

**80.99 feet**... easy.Where:

- VD = voltage drop = 2.4 (120v * 2%)
- Length = solved value in ft
- K = 12.9 Ohms (found via several google searches, don't know how it is derived or where to find this value in NEC). I have found that resistivity of copper is 1.724x10^-8 Ohm*meter @ 20 degrees C, but I can't correlate this into the K value @ 75 degreees C.
- CM = Circular mils = 6530 for 12 AWG (I understand this is the wire diameter squared, so this should be in [in/1000]^2). However, in Table 8 of Chapter 9, the area column is given in mm^2 and Circular mils and converting one to the other does not result in the same value.

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

## RE: NEC Voltage Drop

I developed the following Mathcad custom units and functions to help keep things straight:

## RE: NEC Voltage Drop

First, thanks for the key to understanding!

Ok, so my variable 'CM' doesn't have a unit of area. 'cm' is basically a new unit that represents how many defined areas (area of square wire with 1 mil edges) are within an area. So it is unitless because it is square area (using actual wire diameter as leg length) divided by defined square area of (in/1000)^2. I also think I had the wrong units of K and with this new definition of the unitless 'cm', I think I have it all resolved. The units of 'K' should actually be Ohm*1000cm/1000ft and the 1000's cancel out to leave you with Ohm*cm/ft and 'cm' is defined as unity, so it further reduces to Ohm/ft.

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

## RE: NEC Voltage Drop

Thanks again jghrist for explaining the CM value.

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

## RE: NEC Voltage Drop

Buildings require building wiring.

That means Romex or conduited THHN or similar.

Those need to be a minimum of 14AWG unless it's a commercial space which requires 12AWG minimum.

Doing a mess-O-math to come up with an unuseable size wire is not too useful.

14AWG wire is 0.002525 Ω/ft

twice that is the round trip, "dropping resistance"

0.002525 Ω/ft x 2 = 0.00505 Ω/ft

2% of 120V = 2.4V

7.5A x 0.00505 Ω/ft x L ft = 2.4V

L ft = 2.4V / (7.5A x 0.00505 Ω/ft)

L ft = 63ft of 14AWG

or

L ft = 2.4V / (7.5A x 0.00505 Ω/ft)

L ft = 100.8ft of 12AWG

Keith Cress

kcress - http://www.flaminsystems.com

## RE: NEC Voltage Drop

You are using Ohm's law which I think is easier (at least more intuitive to me) if you know where to get the appropriate design resistance (0.002525 ohm/ft for 14 AWG in your example). I don't know where to get these values. Also, I don't know if the Ohm's law approach is acceptable for calculating voltage drop vs the circular mil method. I have used the circular mil method in the past (without understanding the units) and it was accepted by plan reviewers. So, I'm sticking with that method unless I knew otherwise. Using my calculation above and back tracking to get the round-trip resistance for 12 AWG, I get 0.00395 Ohm/ft. Maybe these approaches are equivalent, just a matter of formatting the equations and variables. My statement would be true if your round-trip resistance (0.002525 Ohm/ft) is equal to 2*K/CM of 14 AWG. But regardless if they are the same or not, I now know where to get 'K' and 'CM' values, but I don't know where to look up the resistance value you gave. If the correlation is truly 2*K/CM, then I might as well still use the circular mil equation since I have to look up K and CM anyway. However, if there is a table of AWG resistances per ft, I would interested in changing my approach and I would ask why they decided to break one variable (resistance per ft) into two variables: K and CM? Again, Ohm's law is simple... just tell me what the design resistance value of the 12 AWG wire is NEC!

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

## RE: NEC Voltage Drop

The main issue had been answered by learned contributors.

I wish to add the following for your information:

1. NEC states VD for (a) [branch circuits] not exceeding 3% and (b) [max total on both feeders and branch circuits] not exceeding 5%.

2. For VD, computation see NEC Article

215-2....with basic formulaVD = (2xLxRxI)/ 1000 (volt)where: L=one way length of circuit (ft),

R= conductor resistance in ohm per 1000ft at 75

^{o}C . See Chapter 9 Table 8,I= load current (A)

3.

Chapter 9 Table 8(a) AWG or kcmil 14, 7 strand, uncoated copper 3.14 ohm/1000ft, or 1 strand uncoated 3.07 ohm/1000ft,

(b) AWG or kcmil 12, 7 strand, uncoated copper 1.98 ohm/1000ft, or 1 strand uncoated 1.93 ohm/1000ft.

With these data, they simplify the computation, see 2. above.

Che Kuan Yau (Singapore)

## RE: NEC Voltage Drop

Thanks for your input! As I now understand the units, this is becoming easier to comprehend. I understand NEC has the 3%/5% limits as you stated. I think the 2% that I am using came from ASHRAE. The 1.98 Ohm/1000 ft value of the 12 AWG, 7 strand, uncoated copper aligns nicely with the K/CM value I am using in my calculation snippets above. You are correct, that using the Ohm/1000 ft would simplify my equation as shown below and now I'm back to Ohm's law!

Juston Fluckey, SE, PE, AWS CWI

Engineering Consultant

## RE: NEC Voltage Drop

FYI: the Ohm's law method simplified the computation.

This is used in

UK see BS7671and also in the IEC world; inSIunits.The Length is in meter, cross-sectional area is in mm

^{2}. TheVD is in [mV/A/m].Che Kuan Yau (Singapore)

## RE: NEC Voltage Drop