Advanced Voltage Drop Calculations for 600 volt Building Wire
by Gerald Newton
April 24, 2003


 Determining Conductor Operating Temperature

Approximate conductor operating temperature can be determined using the fourier heat transfer equation.  Both Samuel Rosch and Neher-McGrath used variations of this equation to determine ampacities.  Ampacity tables are created using the heat transfer equation.  The general equation is given in equation 1.

nm equation
equation 1

i = kiloamperes
tc = conductor temperature in degrees C.
ta = ambient temperature in degrees C.
rdc = resistance of one foot of conductor in microhms
rca = thermal resistance in thermal ohm feet
1+yc = multiplier for converting rdc to ac resistance and accounts for proximal heating effect from adjacent conductors.


By solving for rca(1+yc) given in equation 2 and using values for Table 310.16 and Table 8 of Chapter 9 of the NEC a table
of rca(1+yc) values can be found.
We can estimate the rca(1+Yc) values by using the 75 degree columns for copper and aluminum in 310.16 to find i or current.
For rdc we can use Table 8 in Chapter 9 of the NEC and move the decimal place three places to the left in the ohms/1000 ft
column to get microhms per foot. tc = 75 degrees C and ta = 30 degrees C.  We can then develop a table of rca(1+yc values
for the respective wire sizes for copper and aluminum.

rca
equation 2


Let rca' represent the values found in equation 2 for use in equation 4.

rcaprime .

We need one more equation before we can find tc, the conductor temperature.  That is the equation for rdc in terms of tc.  See equation 3.


rdc
equation 3

rdc = ohms
pc = circular mil ohms per foot of conductor at 20 degrees C. (10.371 ohms for 100% IACS copper, 17.002 ohms for 61% IACS aluminum)
tah = absolute value of inferred temperature of zero resistance. (234.5 degrees C. for copper and 228.1 degrees C. for aluminum)
cma = circular mil area of conductor from Chapter 9 Table 8 of NEC
tc = conductor temperature in degrees C.

Next we substitute equation 3 for rdc into equation 1 and solve for tc to get equation 4 where i is in amperes.

tcprime
 
equation 4


We find the tc for the given i and ta and then find K using equation 5.

k
equation 5

Next we find voltage drop using the standard voltage drop equation in 6.

vd
equation 6

l = conductor length in feet

Advanced Voltage Drop Calculator
for NEC Annex B Table 310.10 Detail 9

by electrician2.com

Also use ampacity tables to select correct size conductor.
This calculator only determines voltage drop for a given conductor.

Select Material
 Select Size

Select Voltage
and Phase
 Select Ambient
Temperature C
(use 30 C if unsure)

Degrees F
Enter 1-way circuit
length in feet

 Enter Load
in amperes
Voltage
drop
 Voltage at load
end of circuit
 Per Cent
voltage drop
Data
(Conductor temperature should not exceed temperature for which
insulation is rated)
cma of
conductor
 RCA
thermal
 tah
Temp
 Pc
resistance
 Conductor
Temp
 K for
temp