Voltage Drop Calculation
Cuρ 20°C =
10.37 (Annealed)
Conversion Factor
Circular mil = d²
Cuρ 20°C =
mil² = π r²
10.65
(Hard Drawn)
6
mil² = in² / 10
mil² = Circular mil x (4/π) or 1.273
Circular mil = mil² x (π/4) or 0.7854
(mm² = Circular mil x 0.0005067)
MCM stands for thousand circular mils
in review center mm² = MCM / 2 nearest answer is correct
(ρ)(L)
A
R=
Where:
RρLA-
Resistance (ohm)
Resistivity of wire @ 20°C (ohm-cir mils per ft.)
Length (foot)
Area of wire (cir. Mils)
To convert ρ to ohm-cm² per cm (Cu)
10.37 ohm - cir mils
ft
ρ=
mil² (π/4)
cir mil
x
x
in² / 10
mil²
6
-6
= 1.724 x 10 ohm - cm² / cm
Inferred absolute temperature of Cu = -234.5 °C (annealed)
For computing resistance of wire at different temperature:
R2
T + t2
=
R1
T + t1
Where:
R2
= Resistance of conductor @ t2 temp.
R1
= Resistance of conductor @ t1 temp.
And
R2 = R1 [ 1 + α1 (t1 - t2 )
Where:
α1 = Temperature coeficient of resistance @ t1 temp.
α20 = 1/( 234.5 + 20 ) =0.00393
α100 = 1 / (234.5 + 100) = 0.00299
Calculating the resistance of 1 meter length of cable at 20°C & 1mm² area:
(ρ)(L)
A
R=
ρ=
-6
1.724 x 10 ohm - cm² / cm
L = 1m
A = 1mm²
=
6
1.724 x 10 Ω - cm²
cm
x
100cm
1m
x 1m
1mm² x 1cm²/ (10mm)²
0.000172
0.01
R = 0.01724 Ω ≈ 1 / 58 Ω
=
(For every 1meter length & 1mm² copper wire)
For 3Ø 3 Wire System :
VD =
RxLxI
A
Where:
R=
L=
A=
VD=
Resistance (Ohm)
Length, meter
3Ø current (amp)
voltage drop (amp-ohm or volt)
@ 20°C, 1mm² area & 1m length & 97% Cu conductance
VD= √3 (0.01724)
0.97
xLxI
A
VD=
30.8 x L x I
1000 x A
x
ft
30.48 cm
x
(2.54cm)²
in²
For 3Ø 4 Wire System :
VD=
0.0172
0.97
xLxI
A
VD=
17.8 x L x I
1000 x A
For 1Ø 3 Wire System :
VD= (2) (0.01724)
0.97
xLxI
A
VD=
35.6 x L x I
1000 x A