ECE285: Design Project 2 – Resistance of a Wire and Resistive Ladder Network
Calculations
1.
Resistance of a Wire
All wires have the property that they exhibit a certain resistance to the flow of electric current. The
resistance of any wire can be calculated if we know (1) the material the wire is made from, (2) the length
of the wire, and (3) the cross sectional area of the wire. These quantities must be expressed in a
consistent set of units. The property of the wire material used in calculating the resistance is called
resistivity and is listed in wire tables using the units “ohmcircular mil/ft” or
Ω
m (ohmmeters). See
http://www.tpub.com/neets/book4/11b.htm
for a resistivity table for several common materials
expressed
in
ohmcircular
mil/ft
or
http://www.engineeringtoolbox.com/resistivityconductivity
d_418.html
for materials with resistivity expressed in
Ω
m.
Using ohmcircular mil/ft units requires that the length of wire be given in feet and the crosssectional
area be given in circular mils if the resistance is to be calculated in ohms. Using
Ω
m units, the length
of the wire should be expressed in meters (m) and the cross section area expressed in square meters
(m
2
). The symbol for resistivity is
ρ
(rho) and the (basic) formula for resistance is
R=
ρ
l/A
where
ρ
is the
resistivity,
l
is the length, and A is the crosssectional area.
The circular mil (CM) is a unit that makes calculation of the crosssectional area of a round wire easier.
A mil is 0.001 inch, so a square mil is the area of a square that is one mil on a side. For a circle having
a diameter of 1 mil, the crosssectional area is A=
π
r
2
=
π
(.5)
2
=
π
/4 square mil. Stated another way, 1
square mil=4/
π
CM. For a wire of diameter
k
mils, its area in square mils in
π
(
k
/2)
2
=
π
(
k
2
/4). Thus, the
area in CM would be
k
2
CM. Using ohmcircular mil/ft units, early engineers did not have to include
π
in
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 Spring '12
 HAO

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