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dp2(1).pdf - ECE285 Design Project 2 Resistance of a Wire...

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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 “ohm-circular mil/ft” or -m (ohm-meters). See http://www.tpub.com/neets/book4/11b.htm for a resistivity table for several common materials expressed in ohm-circular mil/ft or http://www.engineeringtoolbox.com/resistivity-conductivity- d_418.html for materials with resistivity expressed in -m. Using ohm-circular mil/ft units requires that the length of wire be given in feet and the cross-sectional area be given in circular mils if the resistance is to be calculated in ohms. Using -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 cross-sectional area. The circular mil (CM) is a unit that makes calculation of the cross-sectional 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 cross-sectional 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 ohm-circular mil/ft units, early engineers did not have to include π in
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