Conductors and Insulators Chapter 11 Conductors and Insulators Topics Covered in Chapter 11 11-2: Standard Wire Gage Sizes 11-8: Wire Resistance 11-9: Temperature Coefficient of Resistance

11-2: Standard Wire Gage Sizes Sizes are specified by the American Wire Gage (AWG) system (p. 317, Table 11-1). Higher gage numbers mean thinner wire. Typical sizes are 22 AWG for electronic hookup wire and 12 AWG for home electrical wiring. The cross-sectional area of round wire is measured in circular mils. The higher the gage number and the thinner the wire, the greater its resistance for any length.

11-2: Standard Wire Gage Sizes Wire Size p. 317 Table 11-1 Diameter in mils = 25.35 Circular mil area = Diameter2 = 642.4 R / 1000ft of copper wire @ 25C = 16.46 

11-2: Standard Wire Gage Sizes Wire Size The circular area of the wire doubles for every three gage sizes. # 19 is three gages larger than # 22 and has approximately twice the circular mil area. This is always the case when the gage number is decreased by 3. Gage CMA 17 2048 18 1624 19 1288 20 1022 21 810 22 643

11-2: Standard Wire Gage Sizes Determine the resistance of a 30 feet section of #30 wire. Determine the maximum length of a #25 cable if the wire resistance must be below 5 . The resistance of a 200ft section cable must be less than 2 W, determine the required wire gage #.

11-8: Wire Resistance Wire Resistance R = ρ(l / A) Resistance is proportional to the length of the wire. The resistance of a conductor can be found by the formula: ρ = specific resistance of the conductor R = ρ(l / A) cross-section of the wire length of the wire

11-8: Wire Resistance r Specific Resistance Specific resistance = ρ = CMA [circular mil area] •Ω/ft Resistance of a conductor = R = ρ (length/CMA) Material Gage CMA r Aluminum 17 2048 Copper 18 1624 10.4 Iron 19 1288 58 Nichrome 20 1022 676 Silver 21 810 9.8 Tungsten 22 643 33.8 Find R for 1000 ft. of #18 cu R = ρ (length/CMA) R = 10.4 (1000/1624) R = 6.4 Ω

11-9: Temperature Coefficient of Resistance Temperature coefficient of resistance indicates how much the resistance changes for a change in temperature. It is indicated by the alpha symbol (α). A positive α value means R increases with temperature. A negative α value means R decreases with temperature. A value of 0 means R stays constant.

11-9: Temperature Coefficient of Resistance α is generally positive for pure metals. α is generally negative for semiconductors (silicon, germanium) and electrolyte solutions (sulfuric acid, water). The increase in resistance may be calculated using the formula: Rt = R0 + R0(αΔt) R0 = the resistance at 20 °C. Rt = the resistance at the higher temperature Δt = the temperature rise over 20° C.

11-9: Temperature Coefficient of Resistance Positive Temperature Coefficient () Some devices show a large increase in resistance when energized. What’s the lamp’s resistance at 2020 °C? Rt = R0 + R0(t) Rt = 2 Ω + 2 Ω × 0.005 × 2000 = 22 Ω