Different types of wire are rated according to their gauge. Each gauge correspon

Question

Different types of wire are rated according to their gauge. Each gauge corresponds to a different cross-sectional area bya complicated formula that is unimportant for our purposes. In the American Wire Gauge (AWG) system, the smaller thegauge, the larger the diameter of the wire. A #10 AWG wirehas a diameter of 0.100 in. The Underwriters Laboratories,Inc. (UL), which sets many safety standards for the United States,requires that this gauge of copper wire should carry no more than55.0 A in power transmission applications in order to prevent thepossibility of it becoming too hot and causing a fire.


a. What is the resistance of 1,000.0 ft of #10 AWG copperwire?


b. At what rate would heat energy be dissipated by this length of#10 AWG copper wire if it is required to carry the maximum ratedcurrent of 55.0 A?

Explanation / Answer

   a.   Resistance    R   =   * L / A    resistivity ofcopper      =   1.67* 10-8    - m    Length   L   =   1000.0   ft                      =   1000* 0. 3048                      =   304.8   m    Area of crosssection   A   =   * r2    r   =   0.100in / 2          =   0.050* 0.0254         ( 1in   =   0.0254   m)          =   1.27* 10-3   m    A   =   3.14 *(1.27 * 10-3)2          =   5.06* 10-6   m2    R   =   1.67 *10-8 * 304.8 / 5.06 * 10-6          =   1.006             =   1.006       b.   Heatproduced   H   =   I2* R                                           =   55.02* 1.006                                           =   3043.15   J/s

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