quires a graph of current density (J /A) on the y-axis and the diameters on ais.
ID: 2040320 • Letter: Q
Question
quires a graph of current density (J /A) on the y-axis and the diameters on ais. Include the graph with the exam with the question ANSWERED. Make sure axes are titled The (United States) National Electric Code. which sets maxi- mum safe currents for insulated copper wires of various diameters. is given (in part) in the table. Plot the safe current density as a function of diameter. Which wire gauge has the maximum safe cur rent density? (Gauge" is a way of identifying wire diameters. and I mi 10- in.) 4 6 810 12 14 16 18 Gauge Diameter. mils 204 162 129 102 81 64 51 40 Safe current. A 70 50 35 25 20 15 6 3Explanation / Answer
we know that the current density J = I/A
A = pi*r^2 = pi*d^2/4
and given 1 mil = 10^-3 m= 1 mm
current density for diameter 204 mils is J = 70/(pi(204*10^-3)^2/4) A/m2 = 2141.6467 A/m2
current density for diameter 162 mils is J = 50/(pi(162*10^-3)^2/4) A/m2 = 2425.7726 A/m2
current density for diameter 129 mils is J = 35/(pi(129*10^-3)^2/4) A/m2 = 2677.9271 A/m2
current density for diameter 102 mils is J = 25/(pi(102*10^-3)^2/4) A/m2 = 3059.4953 A/m2
current density for diameter 81 mils is J = 20/(pi(81*10^-3)^2/4) A/m2 = 3881.2362 A/m2
current density for diameter 64 mils is J = 15/(pi(64*10^-3)^2/4) A/m2 = 4662.7425 A/m2
current density for diameter 51 mils is J = 6/(pi(51*10^-3)^2/4) A/m2 = 2937.1154 A/m2
current density for diameter 40 mils is J = 3/(pi(40*10^-3)^2/4) A/m2 = 2387.32415 A/m2
from the data
the most safe current density is for 14 gauge wire
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