A number 14 copperwire has a diameter of 1.628 mm. (Use 1.72×10 -8 ?m for the re

Question

A number 14 copperwire has a diameter of 1.628 mm.
(Use 1.72×10-8 ?m for the resistivity ofcopper.)For safety, theNational Electrical Code limits the allowable amount of currentwhich such a wire may carry. When used in indoor wiring, the limitis 15.0 A for rubber insulated wire of that size.
L piece=31.0m;r=0.000814m; V= 3.842V

a-What is the currentdensity in the wire when it is carrying the maximum allowablecurrent? (Current density is the current in the wire divided by thecross sectional area of the wire.)

b-What is the drift velocity ofthe electrons when the wire is carrying the maximum allowablecurrent?
(The density of electrons in copper is 8.47×1028m-3.)

Explanation / Answer

A number 14 copper wire has a diameter of 1.628mm.
(Use 1.72×10-8 m for the resistivity ofcopper.)For safety, the National Electrical Codelimits the allowable amount of current which such a wire may carry.When used in indoor wiring, the limit is 15.0 A for rubberinsulated wire of that size.
L piece=31.0m; r=0.000814m; V= 3.842V

a-What is the current density in the wire when it is carrying themaximum allowable current? (Current density is the current in thewire divided by the cross sectional area of the wire.)

J = I/A= 15.0 / ( (1.628 x10-3 / 2)2)
J=7.21x106A/m2
b-What is the drift velocity of the electrons when the wire iscarrying the maximum allowable current?
(The density of electrons in copper is 8.47×1028C/ m3.) J = vdrift J - current density , - charge density in units C/m3, and vdrift - average velocity of the carriers(driftvelocity) then vdrift = J/ vdrift =7.21x106/8.47×1028 = vdrift = 8.51x10-23m/s
Have fun.
J = vdrift J - current density , - charge density in units C/m3, and vdrift - average velocity of the carriers(driftvelocity) then vdrift = J/ vdrift =7.21x106/8.47×1028 = vdrift = 8.51x10-23m/s
Have fun.
J - current density , - charge density in units C/m3, and vdrift - average velocity of the carriers(driftvelocity) then vdrift = J/ vdrift =7.21x106/8.47×1028 = vdrift = 8.51x10-23m/s

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