A number 16 copper wire has a diameter of 1291 mm. Calculate the resistance of a

Question

A number 16 copper wire has a diameter of 1291 mm. Calculate the resistance of a 31 m long piece of such wire. Use Q = 1.72 times 10^-8 ohm m for the resistivity of copper. ____ For safely, the National Electrical Code limits the allowable amount of current which such a wire may carry. When used in indoor wiring, the limit is 6 amperes for rubber insulated wire of that size. How much power would be dissipated in the wire of the above problem when carrying the maximum allowable current? ______ What would be the voltage between the ends of the wire in the above problem? ___ What is the current density in the wire when it is carrying the maximum allowable current? _______ What is the drift velocity of the electrons when it is carrying the maximum allowable current? (The density of electrons in Copper is 8.47 times 10^28 m^-3.) _______

Explanation / Answer

diameter, d=1.291 mm

radius, r=0.6455*10^-3 m

length, l=31 m

resistivity , rho=1.72*10^-8 ohm*m

a)

R=rho*l/A

R=1.72*10^-8*31/(pi*(0.6455*10^-3)^2)

R=0.407 ohms

b)

current , I=6 A

Power P=I^2*R

P=6^2*(0.407)

P=14.7 W

c)

voltage V=I*R

V=6*0.407

V=2.44 V

d)

current density, j=I/A

=6/(pi*(0.6455*10^-3)^2)

=4.6*10^6 A/m^2

e)

vd=j/n*q

vd=4.6*10^6/(8.47*10^28*1.6*10^-19)

vd=3.4*10^-4 m/sec

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