A number 12 copper wire has a diameter of 2.05 mm. (a) Calculate the resistance

Question

A number 12 copper wire has a diameter of 2.05 mm. (a) Calculate the resistance of a 42.0 m long piece of such wire. (Use 1.72 times 10^-8 Ohm m for the resistivity of copper.) (b) How much power would be dissipated in the wire of the above problem when carrying the current of 15A? (c) What would be the voltage between the ends of the wire in the above problem? (d) What is the drift velocity of the electrons when the wire is carrying the current of 15A? (The density of electrons in copper is 8.47 times 1028 m^-3.)

Explanation / Answer

here,

diameter , d = 2.05 mm

radius , r = d/2 = 1.025 * 10^-3 m

a)

l = 42 m

the resistance , R = p * L /area

R = 1.72 * 10^-8 * 42 /(pi * (1.25 * 10^-3)^2)

R = 0.15 ohm

b)

I = 15 A

the power , P = I^2 * R

P = 15^2 * 0.15 = 33.75 W

c)

the volage between the ends , V = I * R

V = 2.25 V

d)

the drift velocity , vd = I /( n * area * q)

vd = 15 /( 8.47 * 10^28 * pi * ( 1.025 * 10^-3)^2 * 1.6 * 10^-19)

vd = 3.36 * 10^-4 m/s

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