Question

a) How much is the resistance of 5 ft of household 14 guage Cu wire (1.63 mm in diameter)? Resistivity of Cu is 1.70x10^-8 Ohm m.

b) Cu has about 8.5x10^28 free elecrons per cubic meter. What is the speed of the electrons in the Cu wire from part a?

Answer 1

Given

resistivity of cppeer is rho = 1.70*10^-8 ohm m

length of the wire is l = 15 ft = 15*0.3048 m = 4.572 m

diameter is d = 1.63 mm ==> r = 0.815 mm

so the are of cross section is A = pi*r^2 = pi*(0.815*10^-3)^2 m^2 = 2.087*10^-6 m^2

now the relatio between the resitance and resistivit is  

R = rho*l/A

R = (1.70*10^-8*4.572)/(2.087*10^-6) ohm

R = 0.037242 ohm

b) speed of electrons in Copper wire is  

Vd = J/ne

Vd = I/(n*e*A)

where Vd is drift speed of electrons

n is density of electrons

I is the current = ?

A is area of cross section A = 2.087*10^-6

e is charge of electron = 1.6*10^-19 C