Question

a transmission-line cable, of length 3 km, consists of 19 strands of identical copper conductors, each 1.5 mm in diameter. because of the twist of the strands, the actual length of each conductor is increased by 5%. determine the resistance of the cable, if the resistivity of copper is 1.72 mwcm at 20 c

Answer 1

the resistance of the cable is 582.9 ohms

we are given the length of the cable which is  3 km,  of  1.5 mm in, the diameter  and resistivity of copper which is 1.72 m

The formula  we are referring to for calculating the resistance of the  cable is

R = ρl/A.

As there are 19 strands of copper conductors, so the resistance will be

R = 19( ρl/A)

Here  ρ is the resisitivity =  1.72 , l is the length  = 3(1+0.05)*10³3= 3150 m

A=pie/4(1.5 x 10⁻³)^2 =1.766 x 10⁻⁶ =1.766 x 10^-6

Substituting the values in the formula  we  get

R = 19 ( 1.72*3150 )/1.766 x 10⁻⁶

 = 582.9 ohm

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