Question

The first telegraphic message crossed the Atlantic ocean in 1858, by a 3000 km long cable laid between Newfoundland and Ireland. The conductor in this cable consisted of seven copper wires, each of a diameter 0.73 mm surrounded by an insulating sheath.

(a) Calculate the total resistance of the cable.

(b) The return path for the current was the ocean itself. Given that the resistivity of seawater is about 0.25 Ωm show that the return path have a much lower resistance than the cable.

Answer 1

here,

length of each wire , l = 3000 km = 3 * 10^6 m

diameter , d = 0.73 mm

radius , r = d/2 = 0.365 mm = 3.65 * 10^-4 m

resistivity of copper , p = 1.72 * 10^-8 ohm.m

the resistance of each wire , R= p * l /area

R = 1.72 * 10^-8 * 3 * 10^6 /(pi *( 3.65 * 10^-4)^2) ohm

R = 1.23 * 10^5 ohm

a)

when seven wires are connected in parallel

the total resistance , Rt = R/7

Rt = 1.76 * 10^4 ohm

b)

resistivity , p2 = 0.25 ohm.m

the area of the ocean is very large

R2 = p2 * l/area

so, the resistance of ocean is very less

and

much lower than the resistance of cables