Will the Ohm\'s law hold for a high voltage cable? A 200km long cable whose core

Question

Will the Ohm's law hold for a high voltage cable?
A 200km long cable whose core is made of a wire of 4cm diameter is insulated with a high density polyethylene insulator of 1 inch thickness all around and then has a copper ground sleeving along with a polypropylene outside wall. It can easily carry a voltage of 11kv and a maximum current of 1.2kA. If the resistance of the cable is 4.5Ohms

a) how much is the electric field in the insulator

b)what would be the maximum possible current using any other metal of same dimensions in the cable at room temperature if the insulator remains the same

Explanation / Answer

Given that, Length of the cable, L = 200 km Diameter, d = 4cm = 0.04 m Radius, r = d /2 = 0.02 m maximum current, i =  1.2kA Resistance of the cable, R = 4.5 Ohms __________________________________________________________________ a) The potential drop between the ends is, V = iR = (1.2kA)(4.5 Ohms)                                                                 V = 5.4 kV ___________________________________________________________________ b) Electric field intensity, E = V / L                                                                                                   E = 5.4 kV / 200 km                                         E =  0.027 V/m _____________________________________________________________________ c) Area, A = r2 = (3.14)(0.02 m)2  =  0.001256 m2   Therefore, current density, J = i / A                                           J = (1.2kA) / (0.001256 m2 )                                            J = 955414.012 A / m2 _______________________________________________________________________ d) Electric field in the insulator zero, since there is no current flow in the insulator. _______________________________________________________________________ e) Resistance, R = L / A resistivity, = R A / L                   = (4.5 Ohms)(0.001256 m2 ) /  (200 km)                   = 2.826*10-8 -m This is almost equal to the resistivity of aluminium. Therefore, the material is aluminium. _______________________________________________________________________ d) Electric field in the insulator zero, since there is no current flow in the insulator. _______________________________________________________________________ e) Resistance, R = L / A resistivity, = R A / L                   = (4.5 Ohms)(0.001256 m2 ) /  (200 km)                   = 2.826*10-8 -m This is almost equal to the resistivity of aluminium. Therefore, the material is aluminium.                                      

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