Question

Hydro-Quebec transmits power from hydroelectric dams in the far north of Quebec to the city of Montreal at 735kV. The lines are 935 km long and are 3.50 cm in diameter. Given the resistivity of copper is 1.68 x 10^-8 Ω.m. a) find the resistance of one of the lines, and b) the current carried by the wire.

Answer 1

a)

16.33 Ω

b)

45009.18 A

Step-by-step explanation:

a)

L = length of the line = 935 km = 935000 m

d = diameter of the line = 3.50 cm = 0.035 m

ρ = resistivity of the line = 1.68 x 10⁻⁸ Ω.m

Area of cross-section of the line is given as

A = (0.25) πd²

A = (0.25) (3.14) (0.035)²

A = 0.000961625 m²

Resistance of the line is given as

`R=(\rho L)/(A)`

inserting the values

R = (1.68 x 10⁻⁸) (935000)/(0.000961625)

R = 16.33 Ω

b)

V = potential difference across the line = 735 kv = 735000 Volts

i = current carried by the wire

Using ohm's law, current carried by the wire is given as

`i=(V)/(R)`

i = 735000/16.33

i = 45009.18 A