Suppose that 200 km of high-tension power line has a total resistance of 5 . It

Question

Suppose that 200 km of high-tension power line has a total resistance of 5 . It carries theelectricity from a generator which produces a total of 0.6 MW of power.
a) How much power is dissipated in the transmission line if the electricity is delivered in this line at 12 kV?

b) How much power is dissipated in the transmission line if it is delivered at 60 kV?

c) Assuming the cable is copper, and its resistivity is 1.77 × 108 m, and that it is circular in cross-section, what is the diameter of this cable?

Explanation / Answer

a)

resistance ,R = 5 Ohm

power , P =0.6 MW

voltage , V = 12 kV

V = 12000 V

let the current in the line is I

V *I = power

I = 0.6 *10^6/(12000)

I = 50 A

power dissipated in line = I^2 * R

power dissipated in line = 50^2 * 5 W

power dissipated in line = 12500 W

the power dissipated in line is 12500 W

b)

for voltage = 60 kV = 60000 V

as V * I = power

0.6 *10^5 = 60000 * I

I = 10 A

power dissipated in line = I^2 * R

power dissipated in line = 10^2 * 5

power dissipated in line = 500 W

the power dissipated in line is 500 W

c)let the diameter of the cable is d

R = p * L/A

5 = 1.77 *10^-8 * 200 *10^3/(pi * (d/2)^2)

solving for d

d = 0.030 m

the diameter of the wire is 0.030 m

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