A cylindrical copper cable 1.50Km long is connected across a 220.0V potential difference. (a) What should be its diameter so that it produces...

First, the value of the length of the cable will be
converted to meters.

Therefore, the length of the cable is
L = 1.5*10^3 m = 1500 m.

We know, from enunciation, the
value of potential difference:V = 220 volts

The power is
given and it's value is of  P = 50 Watts

P = V^2/R
=> R = V^2/P

Since the area of the  section of the
cable is circular, w'ell recall the formula for the area of the
circle:

A = pi*r^2 (1)

A =
p*L/R (2), where p = 1.72/10^8 ohm/m

We'll equate (1) and
(2) and we'll get:

pi*r^2 =
p*L*P/V^2

r^2 = p*L*P/V^2*pi

r
= sqrt(p*L*P/V^2*pi)

Diameter is d = 2*r =
2*sqrt(p*L*P/V^2*pi)

d =
2*sqrt1.72*10^-10*15*5*10^3/484

d = 2*sqrt
1.72*10^-7*75/22

d =
1.0325/100

d = 0.010325
meters

The diameter of the cable is of d =
0.010325 meters, such as it is producing heat at a rate of
50W.