a) The power delivered to the lines is
[tex]P_{in}= 100 kW=1 \cdot 10^5 W[/tex]
And the voltage at which the lines work is
[tex]V=13014.1 V[/tex]
Since the power delivered is the product between the voltage and the current:
[tex]P=VI[/tex]
We can find the current flowing in the lines:
[tex]I= \frac{P}{V}= \frac{1 \cdot 10^5 W}{13014.1 V}=7.68 A [/tex]
b) The voltage change along each line can be found by using Ohm's law:
[tex]\Delta V = IR = (7.68 A)(10 \Omega)=76.8 V[/tex]
c) The power wasted as heat along each line is given by:
[tex]P_d = I^2 R = (7.68 A)^2 (10 \Omega) = 590 W[/tex]
And since we have 2 lines, the total power wasted as heat in both lines is
[tex]P_d = 2 \cdot 590 W=1180 W[/tex]
