Question

100 kw of power is delivered to the other side of a city by a pair of power lines with the voltage difference of 13014.1 v.

Answer 1

A) The power delivered to the lines is
$P_{in}= 100 kW=1 \cdot 10^5 W$
And the voltage at which the lines work is
$V=13014.1 V$
Since the power delivered is the product between the voltage and the current:
$P=VI$
We can find the current flowing in the lines:
$I= \frac{P}{V}= \frac{1 \cdot 10^5 W}{13014.1 V}=7.68 A$

b) The voltage change along each line can be found by using Ohm's law:
$\Delta V = IR = (7.68 A)(10 \Omega)=76.8 V$

c) The power wasted as heat along each line is given by:
$P_d = I^2 R = (7.68 A)^2 (10 \Omega) = 590 W$
And since we have 2 lines, the total power wasted as heat in both lines is
$P_d = 2 \cdot 590 W=1180 W$