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.

a.how much current flows in the lines? answer in units of
a. 040 (part 2 of 3) 10.0 points
b.each of the two lines has a resistance of 10 ω. what is the voltage change along each line? answer in units of v. 041 (part 3 of 3) 10.0 points
c.how much power is wasted as heat in both lines together? answer in units of w.

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= (P)/(V)= (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`