Question

If a power utility were able to replace an existing 500 kV transmission line with one operating at 1 MV, it would change the amount of heat produced in the transmission line to .

a. none of these.

b. The amount of heat produced would remain the same.

c. one-fourth of the previous value.

d. two times the previous value.

e. one-half of the previous value.

f. four times the previous value.

Answer 1

`(P_1)/(P_2) =(1)/(4)`

That means the heat loss will be one fourth

Step-by-step explanation:

The resistance R is the same in both cases

First case

`P_1=(V_1^2)/(R)`

Second case

`P_2=((V_2)^2)/(R)`

`P_2=((2V_1)^2)/(R) \\\\P_2=(4V_1^2)/(R)`

Since power is double here

Therefore ratio of the power loss is

`(P_1)/(P_2) =(1)/(4)`

That means the heat loss will be one fourth