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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.

Respuesta :

Olajidey

Answer:

[tex]\frac{P_1}{P_2} =\frac{1}{4}[/tex]

That means the heat loss will be one fourth

Explanation:

The resistance R is the same in both cases

First case

[tex]P_1=\frac{V_1^2}{R}[/tex]

Second case

[tex]P_2=\frac{(V_2)^2}{R}[/tex]

[tex]P_2=\frac{(2V_1)^2}{R} \\\\P_2=\frac{4V_1^2}{R}[/tex]

Since power is double here

Therefore ratio of the power loss is

[tex]\frac{P_1}{P_2} =\frac{1}{4}[/tex]

That means the heat loss will be one fourth