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 four times the previous value. two times the previous value. one-fourth of the previous value. none of these. The amount of heat produced would remain the same. one-half of the previous value.

Answer 1

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

That means the heat loss wil be one fourth the previous value

Step-by-step explanation:

Given that,

`V_1 = 500kv\\\\V_2= 1MV\\\\V_2 = 2V_1`

The resistance R is the same in both cases

In the first case

The power loss is

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

In second case

The power loss is

`P_2=(V_2^2)/(R) \\\\P_2=((2V_1)^2)/(R) \\\\P_2=(4V_1)/(R)`

Therefore, the ratio of the poer loss is

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

That means the heat loss wil be one fourth the previous value

Answer 2

Complete 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 four times the previous value.

b two times the previous value.

c one-fourth of the previous value.

d The amount of heat produced would remain the same.

e one-half of the previous value.

f none of these.

Answer:

Option C is the correct answer

Step-by-step explanation:

When the voltage is 500kV

The power is

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

When the voltage is 1MV = 2 × 500kV

The power is

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

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

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

The ratio at which power is lost is

`(P_1)/(P_2)`
`= (V^2_1)/(R) * (R)/(4V_1^2)`

Here Resistance is constant

`= (1)/(4)`

Hence the heat produced would be one fourth of the previous value