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

Answer 1

Answer:

It would change the amount of heat produced in the transmission line to four times the previous value.

Explanation:

Given;

initial voltage in the transmission line, V₁ = 500 kV = 500,000 V

Final voltage in the transmission line, V₂ = 1 MV = 1,000,000

The power lost in the transmission line due to heat is given by;

$P = \frac{V^2}{R}$

Power lost in the first wire;

$P_1 = \frac{V_1^2}{R}$

$R = \frac{V_1^2}{P_1}$

Power lost in the second wire

$P_2 = \frac{V_2^2}{R}\\\\ R = \frac{V_2^2}{P_2}$

Keeping the resistance constant, we will have the following equation;

$\frac{V_2^2}{P_2} = \frac{V_1^2}{P_1} \\\\P_2 = \frac{V_2^2P_1}{V_1^2}$

$P_2 = \frac{(1,000,000)^2P_1}{(500,000)^2}\\\\P_2 =4P_1$

Therefore, it would change the amount of heat produced in the transmission line to four times the previous value.