Answer:
a) In the new transformer there are 42 turns in the secondary per turn in the primary, while in the old transformer there were 32 turns per turn in the primary.
b) The new output is 86% of the old output
c) The losses in the new line are 74% the losses in the old line.
Explanation:
a) To relate the turns of primary and secondary to the ratio of voltage we have this expression:
In the old transformer the ratio of voltages was:
In the new transformer the ratio of voltages is:
In the new transformer there are 42 turns in the secondary per turn in the primary, while in the old transformer there were 32 turns per turn in the primary.
b) The new current ratio is
If the old current output was 425 kV, the ratio of current was:
Then, the ratio of the new output over the old output is:
The new output is 86% of the old output (smaller output currents lower the losses on the transmission line).
c) The power loss is expressed as:
Then, the ratio of losses is (R is constant for both power losses):
The losses in the new line are 74% the losses in the old line.
(l = length , a = area, ρ = resistivity of copper)
(l = length , a = area, ρ₀ = resistivity of copper)