If 29.1 kW of power is to be transmitted from a generating station over two 0.10

Question

If 29.1 kW of power is to be transmitted from a generating station over two 0.109-? lines, estimate how much power is saved if the voltage is stepped up from 120 V(rms) to 1200 V(rms) and then down again, rather than simply transmitting at 120 V. Assume the transformers are each 96 percent efficient

HELP: The efficiency tells you the fraction of the power transferred from the primary to the secondary coils of the transformer. Add the energy loss on each transformer to the energy loss due to the resistance of the transmission lines. Compare that total energy loss to the loss without using the two transformers.
HELP: If the transformers were 99% efficient, the power lost in the first transformer would be 1% of 29.1 kW, but the power lost in the second transformer would be 1% of the power transmitted to the second transformer.

Explanation / Answer

power consumed in transmission by 120V = 2* (P/V)^2*r
= 2* (29,100/120)^2 *0.190
= 22346.375 W

in 1200 V = 2*(P/V)^2*r
= 223.46 W

consumption in transformer = 0.04*29,100
= 1164W
total consumption in 1200 V line = 1387.46 W
power saved = 20958.915 W

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