Power/Step-up and Step-down transformers?

Question

65kW is to arrive at a town over two 0.100ohm lines. How much power is saved in the voltage is stepped up from 120V to 1200V and then down again, rather than simply transmitting at 120V. (It is assumed that the transformers are 100% efficient).

Thanks in advance!

Answer 1

The Power, P = VI, hence

The current at 120V is I = P/V = 65000/120 = 541.667 A
The current at 1200V is = 54.1667 A

However, here the power is carried by TWO parallel lines, each with 0.1 ohms of resistance. That means the effective resistance is given by:

1/Reff = (1/R1) + (1/R2) = 20 or Reff = 0.05 ohms

Therefore, the Power Loss at 120V is

P = I^2R = (541.667)^2(0.05) = 14670.15 watts

The Power Loss at 1200V is = 146.7 watts

Hence the power saving by stepping up to 1200V is

= 14670.15 - 146.7 = 14523.45 watts

Answer 2

At 120 volts, the required current is
65000/120 = 541.667 A
At 1200 volts, it would be 54.1667 A
At 120 volts, the power loss is 541.667² * .2 = 58,680 W
At 1200 volts, 54.1667² * .2 = 586.8 W


Doug