Question

A power plant outputs power at 4000vots and 100amps. It then goes through a step-up transformer to 2.5x10^5volts. The resistance of the high tension lines is 30ohms. Use the fact that power input = power output on a transformer, P=IV=IV to find the secondary current, then work power through 30ohm transmission line.

a. What is the percentage power loss in the lines?

b. If there was no step-up transformer, what would be the percentage power loss?

Answer 1

(a) Turn ration of the transformer -

N1 / N2 = 4000 / (2.5 x 10^5)

so, secondary current of the transformer -

I2 = I1 * (N1 / N2) = (100*4000) / (2.5 x 10^5) = 1.6 A

So, power loss P(L) = I^2 * R = 1.6^2 * 30 = 76.8 W

Total power = V*I = 4000 * 100 = 400000 W

So, percentage power loss in the line = (76.8 / 400000)*100 = 0.0192 %

(b) If there is no step-up transformer -

Power loss P(L) = I^2 * R = 100^2 * 30 = 300000 W

Percentage power loss in this case = (300000 / 400000)*100 = 75 %

Power loss is much higher in this case.