A power transmission line 50 km long has a total resistance

A power transmission line 50 km long has a total resistance of 0.60. A generator produces 100 V at 70 A. In order to reduce energy loss due to heating of thetransmission line, the voltage is stepped up with a transformer with a turns ratio of100:1.

Part A What percentage of the original energy would be lost if thetransformer were not used?

Part B What percentage of the original energy is lost when the transformeris used?

My professor didn\'t go over any questions like this, so I would appreciate a more extensive explanation.

Solution

Ans) First of all power input P =V*I=100*70=7000 W

Original Energy i.e Energy generated =P*time(t)=7000t J

Part A

Now with out transformer Power loss PL=I^2*R=70^2*0.60=4900*0.60=2940 W

Energy Loss=PL*t=2940t J

Percentage of Energy Lost=Energy Loss/Original Energy=2940 t/7000t=0.42 i.e 42 %

So 42% Energy loss without transformer

Part B

When transformer is used Voltage is stepped down but current will be less for same power

as V1/V2=I2/I1 for transformer

So now current in the high voltage side is I=70/100=0.7 A (Where 100 is turns ratio given)

Original energy is same but power loss is

Power loss PL=I^2*R=0.7^2*0.60=0.49*0.60=0.294 W

Energy Loss=PL*t=0.294t J

Percentage of Energy Lost=Energy Loss/Original Energy=0.294 t/7000t=0.000042 i.e 0.0042 %

So 0.0042% Energy loss with transformer