A generator at a utility company produces 1.18x10^2 A of current at 3.68x10^3 V.
ID: 1272772 • Letter: A
Question
A generator at a utility company produces 1.18x10^2 A of current at 3.68x10^3 V. The voltage is stepped up to 2.048x10^5 V by a transformer before being sent on a high-voltage transmission line across a rural area in a city. Assume that the effective resistance of the power line is 26.0 and the transformers are ideal.
(a) Determine the percentage of power lost in the transmission line.
(b) What percentage of the original power would be lost in the transmission line if the voltage were not stepped up?
please show work
Explanation / Answer
a)
Transformer turns Ratio
V2/V1 =I1/I2
(2.048*105/3.68*103) =(1.18*102/I2)
I2 =2.12 A
Power Lost in Transmission
PLost=I22R =2.122*26=116.9 Watts
Power Transmitted through Transmission line
P=V1*I1=(3.68*103)*118
P=4.34*105 Watts
Percantage power lost
% power Lost =(PLost/P)*100 =(116.9/4.34*105)*100 =0.02692 %
b)
PLost =I2R =1182*26 =3.62*105 Watts
% power Lost =(PLost/P)*100 =(3.62*105/4.34*105)*100 =83.41 %
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