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A transmission line that has a resistance per unit length of 4.50 * 10^-4 /m is to be used to transmit 100.0 MW across 200 miles. The output voltage of the source is 4.00 kV. (a) What is the line loss. (b) What will be the line loss if the voltage is stepped up to 250 kV and (c) 500 kV.
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1 mile = 1609.34m

resistance per unit length=4.50 * 10^-4 /m

total resistance=4.50 * 10^-4 *1609.34ohm for 1mile conductor

0.7242

for 200 mile

R=200*0.7242=144.84 ohm

1. For 4kV system

current in line I= (100*106)/(4*103)

I= 2.5*104

losses in line =I2R=(2.5*104)2*144.84

losses in line =9.05*1010W

2.For 250kV system

current in line I= (100*106)/(250*103)

I= 4*102A

losses in line =I2R=(4*102)2*144.84

losses in line =2.31*107W

3. For 500kV system

current in line I= (100*106)/(500*103)

I= 2*102A

losses in line =I2R=(2*102)2*144.84

losses in line =5.79*106W
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