A small town with a demand of 800 kW of power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire line carrying power is `0.5Omega`.`km^-1`. The line gets power from the line through a 4000-220 V step-down transformer at a substation in the town.
Estimate the line power loss in the form of heat?

Explanation

Generating power of Electric plant = 800
kW at V = 220 V
Distance = 15 km,
Generating voltage = 440 V
Resistance/length `= 0.5 Omega//km`
Primary voltage VP = 4000 V
Secondary voltage Vs = 220 V
Power `= I_(P).V_(P)`
`800xx1000=I_(P)xx4000`
`I_(P)=200A`
Line power loss in form of heat
`= (I_(P))^(2)xx` Resistance of line
`= (I_(P))^(2)xx0.5xx15xx2`
`= (200)^(2)xx0.5xx15xx2`
`= 60xx10^(4)W`
`= 600 KW`