A small town with a demand of 800 kW of electric 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 `0.5 Omega` per km. The town gets power from the line through a 4000-220 V step down transformer at a substation in the town . The line power loss in the form of heat is

Explanation

Power requirement of the twon is given by EI, where E is the voltage at the receiving end of the line and I is the line current. Here `P=800xx1000W,E=4000V` then `I=(P)/(E)=(800xx1000)/(4000)=200A`
(i) Line power loss `=I^(2)R=(200)^(2)xx(2xx15xx0.5)`
`=600,000W=600kW`
(ii) Total power delivered by power plant
`=800+600=1400kW`
(iii) Voltage at sending end of line
`="Receiving end line voltage "+" voltage drop in line"`
`=4000+(IR)=4000+200(2xx15xx0.5)`
`=4000+3000=7000V`
`therefore" Step up transformer of "(7000V)/(440V)" is required"`