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A town situated 20 kW away from a power ...

A town situated 20 kW away from a power plant generating power at 440 V requires 600 KW of electric power at 200 V. The resistance of two wire lines carrying poweris `0.4 Omega` per km. The town gets power from the line through a 3000-220 V step down transformer at a substation in the town. Find line power losses in the form of heat. How much power must the plant supply assuming that there is negligilbe power loss due to leakage ?

Text Solution

Verified by Experts

Resistance of two line wires,
`R = 20 xx 2 xx 0.4 = 16 Omega`
For the transformer, `E_(p) = 3000 V, E_(s) = 220 V`
and `P = 600 kW = 6 xx 10^(5) W`
`:.` Current carried by line wires,
`I_(v) = (P)/(E_(p)) = (6 xx 10^(5))/(3000) = 200 A`.
Power loss in the form of heat ` = I_(v)^(2) xx R`
`= (200)^(2) xx 16 = 640000 W = 640 kW`
Power supplied by plant = power demand + power loss
`= 600 + 640 = 1240 kW`
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