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 ?

Explanation

Distance of twon from power plant d = 20 km
Total length of wire line `l = 2 d =2xx20 =40` km
Resistance per unit length `(R )/(l) = 0.4 Omega` / km
`:. R = 0.4 xx40 = 16 Omega`
Power demand P = 600 kW
Input voltage V = 3000 V
rms value of current
`I_("rms")= (P)/(V) = (600xx10^(3))/(3000) = 200 A `
(i) Power loss in the form of heat is
`P = I_("rms")^(2) xxR `
`= (200)^(2)xx16 = 640 kW `
(ii)Power supplied by the plant
= Power demand + Power loss
= (600 + 640) kW = 1240 kW