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A town, situated 20 km away from a power plant generating power at 440 V, requires600 kW of electric power at 220 V. The resistance of the two-wire line carrying power is 0.4 Omegaper km. The town gets power from the line through a 3000 - 220 V step down transformer at a substation in the town. (i) Find the line power losses in the form of heat. (ii) How much power must the plant supply, assuming there is negligible power loss due to leakage ? |
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Answer» Solution :Here, total length of LINE wier `=20 xx 2 = 40 km` Total resistance of line wier `R = 40 xx 0.4 = 16 OMEGA` (i) As 600 kW power is received through a line at 3000 V, hence the current `I = P/V = (600 kW)/(3000 V) = (600 xx 1000 W)/(3000 V) = 200 A` `therefore` Line power loss in the form of heat `= I^(2)R =(200)^(2) xx 16 = 640,000 W = 640 kW` (ii) Total power to be supplied by the plant = Power NEED + Power loss = 600 kW + 640 kW = 1,240 kW |
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