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NCERT Class XII Chapter
Alternating Current
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Question : 25 of 26
Marks: +1, -0
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 440V. The resistance of the two wire line carrying power is 0.5 Ω per km. The town gets power from the line through a 4000-220 V step-down transformer at a sub station in the town.
(a) Estimate the line power loss in the form of heat.
(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?
(c) Characterise the step up transformer at the plant.
Solution:  
Line resistance = length of two wire line × resistance per unit length
Line resistance (R) = 2 × 15 km × 0.5 Ω/km\text{Ω/km} = 15 Ω
Virtual a.c. in the line, P = EvIvE_vI_v
800 × 10310^3 = 4000 IVI_V or IvI_v = 200 A
(a) Line power loss, PlossP_{\text{loss}} = lv2Rl_v^2 R = (200)2(200)^2 × 15 = 600 kW
(b) Assuming no power loss due to leakage, total power need to be supply by the power plant
PtotalP_{\text{total}} = PlossP_{\text{loss}} + PoutputP_{\text{output}} = 600 kW + 800 kW = 1400 kW
(c) Potential drop in the line, V = IvRI_vR = 200 × 15 = 3000 V
So, the voltage output of step-up transformer at the plant should be 4000 + 3000 = 7000 V.
hence at the plant the step-up transformer should be 440 – 7000 V.
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