# Q7.25 (c)  A small town with a demand of $800 kW$ of electric power at $220V$ is situated $15km$ away from an electric plant generating power at $440V$. The resistance of the two wire line carrying power is $0.5\Omega$  per km. The town gets power from the line through a $4000-220V$ step-down transformer at a sub-station in the town.  Characterise the step up transformer at the plant.

P Pankaj Sanodiya

Power required

$P=800kW=800*10^3kW$

The total resistance of the two-wire line

$R=2*15*0.5=15\Omega$

Input Voltage

$V_{input}=4000V$

Output Voltage:

$V_{output}=220V$

RMS Current in the wireline

$I=\frac{P}{V_{input}}=\frac{800*10^3}{4000}=200A$

Now,

Voltage drop in the power line = $IR=200*15=3000V$

Total voltage transmitted from the plant = 3000+4000=7000

as power is generated at 440V, The rating of the power plant is 440V-7000V.

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