Question

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 440 V. The resistance of the two wire line carrying power is 0.5 $\Omega$ per kin. The town gets power from the line through a 4000-220 V step down transformer at a substation in the town, the line power loss in the form of heat is then

• A. 400 kW
• B. 600 kW
• C. 300 kW
• D. 800 kW

Answer 1

Answer: (B)

600 kW

given variables :

We have a step - down transformaer at the substaion with a arating 4000 - 220 V

so,

Input voltage, $V_1=4000V$

Output Voltage, $V_2=220V$

and

Total electric power, $P=800Kw=800\times {10}^{3}W$

and also

Generation voltage $=V=440V$

Supply Voltage $=V=220V$

Disftance or length of wires $=d=15km$

Resisftance of the two wire lines carrying power $=0.5ohm/km$

so,

Total resisftance of the wores (for a two wire line), $R=(15+15)x0.5$

or

$R=15ohms$

now,

also

Line power loss $I^{2}R$

here

$I=P/V=(800\times {10}^3)/4000$

so, $I=200A$

now

$P_{loss}=(200{)}^2\times 15$

$=600\times {10}^{3}W$

$=600kW$