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 km. 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 from of heat is:

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

Answer 1

Answer: (B)

600 kW

Answer 2

: Here, $P = 800kW = 800 \times 10^{3}W$

Total resistance of two wire line

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

As supply is through 4000 - 220 V transformer

$\therefore V_{rms} = 4000V$

$\therefore I_{rms}\frac{P}{V_{rms}} = \frac{800 \times 10^{3}}{4000} = 200A$

Line power loss

$= {I^{2}}_{rms}R = (200)^{2} \times 15$

$= 60 \times 10^{4}W = 600kW$